Designing the Intermodal Multiperiod Transportation Network ofa Logistic Service Provider Company for Container Management

Tobias Sahlin

Master of Science in Industrial Engineering and ManagementOptimization and Supply Chain Management

Master’s Thesis, 30 credits27th of May 2016

Abstract

Lured by the promise of bigger sales, companies are increasingly looking to raise the volumeof international trade. Consequently, the amount of bulk products carried in containersand transported overseas exploded because of the flexibility and reliability of this type oftransportation. However, minimizing the logistics costs arising from the container flowmanagement across different terminals has emerged as a major problem that companies andaffiliated third-party logistics firms face routinely.

The empty tank container allocation problem occurs in the context of intermodal distributionsystems management and transportation operations carried out by logistic service providercompanies. This master thesis considers the time-evolving supply chain system of an in-ternational logistic service provider company that transports bulk products loaded in tankcontainers via road, rail and sea. In such system, unbalanced movements of loaded tank con-tainers forces the company to reposition empty tank containers. The company’s motivationis to study whether or not there is any incentive to further investigate and develop a modelsupporting the planning decisions for transportation of empty tank containers. The probleminvolves dispatching empty tank containers of various types to the meet on-time deliveryrequirements and repositioning the other tank containers to storage facilities, depots andcleaning stations. To this aim, a mixed-integer linear programming (MILP) multiperiod op-timization model is developed aiming to make tactical decisions for the empty tank containerallocation problem, or more specifically, for determining the best strategy for distributingthe empty containers through the transportation network of the company.

The model is analyzed and developed step by step, and its functionality is demonstrated byconducting experiments on the network from our case study problem, within the boardersof Europe. The case study constitutes three different scenarios of empty tank container allo-cation. In addition, the case study network topology is utilized to create random instanceswith random parameters and the model is also evaluated on these instances. The computa-tional experiments show that the model finds good quality solutions, and demonstrate thatcost and modality improvement can be achieved in the network, through repositioning ofempty containers. Furthermore, an extensive sensitivity analysis is conducted to show theeffect of the model’s parameters on its performance. The sensitivity analysis employs a setof data from our case study and randomly generated data to highlight certain features ofthe model and provide some insights regarding the model’s behavior.

Keywords: Supply chain, Distribution network, Repositioning, Intermodal transport, Sen-sitivity analysis.

Sammanfattning

Internationell handel okar i takt med foretags stravan om att uppna hogre forsaljningsresultatgenom okade exportvolymer. Transporter mellan kontinenter av containrar lastade medbulkprodukter har okat avsevart pa grund av den flexibilitet och tillforlitlighet denna typav transport erbjuder. Att minimera logistikkostnaderna for transporter mellan olika ter-minaler har mynnat ut i ett betydande problem for foretag som erbjuder tredjepartlogistik.

”Tomcontainer allokerings problemet” involverar foretag som erbjuder logistiska tjansterinom intermodala distributionssystem genom att lagga ut dessa tjanster pa externa lever-antorer. Denna masteruppsats fokuserar pa ett internationellt foretag som erbjuder trans-porter av bulkprodukter lastade i tankcontainrar via vag, jarnvag och sjo. I system av dettaslag utfors obalanserade transporter av lastade tankcontainrar, vilket tvingar foretaget tillatt ompositionera tomma tankcontainrar. Foretaget motiveras av att undersoka om detfinns incitament till att vidare analysera eller mojligtvis implementera en matematisk mod-ell som stodjer ompositioneringsbeslut for tomma tankcontainrar. Ompositionerings beslutbaseras pa kundorder samt antaganden om huruvida framtida efterfragan kommer uppstaeller ej. Problemet inkluderar att mota efterfragan och tillhorande krav fran foretagets kun-der. Kraven specificerar vilken tid leverans ska ske, vilket skick tankcontainern bor vara isamt vilken typ av tankcontainer som efterfragas. En dynamisk blandad heltalsmodell somar anpassad for intermodal transporter samt den varierade efterfragan av olika dimensionerav tankcontainrar utvecklas, med syftet att generera taktiska beslut for det aktuella allok-eringsproblemet. Mer specificerat ar malet att bestamma en optimal distributionsstrategiinom foretagets transportnatverk.

Modellen utvecklas och valideras steg for steg och dess funktionaliteter demonstreras genomen kanslighetsanalys baserat pa det Europeiska natverket inkluderat i var fallstudie. Fallstu-dien inkluderar tre olika scenarion for allokering av tomma tankcontainrar. Vidare nyttjastopologin av natverket i fallstudien till att utfora slumpmassigt utvalda instanser for attutvardera modellen. Dessa berakningsresultat visar att modellen finner losningar av godkvalitet och indikerar att det finns rum for forbattringar gallande fordelningen av trans-portmedel. En utforlig kanslighetsanalys presenterar vilken effekt modellens parametrarhar pa modellens utforande. Vi anvander slumpmassigt utvald data for kanslighetsanalysenoch betonar vissa funktionaliteter av modellen samt delger insikter om modellens beteende.

Nyckelord: Forsorningskedja, Distributionsnatverk, Ompositionering, Intermodala trans-porter, Kanslighetsanalys.

Acknowledgements

I wish to thank various people for their contribution to this project. Firstly, I would like toexpress my very great appreciation to my supervisor at Umea university, Ahmad Hosseini, forhis professional guidance, patience and willingness to share his knowledge and all the time hedevoted to this work. I would also like to address my deepest gratitude to my supervisor atORTEC, Ronald van Schieveen for an enthusiastic encouragement, patient guidance, and usefulcritiques during this project. Special thanks should be given to Robert Zwetsloot at Hoyer.Sharing knowledge and giving time so generously have been very much appreciated. A greatthanks also goes to Martijn Leenstra at ORTEC, who made this project possible in the firstplace. I would like to extend my thanks to all the employees’ at both Hoyer and ORTEC thathave contributed to this master thesis.

Tobias Sahlin

Contents

1 Introduction 1

1.1 Project situation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Hoyer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.3 ORTEC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.4 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.5 Tank container management at Hoyer . . . . . . . . . . . . . . . . . . . . . . . . 4

1.6 Aim, scope & research question . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 Literature Review & Motivation 10

2.1 Introduction to multi-modal transportation planning . . . . . . . . . . . . . . . . 10

2.2 The empty repositioning problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3 Mathematical Theory 15

3.1 Network flow problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.1.1 Minimum Cost Flow Problem . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.1.2 Distribution Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.1.3 Transportation Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4 Solution Methodology & Container Management Model 18

5 Computational Study & Sensitivity Analysis 32

6 Summary and Discussion 42

7 Final Recommendations & Future Research 44

References 47

List of Abbreviations

ORTEC Operation Research TechnologyORD ORTEC Routing and DispatchLP Linear ProgramNLP Non Linear ProgramIP Integer ProgramMILP Mixed-Integer Linear ProgrammingMIP Mixed Integer ProgramAIMMS Advanced Interactive Multidimensional Modeling SystemIDLE Integrated Development and Learning Environment3PL Third-Party Logistics ProviderISO International Standards Organization regulationsOECD Organization for Economic Co-operation and DevelopmentTMS Transportation Management System

cefic The European Chemical Industry Council

Dictionary

Empty repositioning:transportation of empty tank containers can be referred to as repositioning of empty containersfrom surplus areas to demand areas.

Third party logistics service provider:Company that provides their customers with outsourced logistical services. These logisticalservices are typically customized, based on requirements from their customers and market con-ditions.

Intermodal transportation:transportation that includes a sequence of at least two different transportation modes wherethe transfer from one mode to another being performed at an intermodal terminal.

Intermodal terminal:Interface between the different transportation modes included in a intermodal transport, suchas a port or rail terminal. Intermodal terminals provides logistical services such as short-termstorage, load and unload operations.

Tank container:An intermodal container for transportation of bulk products such as liquids and gases.

Route: constitute a combination of sections or legs.

Pre-haulage:section or leg representing the first miles of a route.

Long-haulage:section or leg that constitutes the transportation after pre-haulage and before the end-haulage.Often called terminal-to-terminal transit or door-to-door transit.

End-haulage:section or leg representing last miles of a route.

List of Figures

1 Intermodal transportation as a concept . . . . . . . . . . . . . . . . . . . . . . . . 4

2 The tank container . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3 An example of a typical tank container cycle . . . . . . . . . . . . . . . . . . . . 6

4 The empty repositioning problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

5 Planning levels for the empty repositioning problem . . . . . . . . . . . . . . . . 11

6 Production-distribution model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

7 Generalized distribution network . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

8 Topology of Hoyer’s distribution network . . . . . . . . . . . . . . . . . . . . . . 33

9 Computational experiments under scenario 1 with different time discretizations . 36

10 Computational experiments under scenario 1 with different lengths of the plan-ning horizon, 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

11 Computational experiments under scenario 1 with different lengths of the plan-ning horizon, 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

12 Computational experiments under scenario 1 with transportation capacities, 1 . . 39

13 Computational experiments under scenario 1 with transportation capacities, 2 . . 39

14 Computational experiments under scenario 2 with limited storage time at inter-modal terminals, 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

15 Computational experiments under scenario 2 with limited storage time at inter-modal terminals, 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

List of Tables

1 Tank container classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2 Topology of Hoyer’s distribution network . . . . . . . . . . . . . . . . . . . . . . 32

3 Computational experiments, scenario 1, Performance . . . . . . . . . . . . . . . . 35

4 Computational experiments under scenario 1 with different time discretizations . 35

5 Computational experiments under scenario 1 with different lengths of the plan-ning horizon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

6 Computational experiments under scenario 1 with capacity restrictions of trans-portation modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

7 Computational experiments under scenario 2 with limited storage time at inter-modal terminals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

8 Computational experiments under Scenario 3 with the end-haulage . . . . . . . . 41

9 Hoyer’s distribution network, countries and regions . . . . . . . . . . . . . . . . . 49

1 Introduction

This section describes the project’s situation and its stakeholders. Subsequently, it providesa background to the case study problem by describing Hoyer’s challenges and operations, andby introducing one of the main industries the company is active in; the chemical industry.The aim, delimitation and research question of this project is presented at the end.

1.1 Project situation

This master thesis is proposed by Hoyer Gmbh in cooperation with ORTEC B.V. Hereafter willthese companies be referred to as Hoyer and ORTEC, respectively. Hoyer is a current customerto ORTEC. The later company has implemented a transportation planning tool called OR-TEC Routing and Dispatching (ORD) into the transportation planning system of Hoyer. Thisproduct supports the process of distribution goods to customers with a fleet off vehicles. ORDsupport loading- and unloading actions or a combination of both. However, this solution is notimplemented at Hoyer for any optimization procedures. Currently, Hoyer and ORTEC are in-vestigating whether or not an extended collaboration could include optimization. This researchfocuses on investigating if an optimization model supporting decisions regarding transportationof empty tank containers could be a part of this next step amongst the companies.

1.2 Hoyer

Hoyer has been a leading bulk logistic provider since 1946. The German family-owned companyis an international third party logistics service provider, specializing in bulk, particularity inthe chemical, oil, gas, petroleum and foodstuff industries. Hoyer executes transportation ordersvia road, train, short-sea and deep-sea, supported by strategically located terminals. Shortsea shipping refers to coastal trade without crossing continents. Deep sea shipping or oceanshipping refers to maritime traffic that crosses continents. The company offers other servicessuch as cleaning process of tank containers, heating and cooling, filling and blending proceduresof bulk products. Hoyer owns approximately 34,000 tank containers, often mentioned as thecompany’s key resource.

1.3 ORTEC

ORTEC is one of the market leaders of providing advanced planning and optimization solutionsand services. The result of these solutions and services are optimized vehicle and pallet loading,workforce scheduling, warehouse control, routing and dispatch and logistics network planning.Some solutions are standardized products whereas others are tailor made after customers re-quests. ORTEC is active in a variety of industries which includes the retail, transportation,consumer goods, food and beverage, healthcare and the oil, gas and chemical industry.

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1.4 Background

Third party logistical service providers are independent companies providing logistics servicesto their customers. Although they do not hold ownership of the product to be shipped, they arelegally bound and responsible to perform the requested logistic activities from their customers.It was revealed during one of the interviews with Hoyer that the European market of thirdparty logistical service providers, offering logistical services for shipments of bulk products ischaracterized by an oligopoly market condition. The number of actors offering transportationof bulk products, such as chemical products, is highly restricted due to the high entering costsin this type of business. The main cause of this is the high valued tank container that can beseen as the key asset in this industry, providing safety of the shipment, maintains the qualityof the product and facilitates shipments to be carried out via intermodal transports.

A high utilization grade of the tank containers is of great importance for any logistical ser-vice providers success. The high customer service level required from the clients reflects thecompetitive environment these companies are operating under. Furthermore, 3PL companiessuch as Hoyer are subject to a great deal of complexity not present in other industries. Firstly,the complexity stems from the uncertainty of trade patterns across the network and the un-balanced movements of loaded tank containers. This forces the actors to correct imbalancesby transportation of empty tank containers, more commonly phrased as empty repositioningor empty moves. Secondly, the heterogeneous character of the chemical products requires suit-able means of transportation; certain products requires a certain type of tank container for itstransportation in order to maintain the quality of the product and to ensure the safety of theshipment.

To match products and suitable tanks across geographically regions in a time wisely suitablematter is often a difficult task. In addition, the condition of the tank container is anotherimportant topic. If previous loaded product is not the same as the product for reloading, thetank container must be cleaned before reloading, necessitating availability of cleaning stations.Furthermore, logistical service providers are operating under relatively narrow time frameswhile trying to fulfill the demand from their customers. The complexity in wise empty tankcontainer assessment comprises two major causes of distress. The first regards the unavailabilityof empty tank container resulting in not being able to comply customer demand. This may leadto a customer loss and bad reputation. On the contrary, emergency shipment of empty tankcontainers attached with a high cost results in lower profit margins. The second governs asurplus of tank containers in some region or cluster which would imply lower tank containerutilization.

An interview with Hoyer provided insight into their business model as an third party logisticsservice provider. In particular, the interview revealed that the success of the company’s businessmodel depends to a large extent on the ability to establish customized services. On the otherhand, the willingness from the customer to adapt to the logistical service providers could beanother important factor to further improve the efficiency of the third party logistics relation-ship. Consequently, customer adaption is a crucial characteristic of a service logistic provider,necessitating a sufficient understanding of their clients business as well. Hoyer is active withina number of different industries and it is not possible to cover all these, neither is it part of thescope of this project. However, customers from the chemical industry represents a major partof Hoyer’s business. An introduction to the chemical industry is given below, providing furtherinsight of the company’s operations and the challenges Hoyer are facing.

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The European chemical industry accounts for 17% of the world’s chemical production, con-tributes e551 billion annually and have 1.2 million employed workers (cefic, 2016) . Currently,there is an ongoing production shift within this field which will impact the global chemicallogistic supply chain. Historically, the production of chemicals has been dominated by theOECD (Organization for Economic Co-operation and Development) countries. During the lastdecade the production has rapidly grown in non-OECD countries e.g. Asia and the MiddleEast due to lower energy price and increasing demand in these regions (Broeren, 2009). As aconsequence, the European chemical industry’s competitive position is at risk. However, it wasrevealed during one of the interviews with Hoyer that the majority of the chemical products arenot profitable enough for the non-OECD countries to ship to Europe due to its low margins.Thus, the expected higher competition will rely more on the exports from Europe rather thanimports.

Clusters plays an important role for the European chemical industry. The majority of the 300European production sites included in an investigation conducted by the European Commissonwere located in one of 30 strategically positioned clusters. Many upstream and downstreamactivities are integrated between the chemical plants in these clusters. Having a combinationof key assets in place and the proxity to the customer market often determines the success ofa cluster. However, complete supply chain integration is often non-existent. Despite numer-ous attempts of decreasing shipments of chemical goods by clustering, freight volume is stillestimated to increase annually by 2.5 %. The industry is still widely spread out, often locatedclosely to some major energy or other important raw material resource. In addition, chemicalcompanies are often specialized and one company may supply the entire European market (TheEuropean Commisson, 2009). Thus, long distance transportation is a common practice in thisfield. This emphasizes the need of cost efficient and safe shipments.

While considering trade-offs regarding the cost, quality and safety of the shipment, Hoyer al-ways prioritize intermodal transportation, making the transportation safer, more competitiveand environmental friendly. It was declared in a report conducted by the The European Chem-ical Industry Council (cefic) that the share of road transportation is in general very high, adeclining usage of rail transportation has become evident due to the bottlenecks intermodalterminals may bring. At the same time, many actors argues that a large extent of the currentintermodal transportation possibilities already have been captured; logistical service providersfinds it difficult to increase intermodal movements and still secure high service levels. However,the majority of the chemical production companies and the logistical service providers still havepositive view of reaching EU’s proposed goal of moving all transportation over 300 km to inter-modal transportation. In the endeavor of pursuing this goal, a number of obstacles that needto be tackled have been stated (cefic, 2014). The top four issues are as follows:

1. High costs. The cost structure of intermodal transportation compared to road trans-portation is the main issue that prevents further shifts from road to intermodal movements.

2. Intermodal connections missing. There is a lack of intermodal connections in Europe,especially while considering train connections between Benelux (Rotterdam) and France.

3. Insufficient frequency or capacity of intermodal connections. Already existentintermodal connections is insufficient in terms of frequency and capacity.

4. Last mile solution. The last leg of intermodal moves for the chemical industry isvery complex with respect to quality, safety and costs. For example, cleaning stations orheating/cooling stations might be missing.

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1.5 Tank container management at Hoyer

Intermodal transportationIn the perspective of a transport planner at Hoyer, two different transportation options arealways considered; transportation via road or by a sequence of at least two different modes i.e.intermodal transportation. Intermodal transportation is prioritized whenever possible and canbe defined as a shipment from its origin to its destination by a sequence of at least two differenttransportation modes where the transfer from one mode to another being performed at anintermodal terminal (loading/unloading terminal in Figure 1). In general, the transportationchain can be divided into three sections, (1) pre-haul; first miles after the loading process,(2) long-haul; terminal-to-terminal transit or as often mentioned, door-to-door transit and (3)end-haul; last miles for the unloading process. The pre-haul and long-haul transportation arecarried out by road whereas for the long-haul transportation, all modes (road, rail, sea) can beconsidered (Steadieseifi, 2014). Pre, long or end haul may be referred to as a section or leg anda combination of sections or legs may be called a route.

Figure 1: Illustration of intermodal transportation as a concept.

For transportation via road Hoyer has entered into subcontracts with trucking companies. Av-erage drivers are not sufficient for transportation of chemical products. Drivers that transportchemical products must pass strict background checks and complete federally certified trainingand in-house-training for the company they are working for. However, these shipments may beseen as all three types of sections (pre-haul, long-haul and end-haul, (Figure 1). For transporta-tion via sea and railway, Hoyer has entered into subcontracts with external logistical servicecompanies, providing not only transportation but also storage and handling services at inter-modal terminals. Each of these transportation service contracts represents long-haul sections(Figure 1).

Typically, the company charges their customers a fixed price for a logistical service. Each sectionand its associated transportation and operational costs are quoted and constitute the total priceof the shipment. Thus, the profit (loss) obtained by Hoyer mainly depends on the costs from theexternal subcontracted logistical service providers and the costs from the subcontracted truckingcompanies. For this reason, there is strong incentives to minimize these costs, especially forempty movements as these shipments are not considered to generate profit.

For intermodal distribution of tank containers, the modern trend is towards flexibility andcompability. Tank containers are designed as self-contained units; they can be transportedvia different modes without disturbing its content or violating security terms. Surely, this isvery helpful for door-to-door delivery. Hoyer is required to allocate an suitable empty tankcontainer for respective product that is demanded to be loaded and shipped. The tank mayhold chemicals, gases, food-stuff or other products. A certain type of tank container for eachkind of product is required to ensure the safety of the shipment and to maintain the quality of

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the product as well as not to violate legal terms. For instance, it may be required to provide tankcontainers in the right condition. It can also be demanded to maintain a certain temperatureof the product and a certain pressure and filling grade of the tank container. This emphasizesthe need of different functionalities of the the tank container, illustrated by 2. Further, tanksfor these purposes must comply with International Standards Organization regulations (ISO).

Figure 2: An illustration of a set of different functionalities of a tank container.

The tank container cycleA transportation order of an empty tank container from a loading site may be seen as the firststep of the transportation planning process. This is part of the planning of empty tank containerlogistics. The loading site may be a producer of chemical products that demands products to betransported to one of their customers. Subsequently, the transport planner allocates a suitableempty tank container for transportation via road to the customer for loading of products.Whether or not it is possible to allocate the empty tank container in the neighborhood of thisloading site depends on the planing of the empty tank logistics. Empty tank logistics will beexplained in more detail later in this section.

Figure 3 illustrates a typical cycle for an intermodal transportation of a tank container. Thepre-haul section in Figure 3 represents a loaded move from the loading site to an intermodalterminal, in this case a port terminal, but it could also be a train terminal. The long-haulsection is the next step of the cycle. The transport planner sends a booking requests to alogistical service provider for transportation via a vessel. A database of departure and arrivaltimes for train and vessels is used to find available trains and vessels. The rule of thumb isto only allocate tanks for shipments via road under 400 kilometers. For shipments over 400kilometers the transport planner may choose between the modalities rail and sea. The criteriafor this decision constitutes of the associated transit time, operational costs, safety and qualityfactors. The end-haulage take place after the door-to-door transit or the long-haul. The lastmiles for delivery is carried out via road (Figure 3).

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Figure 3: An example of a typical tank container cycle. The tank container cycle is representedby the loaded moves; pre, long and end-haul and the empty tank container logistics.

As Figure 3 suggests, the empty container logistics takes place after the end-haul and theunloading of products at the unloading site until reloading at the loading site. The reader isencouraged to note that empty logistics itself may include all previous mentioned conceptualshifts; end, long and pre-haul. The planning of empty repositioning are trivial in some cases andmore difficult in others. In the trivial scenario, there is a known demand of the tank containerthat just have been unloaded at an unloading site. The tank container is then reallocated to acleaning station and subsequently transported to the demanding customer for reloading.

On the contrary, if there is no known demand for reloading after unloading, the situationbecomes more complex. It is no longer obvious to what location the tank container should berepositioned to. In this situation, the transport planner has some different options to consider.Firstly, the tank container can be moved to a region where demand of empty tank containersis expected to arise in the near future. Secondly, the tank can be shipped to one of the majorinternal depots located in, for instance, the Netherlands or Belgium for storage or it can simplybe decided to store the tank in the current region. These decisions are based on communicationamong the transport planners and their business experience.

The empty repositioning problemEmpty repositioning is an important component of the container tank management. It iscrucial to meet the demand of empty tank containers in order to reduce the risk of competitorsproviding the tank containers as requested and suffer loss of customers. In addition to this, tankcontainer utilization can be improved and the storage, handling and transportation costs can bereduced if empty repositioning is planned wisely. Figure 4 illustrates the repositioning of emptytank containers (dotted lines) and transportation of loaded units (solid lines). Intuitively, thedemand of empty tank containers varies across geographically regions or in other words, theloaded moves are unbalanced.

Recall that customers from the chemical industry tends to form strategically clusters. As aresult of this may regions be distinguished by two different main characteristics. Some of theregions included in the distribution network of Hoyer can be called net exports regions. Fornet export regions, the total outgoing flow of loaded tank containers is relatively larger thanthe total incoming flow of loaded tank containers. In opposition, the total incoming flow isrelatively larger than the total outgoing flow for import regions. The net export regions arecharacterized by major producers of chemical products. The net import regions are character-

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ized by companies that demand the chemical product itself. In general, a net surplus of emptytank container can be associated with net import regions and a net demand with net exportregions.

Given the unbalanced moves of loaded units, Hoyer is forced to reposition empty tank containersfrom net import regions to net export regions in order to supply the demand of empty tankcontainers. If the empty repositioning is not planned carefully the entire transportation networkwill operate inefficiently. For instance, the empty container management of Hoyer must accountfor the situation where loaded tank containers shipped away from some region do not matchthe incoming flow of tank containers to that region. However, if the flows would match, there isno guarantee that demand of these unloaded empty tanks container will arise in that particularregion in the near future. Further, when an empty tank container is available after unloading,it may not be time wise possible to match this tank to a new demand for reloading. In addition,there are different types of tank containers with different functions that are matched to theproducts demanded to be shipped. This is illustrated by Figure 2. Neither is it preferably tokeep the stock to high, this will reduce the tank container utilization significantly.

Figure 4: An illustration of the empty repositioning problem. Loaded moves are illustrated bysolid lines and empty moves by dotted lines.

The tank containers managed by the company are either owned by Hoyer or leased. Theopportunity of leasing may help to reduce regional imbalances. On the contrary are leasingcontracts often long term based and expensive. It may therefore be difficult to save costs withthis alternative. On the other hand may an increased owners ship be to risky or financiallycomplex. In addition will leased tank require some extra attention, especially close the expiredate of the leasing term. Leased tanks must then be allocated to a certain depot at a certaindate for return to its owner.

In order to analyze and manage imbalances that occurs, Hoyer’s distribution network has beenmapped after country and region. This can be obtained from Table 9 included in Appendix A.Furthermore, imbalances are often analyzed after the dimensions (cbm) of the tank containers,indicated by Table 1 in chapter 4.

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The following factors and business rules are taken into account while planning a shipment as atransport planner at Hoyer:

1. Matching the type of tank containers with the products to be shipped.

2. Previous product; Some products does not have any quality impacts on each other andtherefore can cleaning process be avoided.

3. Frequency of intermodal connections; time schedule of the departures and arrivals forvessels and trains.

4. Capacity of intermodal connections; storage capacities at intermodal terminals and trans-portation limitations for the modes train and vessel.

5. Transportation, storage, and handling costs.

6. Condition of the tank container; cleaning processes and maintenance.

7. Management of leased tank containers; additional tanks may be brought into or out fromthe system.

8. Flow balance between empty and loaded tank containers across regions.

1.6 Aim, scope & research question

The aim of this thesis is to verify if there exists incentives to further investigate or possibleimplement a model supporting decisions for transportation of empty containers into the currenttransportation planning system of Hoyer. The reason why Hoyer shows interests in such modelis to be able to reduce the costs for empty moves while still ensuring that customer orders canbe met in time. Wise empty tank container management may improve the utilization grade ofthe tank containers and enhance the competitive edge of the company.

Outcome goalsSince both stakeholders of this project seeks an answer to the question whether or not thereexists incentives to further analyze or possible implement an optimization model supporting theplanning process of empty repositioning, is an answer to this question considered as a preferredoutcome goal. Another goal is to mathematically formulate the problem as a mixed integerlinear program. The program should meet the requirements stated by Hoyer and its validityshould be confirmed.

DelimitationsHoyer is an international logistic service provider and is operating world wide. However, deepsea shipments or ocean shipping, referring to shipments carried out by carriers that crossesoceans are excluded in this paper. The scope of this study regards hinterland- and intermodaltransportation within the boarders of Europe.

There is two different types of transportation orders that Hoyer are receiving from their clients.Namely, spot orders and dedicated orders. The spot orders are standardized orders that rarelyare rejected. The dedicated orders refers to more advanced, customized shipments where theproducts may have an impact on the tank container. For instance latex is a chemical component

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of glue which often is shipped in a tank container, this chemical product tends to fasten on theinside of the tank container, creating growing layers that eventually needs to be removed at acleaning station. This work will be focused on spot orders only.

The planning level of the problem under consideration is referred to as a service planning level,which means that we are considering a medium term planning horizon. This project focuses ondeveloping a service network model for Hoyer’s intermodal distribution system. In contrast tothis includes operational models real-time decisions which are out of scope for this work.

Research questionThe company, Hoyer, wishes to know whether or not there exists any incentive to furtherinvestigate and develop a mathematical model supporting the planning tactical decisions forflow management of empty tank containers.

9

2 Literature Review & Motivation

Prior to focusing on the empty repositioning problem, we first provide an introduction tomultimodal transportation planning. The intent is to provide insights of why transporta-tion planning is of great importance and to describe the different planning levels trans-portation planning may constitute. Subsequently, we map the empty repositioning problemand present previous models carried out for this problem. We close this section with themotivation of this work.

2.1 Introduction to multi-modal transportation planning

Transportation planning has become a key component of the entire supply chain for many com-panies. The costs associated with transportation adds up to one third of the total logistics costswhich emphasizes incentives for a cost efficient transportation coordination. The increasingpressure on companies to obtain higher profitability and operate more efficiently due to in-creasing competition makes the transportation planning even more important (Bhattacharyaa,2014). Since the globalization has increased tremendously during recent decades and also newregulations making the international trade easier, new markets are rising where the produc-ers and customers are geographically apart from each other (Bhattacharyaa, 2014; Steadieseifi,2014). In line with globalization, it is not possible to only transport by road, necessitatingcombinations of different modes i.e. multimodal transportation (Steadieseifi, 2014).

The existing literature in the research area for multimodal transportation problems is exten-sive. The multimodal transportation industry employs numerous application of optimizationat the strategic, tactical, and operational level. The strategic level concerns problems relatedto investment decisions for the infrastructure of the transportation network. Tactical planningproblems concerns the service network design of the infrastructure of the given network. Theseproblems deal with issues related to the selection of routes on which services are offered and theallocation of resources to its demand. The planning problems associated with the operationallevel concerns the same issues described for tactical planning. But, for operational planningproblems, real-time decisions are required. This makes the operational planning problems muchmore complex compared to strategic and tactical planning problems. An interested reader isrecommended to read the paper conducted by Steadieseifi (2014) for an excellent review ofmultimodal transportation planning. This paper concerns the design of a planning system foran intermodal distribution network.

2.2 The empty repositioning problem

The literature domain of empty container repositioning may be classified into three differentgroups due to the research context. The first group focuses on seabourne networks ((Du andHall, 1977), (Li et al., 2004) and (Song and Zhang, 2010)). The second group focuses on inlandand intermodal transports and the third group includes empty repositioning as a subprob-lem ((Jula et al., 2006)). In general are intermodal networks more complicated compared toseaborne shipping networks. In addition is the time-scale between intermodal transportation

10

and seaborne shipping significantly different (Song and Dong, 2012). The subject of this workconcerns inland and intermodal transportation. Subsequently, the literature from the secondgroup will be emphasized in this section. In addressing the empty tank container repositioningproblem, several decisons have to be taken under consideration. As previously mentioned, eachdecision belongs to a certain planning level. This is also shown in Figure 5. Braekers (2013)conducted an overview of the different planning levels for the problem under consideration. Themain problem for each planning level is presented in the second column whereas the decisionsrelated to these problems are presented in the third column. The arrows indicates the hier-archical relationship between these planning levels. At the strategic level, general policies areformed as guidelines for the next level; tactical planning. Similarly, will the tactical decisionsset the framework for operational and real-time decisions (Braekers 2013; Crainic et al., 1993).

Figure 5: Overview of decisions for empty tank container repositioning (Braekers 2013; Crainicet al., 1993)

Strategic planning concerns long term decisions such as designing the physical network bydeciding the locations for depots, cleaning stations and other facilities. At this level the sizeof the fleet is decided, customer zones are defined and general service policies are determined.Tactical planing aims to secure an efficient allocation of the existing resources over a mediumhorizon. Typically, most of the decisions taken at this level concerns the problem of servicenetwork design. The following decisions should be included at the tactical level:

1. Service selection: the selection of routes/sections on which services are offered and thefrequency of these services.

2. Distribution specification: specification for each origin-destination pair; service used, ter-minals passed through and operations/processes performed at terminals.

3. Empty balancing strategies: How empty container tanks have to be repositioned to meetfuture on-time delivery requirements.

4. Assignment of customer clusters to terminals: This assignment can be specified by thetank container type and the direction of the movement. The balancing flow should havethe same relationship between any other pair of locations. However, these results should

11

not be carried out in practical operations, it only indicates the magnitude of the balancingrequired over a given planning horizon.

5. Purchasing and leasing: Determination of number of tank containers to be brought in tothe system form an external source or the amount to be returned and carried out fromthe system.

The operational level concerns problems in a highly dynamic environment. Two factor playsan important role at this level; time and the stochastic inherent of the system. The schedulingof services and the routing and dispatching of resources such as vehicles, tank containers andlabour is considered at this level. Operational planning aims to make sure that all demands ofempty tank containers are satisfied and to determine the transportation service in a cost efficientcourse of action as possible. In contrast to the tactical planing level, operational planningconcerns the exact routing and allocation of resources in a real time fashion. Traditionally isthe operational planning problem broken down into two separate optimization problems: (1) acontainer allocation problem and (2) a container routing model. The empty container allocationmodel aims to determine the best distribution among all locations in the system while makingsure that the known and the predicted demand is satisfied. Given the distribution from theallocation model, the vehicle routing model aims to determine the most cost efficient routes(Braekers, 2013).

Empty repositioning problems were initially developed for empty freight cars in the railwayindustry. Misra (1972) (cited in Dejax and Crainic, 1987) addressed a deterministic model forfreight cars distribution. The author provides an allocation model where the cost of correct-ing imbalances of empty freight cars are minimized. The problem was formulated as a linearprogram model and was solved with a solution approach based on the transport algorithm(Ford and Fulkerson, 1962) and the Simplex algorithm (Dantzig, 1963). White and Bomberault(1969)(cited in Crainic & Dejax, 1987) addressed a similarly problem as Misra (1972), modelinga linear program in a multi-period fashion. The introduction of dynamic time domains was asignificant contribution to this research field (Dejax and Crainic, 1987).

Wang and Wang (2007) consider a multi-modal distribution network for ports and inland termi-nals including both demand and supply of empty containers to be meet. The authors presentsa static integer program. Olivo et al. (2005) addressed an integer program for empty containerrepositioning between container depots and ports through an inland transportation network.The integer program were solved by an linearisation technique.Shen and Khoong (1995) pro-posed a single-commodity simulation model applied under a rolling horizon fashion to minimizethe total cost of empty containers. The problem were solved by a heuristic method.

An interesting work for empty repositioning was carried out by Choong (2002). The addressedmodel was developed in order to analyze the effect of the length of the planning horizon onempty container management for intermodal transportation. The research resulted in a single-commodity integer program allowing transportation via three different modes; barge, road andrail. Both long and short term container leasing are considered, however one drawback may bethat the cost of short termed leased containers were considered to be independent of the leaseterm. The authors conclusions states that a longer planning horizon may allow higher utilizationof slower cheaper modes, such as barge. The structure of this model is based on the deterministicsingle commodity model presented by Crainic et al. (1993) . The main difference between thesetwo models is that Crainic et al. (1993) includes schedules for vessels and loaded moves in

12

the model and excludes the option of transportation via different modes and transportationcapacities.

Newman and Yano (2000) addressed the problem of determining day-of-week scheduling con-tainers to be allocated for transportation via rail. The aim was to minimize total operatingcosts, including a fixed cost for each train, variable transportation and handling costs for eachcontainer and storage costs, while satisfying the demand from customers. To this aim emptymoves were not included, however the model presented can easily consider demand as emptycontainers. The model presented is a deterministic linear integer program in a rolling horizonfashion. The solutions technique concerns a decomposition procedure that can be classified asclassical heuristics.

Shintani et al. (2010) models the empty container flow as an integer program to optimize theempty repositioning in the hinterland. The authors shows the possibility to reduce operationalcosts through the use of foldable containers instead of standard containers.

An extension of the empty repositioning problem is to integrate assignments of loaded contain-ers. The demand of transporting loaded tank containers from a depot is rarely equal to theincoming flow of empty tank containers. Thus, the demand of empty movements arises fromthese unbalanced loaded movements. It is therefore natural to try to integrate these two typesof movement into the same allocation model (Dejax and Crainic, 1987). Such models have beencarried out by Errera (2009) and Karimi (2005). The former research resulted in a determinis-tic multi-commodity integer program. They solve the problem by a comercial solver and showsthat integrating loaded assignments with empty moves in a single model can reduce both thefleet of containers and the operational cost. The later authors provided a deterministic linearprogram in a two-step event driven algorithm.

Crainic et al. (1993) presented a linear deterministic multi-period single-commodity model. Inaddition, the authors also address a deterministic mixed integer multi-period multi-period multi-commodity model. The models were developed in order to minimize total inland operationalcost. Further, a mathematical formulation was introduced to deal with the stochastic natureof demand and supply of empty containers. Both loaded and empty moves are considered.However, the authors did not present any results.

The problem considered by Deidda et al. (1987) includes the distribution of truck deliveringloaded containers to import customers, the subsequent allocation of empty containers to exportcustomers and the final dispatch of loaded containers to ports. The aim was to determine theallocation of empty tank containers and the routes for the trucks at a minimal operational cost.A static integer program was presented.

To the best of our knowledge, no research have been reported to investigate the problem of emptyrepositioning in great details of a distribution network with the characteristics described inchapter 1. The current literature fails to capture many practical applications of distributing tankcontainers within this field. Such distribution system includes a number of different locations,each for different purposes. Train, port, and rail ship terminals enable terminal-to-terminaltransits for intermodal transports, where rail ship terminals offers connections for both rail andsea. Cleaning stations and depots offers storage capabilities where the former also includescleaning process. At an operational level the main concerns regards transportation via a certainmodality, storage over space and time, matching the type of the tank container to product

13

requirements and ensuring suitable condition of the tank container. The relevant costs includestransportation, storage and customer demand backorder-costs. With this study we try to fillthis gap and propose a mixed-integer linear programming (MILP) multiperiod optimizationmodel is developed aiming to make tactical decisions for the empty tank container allocationproblem. In this problem a set of empty tanks/supplies are unloaded at several unloading sitesand transported via inland or intermodal moves to loading sites. The goal is to satisfy thedemand of empty tank containers in a cost efficient course of action as possible.

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3 Mathematical Theory

This section provides an introduction to network flow problems by describing and mathe-matically formulating some basic network flow problems.

3.1 Network flow problems

As previously mentioned, linear programs assumes that decision variables are continuous, x ∈Rn. However, in the context of network flow problems such as the topic of this study, fractionalvalues of the decision variables are not appropriate. In this situation should the decision vari-ables and their bounds be discrete, only holding integral values, x ∈ Zn. Below, we introducesome general network flow problems. Herein we do not emphasize whether or not the variablesholds continuous or discrete integral values as this already has been discussed.

Networks appears in many different contexts. For instance, telephone networks allows us tocommunicate, electrical and power network brings light to our homes and manufacturing anddistributions networks permits us easily access food and other products. Within these networkswe wish to move some entity (e.g. product, message or electricity) from one point to another.We seek to arrange these movements as efficiently as possible in order to provide good serviceto the end user at the lowest possible cost. Three commonly used network flow problems arestated below (Ahuja et al., 1993).

1. Minimum cost problem. Addresses the question of how a unit can be sent from one pointto another to a minimal cost. Each route (arc) has a given cost and capacity.

2. Maximum flow problem. Given the capacities on each route (arc), how can we send asmuch as possible between two points without violating the capacities?

3. Shortest path problem. What is the shortest path from one point to another in a givennetwork?

3.1.1 Minimum Cost Flow Problem

Let the graph G = (N,A) represent a directed network, where N is the set of nodes and A is theset of arcs. cij indicates the unit flow cost from node i to node j and uij represents the capacity,ij ∈ A. bi is a constant number, representing the demand (bi < 0) or supply (bi > 0) of nodei. Let xij be the flow from node i to node j. The min cost flow problem can be formulated asbelow (Ahuja et al., 1993).

15

Min∑

(i,j)∈Acijxij , i, j ∈ A

Subject to∑j:(ij)∈A

xij −∑

j:(ji)∈Axji = bi, i ∈ N

0 ≤ xij ≤ uij , i, j ∈ A (1)

3.1.2 Distribution Problem

Supply chain management concerns management of material and information flow both in andbetween facilities such as manufacturing plants, vendors, distribution centers and retailers.One of the main processes in a supply chain is the distribution and logistics planning (Lee etal. 2002). The distribution problem is a large class of network flow problems. A novel modelmay be described as the shipments from plants to retailers. This problem refers to a well-knownspecial case of the min cost flow problem, named the transportation problem. Suppose that acar manufacturer has p number of plants where several car models m are manufactured. Let rrepresent the retailers demanding model m to be delivered. The objective is to obtain the flowthat satisfies the demands in a cost efficient way as possible. The supplies and demands areassumed to be known. Figure 6 illustrates the problem.

Figure 6: Example of a production-distribution model (Ahuja et al., 1993).

Four different nodes is included in this network:

1. Plant nodes. Represents the various plants.

2. Plant/model nodes. Indicates model m to be manufactured at plant p.

3. Retailer/model nodes. Corresponds to the demand of retailer r of model m.

4. Retailer nodes. Represents retailer r.

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The three types of arcs included in the network are as follows:

1. Production arcs. These arcs denotes the connection between plant nodes and a plant/modelnodes. The associated cost of this arc represents the unit production cost of model m. Itis possible to specify minimum and maximum production of each model from each plantby lower and upper bounds of these arcs.

2. Transportation arcs. These arcs connects plant/model nodes to retailer/model nodes.The associated cost of this arc represents the unit transportation cost. These arcs may beincluded in a more complex distribution network. For instance, intermodal transportationrequires at least three legs; (a) a delivery from a plant to a port via road; (b) a deliveryfrom the port to another port by sea; (c) a delivery from the port to a retailer via road. Thearcs may have upper and lower bounds imposed on their flow, representing the capacitiesspecified by the contractual agreement with a logistical service provider.

3. Demand arcs. These arcs indicates the connection between retailer/model nodes andretailer nodes. The associated cost of this arc is zero and positive lower bounds equalsthe demand of model m from retailer r.

3.1.3 Transportation Problem

The transportation problem is a generalization of the min cost problem. For this problem theset of nodes N is divided into the two subsets N1 (supply nodes) and N2 (demand nodes). Thenumber of nodes in these subsets is not necessarily equal. For each arc (i, j) in the set of arcsA ∈ N1 and and j ∈ N2. A classic example of the transportation is the distribution betweenwarehouses and customers. In this example the set N1represents warehouses and N2 representscustomers. An arc (i, j) in the set of arcs A represents a route from warehouse i to customer j(Ahuja et al., 1993).

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4 Solution Methodology & Container Management Model

This section describes an empty tank container management model for an intermodal dis-tribution network, providing transportation planning proposals for repositioning of emptytank containers. A problem definition is provided, followed up by a mathematical formu-lation of the problem as a mixed-integer linear programming (MILP) model in a rollinghorizon fashion. We provide three different scenarios for the model. Scenario 1 representsthe generic empty container repositioning problem. Scenario 2 introduces some additionalstorage capacities to the terminals and so to the model. Scenario 3 considers both knownand unidentified demand.

The first necessary step of this project conveyed a mapping of the current system. It was vitalto map the companies logistic system and its operations in order to develop a service networkmodel adequate for Hoyer’s transportation planning of empty moves. Thereby was the firststep of the project to gain a fundamental understanding of Hoyers distribution network and itsservices; How is the distribution system structured, imbalances of loaded flow managed and whatrequirements are demanded by Hoyer’s customers? Answers to such questions were obtainedduring interviews with Hoyer. The project also included several progress meetings with Hoyerwhere the status of the project was updated, additional requirements added and the planningfor the next steps scoped. These meetings were used as a foundation to develop the proposedmodel. Apart from the meetings with Hoyer, internal meetings at ORTEC have taken place.These meetings included further decisions about in what course of action the project shouldproceed.

Other internal meetings included the topic of how to integrate the proposed model into ORD.The contribution of these meetings lead to future ideas for the next steps that will take placeafter this project has been finalized. For instance, the idea of a ”sandbox environment” whereORD is connected to the proposed model in order to gain further knowledge about how theintegration process should be performed in the future, was one result of these meetings. Further,it was decided to create a road map of the company’s planning procedures in a global perspective,not only focusing on empty moves. The road map would then be used to prioritize futureimplementation procedures and other improvements at Hoyer. The data gathering was anongoing procedure until almost the end of the project. The complexity of gather adequate datastems from the fact that Hoyer is currently shifting from their older TMS system to ORD.The obtained data was collected in the form of historically planning executions performed from20150101 to 20160421.

Subsequently, this data was used to construct the distribution network and create samples ofsupply and demand of empty tank containers. As the data provides actual planning actions,further insights of the company’s operations were obtained by additional analysis. A profounddiscussion about the data collection will be presented in the case study of this work (Chapter5). A literature review was conducted including different mathematical models and solutionstechniques carried out in order to solve the empty container repositioning problem. The aimof this investigation was to find a basic model, adequate to the problem under consideration.The basic model was subsequently adapted after the requirements provided by Hoyer in threedifferent scenarios that will be presented later in this chapter. To solve the model in thesescenarios we used the modeling software AIMMS combined with the CPLEX solver.

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Problem descriptionThis work centers on to designing a model for Hoyers’ intermodal distribution service network.The model may facilitate decisions for the empty container management at a tactical level andhelp setting the framework for operational decisions. In order to provide a high service leveland gain desired margins concurrently, the empty tank container management at Hoyer seeksto correct imbalances in a cost efficient course of action as possible while ensuring the on timedelivery requirements are met. We consider transportation, storage and shortage costs.

We consider the company’s difficult problem of cost-efficiently repositioning empty tank con-tainers, given imbalanced trade flows. Typically, a logistics managers concerns regards the flowof loaded tank containers. Recall that a high loaded tank container utilization is crucial inthis industry, given the high cost of the tank containers. As opposed to loaded transports,empty moves does not generate profit. Preferably, empty tank container management wouldnot be considered at all. However, due to imbalances in loaded flows, the importance of emptycontainer logistics becomes evident. The logistics in this aspect will have a direct impact onthe profit margin. Minimizing these costly moves may reduce the operational cost considerably.More specifically, the problem consists of deliver planning proposals regarding repositioning ofempty tank containers, specifying the quantity, dimension (cbm), at what point in time, fromwhat origin to what destination via a certain mode of transportation. These planning propos-als should in a cost efficient course of action as possible ensure the availability of empty tankcontainer required to fulfill customers demand.

The physical network of Hoyers’ intermodal distribution system consists of depots, cleaningstation, railway terminals, port terminals, rail ship terminals, supply customers (unloading sites)and demand customers (loading sites) and the transportation links between these locations.This is illustrated by Figure 7. The figure also shows the possible alternatives of transportationmodes between these locations, indicated by the arrows shape. The later part of the figurerepresents the possibilities to arrange shipments between the same type of location, for examplemay one depot be linked to another depot or several other depots. This model is developedin order to reallocate empty tank containers for a certain type of transportation order, namelyspot orders. These orders regards standardized shipments. A request of a sport order is rarelyrejected to be fulfilled. For precaution, we assume that any origin-destination pair associatedwith each of the three different modalities may have some transportation capacity limit.

It is important to distinguish between the locations presented in Figure 7. Each type of locationcan be distinguished to other types by its properties. Depots are mainly utilized for storage andcleaning stations for both storage and cleaning processes. A few depots and cleaning stationsare controlled by Hoyer, mentioned as internal locations. The storage costs at these locationsare relatively lower compared to external depots and cleaning stations. Railway, port and railship terminals provides the option for intermodal transportation, each with some correspondingmode or modes used for transportation.

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Figure 7: Generalized distribution network for empty repositioning. Sections for every origin-destination pair are illustrated as directed links, the shape of the link indicates the modality.

Railway and port terminals are self descriptive whereas rail ship terminals requires some expla-nation. As indicated by Figure 7, rail ship terminals includes the option for both trains andferries to arrive and depart from its terminal. The storage capacity of the empty tank containersis unlimited at cleaning stations and depots, in terms of the amount of empty tank containersto be stored. In contrast to this have intermodal terminals limited storage capacity. Further,we distinguish between demand and supply customers. Supply customers provides empty tankcontainers that becomes available after unloading of the products, while demand customersrequires empty tank containers to be delivered to its site for loading of products. Note that thesame customer can be both a demand and a supply customer.

The total supply of empty tank containers is made up of the stocks stored at each location, theamount in transit and the number of containers available for pick up at supply customer sites.Tank containers cannot be stored at demand customer sites to fulfill future demand. Neitheris storage at supply customers sites allowed. This implies that an available tank container atsupply customer must be picked up in the same time period it is unloaded. It is possible todistribute empty tank containers from supply customer sites to all locations except demandcustomer sites. Customer s is linked to depots j, cleaning stations c, railway terminal r, portterminal p and rail ship terminal v in Figure 7.

Recall that distribution of chemical products requires matching of the tank containers function-alities and its dimensions to the products demanded to be shipped. Nevertheless are cleaningprocesses also necessary since demand customers often requires cleaned tank containers. Forthis reason, it is assumed that a dirty empty tank container is always sent to a cleaning stationfor a cleaning process before reloading at demand customer sites. In addition, a number of

20

legal requirements needs to be taken into account. This is of great importance to be able toensure the safety of the shipment and quality of the product. For simplicity, only the condition(dirty, clean) and the volume (cbm) of the tank containers is taken into account in the model.All other quality, safety and legal requirements are excluded. The span of different dimensionsare assumed to be aggregated into different classes, indicated by Table 1. This is logical sinceHoyer aggregates similarly while managing empty moves.

Classes A B C D EDimensions

(cbm)≤ 22.6 [22.7-24.5] [24.6 - 27.5] [27.6 - 32.5] ≥ 32.6

Table 1: Tank container classification, specified by its dimensions (cbm).

The demand of empty tank containers is assumed to be known and the length of the planningperiod horizon is determined to a certain length, assuring that the supply of empty tank con-tainers is known. Therefore can we also assume that the supply of empty tank containers isknown. When the supply is insufficient and it is not time wise possible to reallocate empty tanksto demand customers, an emergency shipment from a resource outside the system is executedand will be indicated as a shortage in the model.

Mathematical formulationThe model we are proposing for this problem is in line with the modeling structure that Crainicet al. (1993) and Choong (2002) have used for their researches. That is a dynamic networkmodel, applied in a rolling horizon framework. We propose a mixed integer program using thenotations described later on in this section. Assumptions necessary to postulate are as follows:

1. The storage capacity at depots and cleaning stations are assumed to be unlimited.2. Empty tank containers located at supply customer sites are always available for pick up

and it is not possible to store at these sites.3. If the demand of empty tank containers cannot be fulfilled, then an emergency transport

is executed.4. All shipment modes are assumed to have a certain capacity.5. The supply and demand of empty tank containers are known for each type of container

in any given time period.6. Shipments to supply customers is not allowed in the model. The transportation cost for

these shipments are infinite.7. A container is assumed to always be dirty after unloading at a supply customer site.8. A dirty tank container is never distributed to a demand customer.9. It is assumed that the demand of empty tank containers are independent of the product

type.10. At all location where storage is allowed, the option for storage is independent of the

condition of the tank container, it may be dirty or clean.11. The option to store a tank container is independent of its condition.12. Arrivals and departures to and from a location, respectively, take place in the beginning

of the time period.13. The unit transportation and the unit storage cost are assumed to be independent of the

dimension and the condition of the tank container.14. Transportation from a location to itself is not allowed. In the model, the cost for these

shipments are infinite.15. The unit handling cost is included in the transportation cost.

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16. The unit cleaning cost is assumed to be the same for each type of tank container at allcleaning stations and is therefore excluded from the model.

17. The unit cleaning time is assumed to be the same at each cleaning station.18. If a dirty tank container is transported to a cleaning station, the cleaning process is

assumed to be started in the beginning of the time period it arrives.19. After a cleaning process has started it is assumed to never be interrupted.20. Shipments of dirty containers from cleaning stations are not allowed in the model.21. There is a certain initial inventory at locations where storage is allowed. This inventory

is considered as input in the beginning of the planning horizon.22. There is both internal and external depots and cleaning stations.

Lastly, it should be mentioned that we do not take into account any uncertainties in the model.For instance, the transit times are generally not constant due to the weather, accidents andcongestion. We use the following notations of the sets and indices, parameters and decisionsvariables:

Sets and indicesT = The integral planning horizonN = The set of time periods: {1, 2, ..., T − 1}I = The set of demand customers, indexed byi = 1, 2, ..., |I|S = The set of supply customers, indexed bys = 1, 2, ..., |S|J = The set of depots, indexed by j =1, 2, ..., |J |P = The set of port terminals, indexed by p =1, 2, ..., |P |R = The set of railway terminals, indexed byr = 1, 2, ...|R|C = The set of cleaning stations, indexed byc = 1, 2, ...|C|V = The set of rails ship terminals, indexed byv = 1, 2, ...|V |M = The set of transportationmodes: {Road, Rail, Sea}K= The set of container types:{A, B, C, D, E}U = The set of conditions of tank containers:{d (dirty), o (orderly)}

Parametersdemandt

iku: The demand from customer i intime period t of type k in condition u.supplyt

sku: The supply from customer s in timeperiod t of type k in condition u.cll′ m: The unit transportation cost (EUR) foran empty tank container from origin l to desti-nation l′ via mode m (l, l′ ∈ I, S, J, P,R,C, V ).τll′ m: The transit time (hours) to transportfrom origin l to destination l

′ via mode m(l, l′ ∈ I, S, J, P,R,C, V,E).τ : Cleaning time at cleaning stations.stl: Unit storage cost (EUR) per time periodat location l (l ∈ J, P,R,C, V ).scl: Total storage capacity at location l for eachtime period t (l ∈ P,R, V ).Capt

ll′ m: The transportation capacity between

l and l′ via mode m for arrival at l′ in time t.

M : A large positive constant.

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Decision variablesxt

ll′ mku: Number of empty tank containers of type k with condition u to be arrived in the beginning

of period t at destination l′ via mode m with origin l (l, l′ ∈ I, S, J, P,R,C, V ).

ztlku: Number of tank containers of type k in condition u at location l in the beginning of time periodt (l ∈ J, P,R,C, V ).sht

iku: Number of stock outs of type k in condition u at demand customer i in time period t.

Scenario 1 represents the general empty repositioning problem whereas scenario 2 and 3 areextensions of scenario 1. Each scenario will be described followed up by its mathematical for-mulation.

Scenario 1: The generic model

The objective in scenario 1 is to minimize the total cost for empty container repositioning overa certain horizon. The modeled criteria are the distribution costs; transportation costs betweenlocations (2)-(8), storage costs (9) and the shortage costs associated with the stock outs thatmay occur at demand customer sites (10).

We model the objective function separately for each type of distribution cost. However, thereader is encourage to note that the model only includes one objective function that consists ofthe three different types of distribution costs previously discussed. In this scenario we assumethat storage capacities for locations where storage is allowed are unlimited in terms of allowedstorage time. In addition is the distribution system only driven by known customer demand.

• Minimize transportation costs between locations

• Transportation costs associated with units that departs from supply customers∑s∈S

∑t∈N

∑k∈K

∑u∈U

∑j∈J

∑m∈M

csjmxt+τsjm

sjmku +∑r∈R

∑m∈M

csrmxt+τsrmsrmku +

∑p∈P

∑m∈M

cspmxt+τspm

spmku

+∑c∈C

∑m∈M

cscmxt+τscmscmku +

∑v∈V

∑m∈M

csvmxt+τsvmsvmku

(2)

• Transportation costs associated with units arriving to demand customers∑i∈I

∑t∈N

∑k∈K

∑u∈U

∑j∈J

∑m∈M

cjimxtjimku +

∑r∈R

∑m∈M

crimxtrimku +

∑p∈P

∑m∈M

cpimxtpimku

+∑c∈C

∑m∈M

ccimxtcimku +

∑v∈V

∑m∈M

cvimxtvimku

(3)

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• Transportation costs associated with units arriving to depots∑j∈J

∑t∈N

∑k∈K

∑u∈U

∑j′∈J

∑m∈M

cj′jmxtj′jmku

+∑r∈R

∑m∈M

crjmxtrjmku +

∑c∈C

∑m∈M

ccjmxtcjmku

+∑p∈P

∑m∈M

cpjmxtpjmku

∑v∈V

∑m∈M

cvjmxtvjmku

(4)

• Transportation costs associated with units arriving to railway terminals∑r∈R

∑t∈N

∑k∈K

∑u∈U

∑r′∈R

∑m∈M

cr′rmxtr′rmku

+∑j∈J

∑m∈M

cjrmxtjrmku +

∑p∈P

∑m∈M

cprmxtprmku

+∑c∈C

∑m∈M

ccrmxtcrmku +

∑v∈V

∑m∈M

cvrmxtvrmku

(5)

• Transportation costs associated with units arriving to port terminals∑p∈P

∑t∈N

∑k∈K

∑u∈U

∑p′∈P

∑m∈M

cp′pmxtp′pmku

+∑j∈J

∑m∈M

cjpmxtjpmku

∑c∈C

∑m∈M

ccpmxtcpmku

+∑r∈R

∑m∈M

crpmxtrpmku +

∑v∈V

∑m∈M

cvpmxtvpmku

(6)

• Transportation costs associated with units arriving to cleaning stations∑c∈C

∑t∈N

∑k∈K

∑u∈U

∑c′∈C

∑m∈M

cc′cmxtc′cmku

+∑j∈J

∑m∈M

cjcmxtjcmku +

∑r∈R

∑m∈M

crcmxtrcmku

+∑p∈P

∑m∈M

cpcmxtpcmku +

∑v∈V

∑m∈M

cvcmxtvcmku

(7)

• Transportation costs associated with rail ship terminals∑v∈V

∑t∈N

∑k∈K

∑u∈U

∑v′∈V

∑m∈M

cv′vmx

tv′vmku

+∑j∈J

∑m∈M

cjvmxtjvmku +

∑r∈R

∑m∈M

crvmxtrvmku

+∑c∈C

∑m∈M

ccvmxtcvmku +

∑p∈P

∑m∈M

cpvmxtpvmku

(8)

• Minimize storage costsThere are both internal and external depots and cleaning stations that offers storage possibilities.It is also possible to store units at intermodal terminals.

∑t∈N

∑k∈K

∑u∈U

∑j∈J

stjztjku +

∑r∈R

strztrku +

∑p∈P

stpztpku +

∑v∈V

stvztvku +

∑c∈C

stcztcku

(9)

• Minimize penalty cost related to stock outs.If the supply is insufficient and it is not time wise possible to meet customer orders, a tank

24

container will be brought from a source outside the system. This will only be applied if it isabsolutely necessary due to the high value of M that penalizes these occurrences.∑i∈I

∑t∈N

∑k∈K

∑u∈U

Mshtiku (10)

Model constraintsConstraint (11) states that demand is satisfied during the pre-specified planning horizon. Ifit is not possible to comply the demand, containers will be brought from a source outside thesystem, denoted by shtiko.∑m∈M

∑j∈J

xtjimko +∑r∈R

xtrimko +∑c∈C

xtcimko +∑p∈P

xtpimko +∑v∈V

xtvimko

+ shtiko = demandtiko, i ∈ I, t ∈ N, k ∈ K (11)

Constraint (12) indicates that empty tank containers available at supply customers sites mustbe transported away in the same time period the tank containers have been unloaded.∑m∈M

∑j∈J

xt+τsjm

sjmkd +∑r∈R

xt+τsrmsrmkd +

∑c∈C

xt+τscmscmkd +

∑p∈P

xt+τspm

spmkd +∑v∈V

xt+τsvmsvmkd

= supplytskd, s ∈ S, t ∈ N, k ∈ K (12)

Inventories of dirty containers at cleaning stations are shown by constraint (13). These invento-ries are derived by the inflow of dirty containers to cleaning station withdrawn by the containersthat have been cleaned. A certain amount of dirty containers may be given as an input in thebeginning of the planning horizon. There are both internal and external cleaning stations.

ztckd =∑m∈M

∑t′∈N, t′≤ t

∑s∈S

xt′

scmkd +∑j∈J

xt′

jcmkd +∑r∈R

xt′

rcmkd +∑p∈P

xt′

pcmkd +∑v∈V

xt′

vcmkd

−

∑m∈M

∑t′∈N t′≤ t−τ

∑s∈S

xt′

scmkd +∑j∈j

xt′

jcmkd +∑r∈R

xt′

rcmkd +∑p∈P

xt′

pcmkd +∑v∈v

xt′

vcmkd

,c ∈ C, t ∈ N, k ∈ K (13)

Constraint (14) shows the inventories of cleaned containers at cleaning stations. These invento-ries are derived by the in and outflow of cleaned containers and the tank containers that havebeen cleaned.

ztcko =∑m∈M

∑t′∈N, t′≤ t

∑c′∈C

xt′

c′cmko+

∑j∈J

xt′

jcmko +∑r∈R

xt′

rcmko +∑p∈P

xt′

pcmko +∑v∈V

xt′

vcmko

−

∑m∈M

∑t′∈N, t′≤ t

∑c′∈C

xt′+τ

cc′m

cc′mko+

∑i∈I

xt′+τcimcimko +

∑j∈J

xt′+τcjm

cjmko +∑r∈R

xt′+τcrmcrmko +

∑p∈P

xt′+τcpm

cpmko

+∑v∈V

xt′+τcvmcvmko

+∑m∈M

∑t′∈N, t′≤ t−τ

∑s∈S

xt′

scmkd +∑j∈j

xt′

jcmkd +∑r∈R

xt′

rcmkd +∑p∈P

xt′

pcmkd

+∑v∈v

xt′

vcmkd

, c ∈ C, t ∈ N, k ∈ K (14)

25

Constraint (15) - (18) shows the inventories at the depots, railway, port and rail ship terminals,respectively. A certain amount of tank containers may be given as an input in the beginning ofthe planning horizon. Note that there are both internal and external depots.

ztjku =∑m∈M

∑t′∈N, t′≤ t

∑s∈S

xt′

sjmku +∑c∈C

xt′

cjmku +∑j′∈J

xt′

j′jmku+

∑p∈P

xt′

pjmku +∑r∈R

xt′

rjmku

+∑v∈V

xt′

vjmku

− ∑m∈M

∑t′∈N, t′≤t

∑i∈I

xt′+τjim

jimku +∑j′∈J

xt′+τ

jj′m

jj′mku+

∑c∈C

xt′+τjcm

jcmku +∑r∈R

xt′+τjrm

jrmku

+∑p∈P

xt′+τjpm

jpmku +∑v∈V

xt′+τjvm

jvmku

, j ∈ J, t ∈ N, k ∈ K,u ∈ U (15)

ztrku =∑m∈M

∑t′∈N, t′≤ t

∑s∈S

xt′

srmku +∑c∈C

xt′

crmku +∑r′∈R

xt′

r′rmku+

∑p∈P

xt′

prmku +∑j∈J

xt′

jrmku

+∑v∈V

xt′

vrmku

− ∑m∈M

∑t′∈N, t′≤t

∑i∈I

xt′+τrimrimku +

∑r′∈R

xt′+τ

rr′m

rr′mku+

∑c∈C

xt′+τrcmrcmku +

∑j∈J

xt′+τrjm

rjmku

+∑p∈P

xt′+τrpm

rpmku +∑v∈V

xt′+τrvmrvmku

, r ∈ R, t ∈ N, k ∈ K,u ∈ U (16)

ztpku =∑m∈M

∑t′∈N, t′≤ t

∑s∈S

xt′

spmku +∑c∈C

xt′

cpmku +∑p′∈P

xt′

p′pmku+

∑r∈R

xt′

rpmku +∑j∈J

xt′

jpmku

+∑v∈V

xt′

vpmku

− ∑m∈M

∑t′∈N, t′≤ t

∑i∈I

xt′+τpim

pimku +∑p′∈P

xt′+τ

pp′m

pp′mku+

∑c∈C

xt′+τpcm

pcmku +∑j∈J

xt′+τpjm

pjmku

+∑r∈R

xt′+τprm

prmku +∑v∈V

xt′+τpvm

pvmku

, p ∈ P, t ∈ N, k ∈ K,u ∈ U (17)

ztvku =∑m∈M

∑t′∈N, t′≤ t

∑s∈S

xt′

svmku +∑c∈C

xt′

cvmku +∑v′∈V

xt′

v′vmku+

∑p∈P

xt′

pvmku +∑j∈J

xt′

jvmku

+∑r∈R

xt′

rvmku

− ∑m∈M

∑t′∈N, t′≤ t

∑i∈I

xt′+τvimvimku +

∑v′∈V

xt′+τ

vv′m

vv′mku

∑c∈C

xt′+τvcmvcmku +

∑j∈J

dt′+τvjm

vjmku

+∑p∈P

xt′+τvpm

vpmku +∑r∈R

xt′+τvrmvrmku

, v ∈ V, t ∈ N, k ∈ K, u ∈ U (18)

A cleaning process is not allowed to be interrupted, this is ensured by condition (19).∑m∈M

∑c′∈C

xt+τ

cc′m

cc′mkd+

∑i∈I

xt+τcimcimkd +

∑j∈J

xt+τcjm

cjmkd +∑r∈R

xt+τcrmcrmkd +

∑p∈P

xt+τcpm

cpmkd

+∑v∈V

xt+τcvmcvmkd

= 0, c ∈ C, t ∈ N, k ∈ K (19)

26

Constraint (20) - (24) ensures that respectively inventory cannot be negative.

ztcko ≥∑m∈M

∑c′∈C

xt+τ

cc′m

cc′mko+

∑i∈I

xt+τcimcimko +

∑j∈J

xt+τcjm

cjmko +∑r∈R

xt+τcrmcrmko +

∑p∈P

xt+τcpm

cpmko +∑v∈V

xt+τcvmcvmko

,c ∈ C, t ∈ N, k ∈ K (20)

ztjku ≥∑m∈M

∑i∈I

xt+τjim

jimku +∑j′∈J

xt+τ

jj′m

jj′mku+

∑c∈C

xt+τjcm

jcmku +∑r∈R

xt+τjrm

jrmku +∑p∈P

xt+τjpm

jpmku +∑v∈V

xt+τjvm

jvmku

,j ∈ J, t ∈ N, k ∈ K,u ∈ U (21)

ztrku ≥∑m∈M

∑i∈I

xt+τrimrimku +

∑r′∈R

xt+τ

rr′m

rr′mku+

∑c∈C

xt+τrcmrcmku +

∑j∈J

xt+τrjm

rjmku +∑p∈P

xt+τrpm

rpmku +∑v∈V

xt+τrvmrvmku

,r ∈ R, t ∈ N, k ∈ K,u ∈ U (22)

ztpku ≥∑m∈M

∑i∈I

xt+τpim

pimku +∑p′∈P

xt+τ

pp′m

pp′mku+

∑c∈C

xt+τpcm

pcmku +∑j∈J

xt+τpjm

pjmku +∑r∈R

xt+τprm

prmku +∑v∈V

xt+τpvm

pvmku

,p ∈ P, t ∈ N, k ∈ K,u ∈ U (23)

ztvku ≥∑m∈M

∑i∈I

xt+τvimvimku +

∑v′∈V

xt+τ

vv′m

vv′mku+

∑c∈C

xt+τvcmvcmku +

∑j∈J

xt+τvjm

vjmku +∑p∈P

xt+τvpm

vpmku +∑r∈R

xt+τvrmvrmku

, v ∈ V, t ∈ N, k ∈ K, u ∈ U (24)

Conditions (25) - (27) ensures that the total number of tank containers to be stored at railway,port and rail ship terminals does not exceed the limit of storage at these locations, respectively.∑k∈K

∑u∈U

ztrku ≤ scr, r ∈ R, t ∈ N (25)

∑k∈K

∑u∈U

ztpku ≤ scp, p ∈ P, t ∈ N (26)

∑k∈K

∑u∈U

ztvku ≤ scv, v ∈ V, t ∈ N (27)

All shipment modes are assumed to have a certain capacity. Condition 28 ensures that thiscapacity cannot be exceeded.∑k∈K

∑u∈U

xtll′mku

≤ Captll′m

, t ∈ N, l, l′ ∈ I, S, J, P,R,C, V, m ∈M (28)

The domain of decision variables prescribed in (29) guarantees that tank containers can flow onthe network only until the end of pre-specified time horizon.xtll′mku

≤ 0, t /∈ N, l, l′ ∈ I, S, J, P,R,C, V, m ∈M, k ∈ K, u ∈ U (29)

27

Constraint (30) indicates that all decision variables can only take non-negative integer values.This constraint ensures that fractional empty tank containers will not be included in the optimalsolution.xtsjmkd, x

tsrmkd, x

tspmkd, x

tscmkd, x

tsvmkd, x

tjimko, x

trimko, x

tpimko, x

tcimko, x

tvimko, x

tjjmku,

xtrjmku, xtcjmku, x

tpjmku, x

tvjmku, x

trrmku, x

tjrmku, x

tprmku, x

tcrmku, x

tvrmku, x

tppmku, x

tjpmku,

xtcpmku, xtrpmku, x

tvpmku, x

tccmku, x

tjcmku, x

trcmku, x

tpcmku, x

tvcmku, x

tvvmku, x

tjvmku, x

trvmku,

xtcvmku, xtpvmku, z

tjku, z

trku, z

tpku, z

tvku, z

tcko, z

tckd, sh

tiku ∈ Z≥0, t ∈ N, m ∈M, k ∈ K, u ∈ U,

s ∈ S, j ∈ J, c ∈ C, p ∈ P, r ∈ R, v ∈ V, i ∈ I (30)

Scenario 2: Storage capacities at intermodal terminals

As mentioned before, intermodal terminals may constitute bottlenecks of an intermodal distri-bution system. We already included transportation capacity restrictions Capt

ll′munder scenario

1. Another bottleneck may occur when the allowed storage time at intermodal terminals is lim-ited. For this reason we include a condition of allowed storage time ∆ at intermodal terminals(railway, port and rail ship terminals) in scenario 2. The objective in scenario 2 is the same asin scenario 1.

Scenario 2 can be modeled by conditions (2) - (30) from scenario 1 and the constraints (31) -(33) given below. Conditions (31) - (33) guarantees that tank containers cannot be stored atintermodal terminal longer than ∆ time periods.∑m∈M

∑s∈S

xtsrmkd +∑j∈J

xtjrmkd +∑r′∈R

xtr′rmkd

+∑c∈C

xtcrmkd +∑p∈P

xtprmkd +

∑v∈V

xtvrmkd

=∑m∈M

∑δ∈∆

∑j∈J

xt+τrjm+δrjmkd +

∑r′∈R

xt+τ

rr′m

+δrr′mkd

+∑c∈C

xt+τrcm+δrcmkd +

∑p∈P

xt+τrpm+δrpmkd

+∑v∈V

xt+τvrm+δrvmkd +

∑i∈I

xt+τrim+δrimkd

, r ∈ R, t ∈ N, k ∈ K, u ∈ U (31)

∑m∈M

∑s∈S

xtspmkd +∑j∈J

xtjrmkd +∑p′∈P

xtp′rmkd

+∑c∈C

xtcrmkd +∑r∈R

xtrpmkd +

∑v∈V

xtvpmkd

=∑m∈M

∑δ∈∆

∑j∈J

xt+τpjm+δpjmkd +

∑p′∈P

xt+τ

pp′m

+δ

pp′mkd+

∑c∈C

xt+τpcm+δpcmkd +

∑r∈R

xt+τprm+δprmkd

+∑v∈V

xt+τpvm+δpvmkd +

∑i∈I

xt+τpim+δpimkd

, p ∈ P, t ∈ N, k ∈ K, u ∈ U (32)

28

∑m∈M

∑s∈S

xtsvmkd +∑j∈J

xtjvmkd +∑v′∈V

xtv′vmkd

+∑c∈C

xtcvmkd +∑r∈R

xtrvmkd +

∑p∈P

xtpvmkd

=∑m∈M

∑δ∈∆

∑j∈J

xt+τvjm+δvjmkd +

∑v′∈V

xt+τ

vv′m

+δvv′mkd

+∑c∈C

xt+τvcm+δvcmkd +

∑r∈R

xt+τvrm+δvrmkd

+∑p∈P

xt+τvpm+δvpmkd +

∑i∈I

xt+τvim+δvimkd

, v ∈ V, t ∈ N, k ∈ K, u ∈ U (33)

Scenario 3: Anticipated demand

As mentioned in the problem definition, a high tank utilization is required to obtain desiredprofit margins, nevertheless must empty tank containers be reallocated in order to meet on timedelivery requirements. If the empty tank container management always await a transportationorder from the demand customers before executing empty moves, it may for some instance notbe time wise possible to supply the demand. Scenario 3 includes both known demand andanticipated demand. Some tank containers are repositioned to storage facilities such as depots,cleaning stations or intermodal terminals based on anticipations of future demand to arise inthe neighborhood of these locations. We assume that all these anticipations are known.

It is also assumed that tank containers that have been reallocated in response to an anticipationcannot be used as supply for any demand in the pre-specified planning horizon. If some antici-pated demand arises, we assume that a certain time λ is sufficient to execute the end-haulagefor delivery of the tank container. The reader should note that the end-haulage itself is notconsidered in the pre-specified planning horizon. The end-haulage denotes the last mile delivery,in this scenario with respect to an empty tank container being transported from either a depot,cleaning station, or an intermodal terminal to some demand customer. The assumptions forscenario 3 follows below:

1. All anticipated demand are known.2. Tank containers that are repositioned in response to anticipated demand cannot be used

as supply for any demand in the pre-specified planning horizon.3. If an anticipated demand arises, we assume that this demand arises in the neighborhood

of some depot, cleaning station, railway, port or the rail ship terminal that the tankcontainer has been repositioned to.

4. We assume that a certain time λ is time wisely sufficient to execute the end-haulage anddeliver the tank container.

5. Realized anticipated demand and the associated end-haulage are not included in the pre-specified planning horizon.

29

We introduce the following notations in scenario 3:

Parameters and decision variablesanticipated demandt

lko: The anticipated demand from location l in time period t of type k in conditionu (l ∈J, P,R, V, C).λ: Time needed to meet on-time delivery requirements outside the pre-specified planning horizon.sht

lku: Number of stock outs of type k in condition u at location l in time period t. (l ∈J, P,R, V, C).

Scenario 3 can be modeled by the constraint (2) - (30) from model 1 and (34) - (44) below. Theobjective in scenario 3 is the same as in the two previous scenarios with the additional objectiveto minimize shortage costs associated with anticipated demand.

• Minimize penalty costs associated with stock outs and anticipated demand.∑l∈J,P,R,V,C

∑t∈N

∑k∈K

∑u∈U

Mshtlku (34)

Constraint (35) - (38) guarantees that the anticipated demand to arise in the neighborhoodof depots, railway, rail ship and port terminals are satisfied during the pre-specified planninghorizon. If the demand cannot be satisfied, containers will be brought from a source outsidethe system.∑j′∈J

∑m∈M

xt−λj′jmko

+∑r∈R

∑m∈M

xt−λrjmko +∑c∈C

∑m∈M

xt−λcjmko

∑p∈P

∑m∈M

xt−λpjmko +∑v∈V

∑m∈M

xt−λvjmko

+ shtjko ≥ anticipated demandtjko, t ∈ N, k ∈ K, j ∈ J (35)

+∑r′∈R

∑m∈M

xt−λr′rmko

+∑j∈J

∑m∈M

xt−λjrmko +∑p∈P

∑m∈M

xt−λprmko +∑c∈C

∑m∈M

xt−λcrmko +∑v∈V

∑m∈M

xt−λvrmko

+ shtrko ≥ anticipated demandtrko, t ∈ N, k ∈ K, r ∈ R (36)

+∑p′∈P

∑m∈M

xt−λp′pmko

+∑j∈J

∑m∈M

xt−λjpmko

∑c∈C

∑m∈M

xt−λcpmko +∑r∈R

∑m∈M

xt−λrpmko +∑v∈V

∑m∈M

xt−λvpmko

+ shtpko ≥ anticipated demandtpko, t ∈ N, k ∈ K, p ∈ P (37)

+∑v′∈V

∑m∈M

xt−λv′vmko

+∑j∈J

∑m∈M

xt−λjvmko +∑r∈R

∑m∈M

xt−λrvmko +∑c∈C

∑m∈M

xt−λcvmko +∑p∈P

∑m∈M

xt−λpvmko

+ shtvko ≥ anticipated demandtvko, t ∈ N, k ∈ K, v ∈ V (38)

Constraint (39) states that the anticipated demand to arise in the neighborhood of cleaningstations must be satisfied. If the demand cannot be satisfied, containers will be brought from asource outside the system.∑c′∈C

∑m∈M

xt−λc′cmko

+∑j∈J

∑m∈M

xt−λjcmko +∑r∈R

∑m∈M

crcmxt−λrcmko +

∑p∈P

∑m∈M

xt−λpcmko +∑v∈V

∑m∈M

xt−λvcmko

+∑j∈J

∑m∈M

xt−τ−λjcmkd +∑r∈R

∑m∈M

xt−τ−λrcmkd +∑p∈P

∑m∈M

xt−τ−λpcmkd +∑v∈V

∑m∈M

xt−τ−λvcmkd

+∑s∈S

∑m∈M

xt−τ−λscmkd + shtcko ≥ anticipated demandtcko

t ∈ N, k ∈ K, c ∈ C (39)

30

Constraint (40) - (43) shows the inventories at the depots, railway, port and rail ship terminals,respectively. For each of these locations, a certain amount of containers may be given as aninput in the beginning of the planning horizon.

ztjku =∑m∈M

∑t′∈N, t′≤ t

∑s∈S

xt′

sjmku +∑c∈C

xt′

cjmku +∑j′∈J

xt′

j′jmku+

∑p∈P

xt′

pjmku +∑r∈R

xt′

rjmku

+∑v∈V

xt′

vjmku

− ∑m∈M

∑t′∈N, t′≤t

∑i∈I

xt′+τjim

jimku +∑j′∈J

xt′+τ

jj′m

jj′mku+

∑c∈C

xt′+τjcm

jcmku +∑r∈R

xt′+τjrm

jrmku

+∑p∈P

xt′+τjpm

jpmku +∑v∈V

xt′+τjvm

jvmku

+∑t′∈N

sht′−λjko −

∑t′∈N

anticipated demandt′−λjko ,

j ∈ J, t ∈ N, k ∈ K,u ∈ U (40)

ztrku =∑m∈M

∑t′∈N, t′≤ t

∑s∈S

xt′

srmku +∑c∈C

xt′

crmku +∑r′∈R

xt′

r′rmku+

∑p∈P

xt′

prmku +∑j∈J

xt′

jrmku

+∑v∈V

xt′

vrmku

− ∑m∈M

∑t′∈N, t′≤t

∑i∈I

xt′+τrimrimku +

∑r′∈R

xt′+τ

rr′m

rr′mku+

∑c∈C

xt′+τrcmrcmku +

∑j∈J

xt′+τrjm

rjmku

+∑p∈P

xt′+τrpm

rpmku +∑v∈V

xt′+τrvmrvmku

+∑t′∈N

sht′−λrko −

∑t′∈N

anticipated demandt′−λrko ,

r ∈ R, t ∈ N, k ∈ K,u ∈ U (41)

ztpku =∑m∈M

∑t′∈N, t′≤ t

∑s∈S

xt′

spmku +∑c∈C

xt′

cpmku +∑p′∈P

xt′

p′pmku+

∑r∈R

xt′

rpmku +∑j∈J

xt′

jpmku

+∑v∈V

xt′

vpmku

− ∑m∈M

∑t′∈N, t′≤ t

∑i∈I

xt′+τpim

pimku +∑p′∈P

xt′+τ

pp′m

pp′mku+

∑c∈C

xt′+τpcm

pcmku +∑j∈J

xt′+τpjm

pjmku

+∑r∈R

xt′+τprm

prmku +∑v∈V

xt′+τpvm

pvmku

+∑t′∈N

sht′−λpko −

∑t′∈N

anticipated demandt′−λpko ,

p ∈ P, t ∈ N, k ∈ K,u ∈ U (42)

ztvku =∑m∈M

∑t′∈N, t′≤ t

∑s∈S

xt′

svmku +∑c∈C

xt′

cvmku +∑v′∈V

xt′

v′vmku+

∑p∈P

xt′

pvmku +∑j∈J

xt′

jvmku

+∑r∈R

xt′

rvmku

− ∑m∈M

∑t′∈N, t′≤ t

∑i∈I

xt′+τvimvimku +

∑v′∈V

xt′+τ

vv′m

vv′mku

∑c∈C

xt′+τvcmvcmku +

∑j∈J

dt′+τvjm

vjmku

+∑p∈P

xt′+τvpm

vpmku +∑r∈R

xt′+τvrmvrmku

+∑t′∈N

sht′−λvko −

∑t′∈N

anticipated demandt′−λvko ,

v ∈ V, t ∈ N, k ∈ K, u ∈ U (43)

Constraint (44) indicates that shtlku can only take non-negative integer values.shtlku ∈ Z≥0, l ∈ J, P,R, V, C, k ∈ K,u ∈ U, t ∈ N (44)

31

5 Computational Study & Sensitivity Analysis

This section discusses our case study problem based on tank container movements inHoyer’s European distribution network. We compare the proposed model under the differentscenarios with actual historical shipments performed by Hoyer in order to investigate themodels’ performance. To reveal the factors on which the solution depends on we presenta sensitivity analysis under each scenario. The intent is to validate the model and todemonstrate its functionality. We start this section by describing the procedure of the datacollection, the scope and the general settings applied in our computational experiments.

Each instance were solved on a laptop with an Intel Core i7-5600U processor, clock rate of 2.6GHz and 16 GB RAM memory. We used the AIMMS modeling software and the CPLEX solverin order to solve the problems. The data used for this case study has been collected from thedata base of Hoyer’s transportation planning tool; ORD, constituting approximately 40% of thetotal planning actions performed by Hoyer. Since the scope of this work concerns shipmentswithin Europe, the data were collected accordingly.

Three different types of transportation planning actions constitutes the foundation of the datacollection: travel instance actions; transportation instances between origin-destination pairs,specifying the mode of transportation, pick-up actions; loading actions, represents the demand ofempty tanks and delivery actions; unloading actions, constitutes the supply of empty tanks. Theadaption of the distribution network were based on the obtained travel instance actions whereasthe demand and supply were derived from pick-up actions and delivery actions, respectively.

The collected data includes transport planning actions performed from 20150101 to 20160421.Figure 8 and Table 2 illustrates the topology of the distribution network under consideration.The structure of the distribution network is classified by countries and regions, see Table 9 inAppendix A.

Depots: 37 (4+34) Supply customers: 1196 Demand customers: 387(Internal+External)

Cleaning stations: 138 (8+130) Railway terminals: 88 Port terminals: 93(Internal+External)

Rail ship terminals: 9 Links/Sections 14590 Total number of loca-tions

2065

Table 2: Topology of Hoyer’s distribution network in the case study.

The cost for transportation via road is denoted by e1/km. Transportation costs and transittimes for shipments carried out via vessel and train were derived by calculating the average priceand the transit time for each origin-destination pair. This data was obtained from the database of Hoyer’s former TMS system. We keep the storage capacities at intermodal terminals (scr, scp and scv) from condition (25) - (27) infinite.

32

Unfortunately we encountered a number of issues during the data collection that comprisessome limitations for this case study. Some important links were missing. We were thereforeforced to add these links in order to avoid infeasibility. For instance, the model would beinfeasible if supply arises at supply customer sites without any link to any other location (seecondition 12 from the generic model in scenario 1). These links were created in the IDLEdevelop environment with the programming language Python.

Figure 8: Topology of Hoyer’s distribution network in this case study. To the left in the figureare depots, cleaning stations, railway, port and rail ship terminals indicated by its color; red,orange, green, blue and purple, respectively. Demand customers (black) and supply customers(grey) are shown to the right in the figure.

Transit times were inaccurate or missing from the collected data. Distances between each origin-destination pair were therefore estimated and related to the average speed of a truck (60 km/h),in order to derive estimated transit times for shipments carried out via road. These distanceswere calculated based on the location’s coordinates and the function great circle distance (45).This function denotes the shortest path between two points on the surface of the earth (James,2004). Let (φ1, λ1) and (φ2, λ2) be the geographical latitude and longitude of two points. Theestimated distance D is then given by:

D = 2παR360

α = arccos [sinφ1sinφ2 + cosφ1cosφ2∆λ] (45)R = Mean earth radius

Storage costs at internal and external depots and cleaning stations are denoted by e1/dayand e2/day, respectively. The storage cost at intermodal terminals are given by e3/day. Thecleaning time at cleaning stations is set to be 1 day. Further, inventories were estimated bysubtracting outflows from inflows for each location one year back in time. This was necessarysince there was no easily accessible data over stored tank containers. Initial inventories will beincluded for some of the instances in the sensitivity analysis and excluded for others. This willbe specified for each instance.

To distinguish between internal and external locations is not sufficient enough to replicate cer-tain business rules performed by Hoyer. For instance, tank containers are sometimes prioritized

33

to be cleaned at certain cleaning stations over other cleaning stations. However, these types ofbusiness rules were excluded from the model since this kind of data was not possible to obtain.Further, we assume in the model that the demand is only dependent of the product volume(cbm) and the condition of the tank container. This comprises another limitation since eachproduct must be matched to a set of different functionalities of the tank container in a practicalpoint of view.

In addition, cleaning of a tank container is not always necessary. If previous loaded productcorresponds to the product at reloading, a cleaning process can sometimes be neglected. For thisreason were all routes including a shipment from supply customers to demand customers withoutany travel instance to a cleaning stations removed while analyzing the models performance.

The fact that ORD only includes 40% of the total number of shipments performed by Hoyeralso have some serious consequences for the investigation of the model’s performance. One partof the tank container cycle may be planned in ORD whereas another part of the cycle maytake place in Hoyer’s older TMS system. For instance, in the scenario where a tank containerhave been planned for unloading within ORD and demand of this tank arises from a customerincluded in the older TMS system, the planning actions for this shipment will take place partlyin both systems. All such routes were removed while analyzing the model’s performance. Thelimitations of this case study follows below:

• Only 40% of the total European distribution network is considered.

• Business rules are excluded according to the company’s requests.

• Some links not based on historically planning actions have been added.

• Transit times have been estimated.

• Based on the company’s requests, it is assumed that the demand is independent of theproduct type.

• Storage costs have been estimated.

• Inventories have been estimated.

The model is analyzed step by step and its functionality is demonstrated by conducting exper-iments on the network from our case study problem, see Table 3. The case study constitutesthree different scenarios of empty tank container allocation. In addition, the case study net-work topology is utilized to create randomly selected instances with random parameters andthe model is also evaluated on these instances.

An extensive sensitivity analysis is conducted to show the effect of the model’s parameters on itsperformance. The sensitivity analysis employs a set of data from our case study and randomlyselected data to highlight certain features of the model and provide some insights regardingthe model’s behavior, see Table (4)-(8) below. The computational experiments show that themodel finds good quality solutions, and demonstrate that cost improvements can be achievedin the network.

34

Scenario 1: The generic model

Table 3 demonstrates the performance of the model for some instances in Scenario 1, indicatingthat the total cost savings varies between 6.54% − 10.3%. These variations may depend on thecase study’s limitations, clearly been pointed out above.

settings Instance 1 Instance 2 Instance 3

Total cost savings (e) 6.54% 6.29% 10.3%

Table 3: Total cost savings representing the performance of the model.

The first sensitivity analysis concerns scenario 1. The objective is to interpret what effects differ-ent discretizations of the planning horizon may have on operational costs, modality utilizationand computational performance. The later is of interest since time discretization methods areused to make the problem possible to solve within a certain time. The two former is of interestsince information from the original problem may be excluded (included) while transforming theproblem by time discretization, see Table 4. As opposed to continuous optimization, discretemathematical programs are restricted to discrete variables, such as integers. We transformedthe problem into some standard optimization problems by discretizing the system as a whole.Although the length of the planning horizon remains constant at 4 days (96 hours) the dis-cretization of the time periods varies.

To clarify, the first instance presented in Table 4 is a time discretization where the time periodsrepresents days. Subsequently, the whole system and its parameters are modified to accom-modate for time periods as days. The second instance from the same table represents a timediscretization where every time period denotes 6 hours.

Supply: 292, Demand: 170, Initial inventory: 0, Captll′ m

= 5000

settings Instance 1 Instance 2 Instance 3 Instance 4 Instance 5

Time periods 4 16 24 32 48Total cost 37,509 40,843 41,350 41,396 -Transportation cost 23,758 26,803 27,122 27,129 -Storage cost 13,751 14,040 14,228 14,267 -Shortages 0 0 0 0 -Modality utilization 100/0/0 100/0/0 100/0/0 99/0/1 -Road / Rail / SeaConstraints 138,468 553,579 830,013 1,106,352 1,925,630Variables 601,761 2,407,041 3,610,561 4,814,081 8,376,501Elapsed time for 261.63 s 912.47 s 1596.56 s 2562.31 s ≥ 1000.00sAIMMS/CPLEXNormal completion/Terminated by solver

Normalcompletion

Normalcompletion

Normalcompletion

Normalcompletion

Terminatedby solver

Table 4: Operational costs, modality utilization and elapsed computational time for a set ofdifferent time discretizations.

35

10 20 30 40 500

25

50

75

Time periods

eT

hous

ands

Operational costs

Total CostTrp. CostStorage Cost

10 20 30 40 500

1.8

3.6

Time periods

Seco

nds

(Tho

usan

ds)

Elapsed time for CPLEX/AIMMS

Total time

Figure 9: Scenario 1; operational cost comparison (to the left), computational time (to theright).

Figure 9 reveals an increasing trend in total cost as a result of the increasing transportation andstorage cost function. The cost functions tends to increase as we are specifying time periodsmore realistic. While comparing the total cost from instance 1 to the other instances it becameevident that the total cost increased approximately between 9% to 10%.

From Table 4 it can be concluded that regardless of the time discretization, almost only roadwere suggested for the means of transportation. Figure 9 indicates that the computational timeincreases rapidly as the planning horizon discretization becomes more realistic.

The limit for this sensitivity analysis turned out to be found at instance 4, suggesting a timediscretization where each time period represents 3 hours. Instance 5 could not be solved sincethe instance was terminated. The instance was terminated since the memory of 16 GB RAMwas insufficient for this instance. The out of memory error occurred in the generation phaseproduced by AIMMS and CPLEX were never initialized.

To further evaluate the sensitivity of the model under scenario 1, we investigated the effectson the optimal solution from the length of the planning horizon and two different amounts ofinitial inventory. We compared the effects on a 4-days planning horizon to a planning horizonof 7-days and 14-days. The net demand and supply is equal under the first 4 days for thethree planning horizons under consideration. We present the operational costs and modalityutilization under the first 4 days. This is specified by Table 5.

36

Supply and demand the first 4 time periods: 361, 170. Captll′ m

= 5000

settings Instance 1 Instance 2 Instance 3

Initial inventory: 0

# Time periods 4 7 21Total cost (e) 53,884 61,874 89,048Transportation cost (e) 52,946 60,895 87,748Storage cost (e) 938 979 1300# Shortages 0 0 0Modality util. (%) 91.9/3.3/4.8 90.2/4/5.8 82.9/6.8/10.3Road / Rail /Sea

Initial inventory clean: 399, Initial inventory dirty: 510

# Time periods 4 7 21Total cost (e) 63,990 65,711 75,394Transportation cost (e) 27,906 37,360 51,457Storage cost (e) 36,084 28,351 23,937# Shortages 0 0 0Modality util. (%) 1/0/0 99.7/0.3/0 99.7/0.3/0Road / Rail /Sea

Table 5: Scenario 1; operational costs and modality utilization as a result of different lengthsof the planning horizon and magnitudes of initial inventory.

Table 5 reveals that the total cost tends to be an increasing function of the planning horizon,regardless of the initial inventory. However, it should be noted that the 7- and 14-day modelconsiders longer planning horizons and the optimal solutions only suggests a higher cost duringthe first 4 days compared to the 4-day model. These observations are also shown in Figure 10.

4 7 14

20

40

60

Time horizon length

eT

hous

ands

Total Cost 0 Inv.Total Cost High Inv.Trp. Cost 0 Inv.Trp. Cost High Inv.Storage Cost 0 Inv.Storage Cost High Inv.

Figure 10: Scenario 1; the resulting operational costs with 0 and high initial inventory.

37

4 7 140

50

100

Time horizon length

Mod

ality

utili

zatio

n(%

)

Road 0 Inv.Road High Inv.Rail 0 Inv.Rail High Inv.Sea 0 Inv.Sea High Inv.

Figure 11: Scenario 1; the resulting modality utilization with 0 and high initial inventory.

Focusing on the instances with 0 initial inventory and comparing the results of the first 4-daymodel to the results from the 7-day and 14-day model, some considerable allocations effects canbe noted. Figure 11 demonstrates that the 7-day and 14-day model propose a lower utilizationof road over the first 4 days, compared to the 4-day model. One reason to this is that tankcontainers not needed for meeting the demands in the next four days may be transported viaslower modes to other regions where demand arises in some future time periods.

The results of the instances with high inventory suggests a high utilization of road, almost 100%,regardless of the length of the planning horizon. High inventories allows demand to be satisfiedfrom facilities closely located to the demand customers i.e. intermodal transportation’s are notnecessary. Figure 11 illustrates a decreasing storage cost function and increasing transportationcost function as a result of the length of the planning horizon. One reason to this may be thatlonger planning horizons allows transportation with transit times longer than 4-days, suggestingmore transportation and less storage. Further, inventories of empty tanks may be repositionedto closely located facilities with relatively lower storage costs.

Supply: 265, Demand: 170, Initial inventory: 0, Time periods: 4

settings Instance 1 Instance 2 Instance 3 Instance 4 Instance 5

Captll′ m

0 10 20 30 40(increase in %)Total cost (e) 51,064 50,910 50,800 50,751 50,704Transportation cost(e)

50,239 50,083 49,970 49,920 49,870

Storage cost (e) 826 828 830 831 834# Shortages 0 0 0 0 0Modality util. (%) 91.7/3.9/4.3 91.3/3.9/4.6 91.2/3.8/5 91/4/5 91/3.8/5.2Road / Rail /Sea

Table 6: Scenario 1; operational costs and modality utilization’s due to capacity restrictions oftransportation modes (Capt

ll′m).

The next sensitivity analysis concerns condition 28 in scenario 1, where each transportationmode may have some capacity restriction (Capt

ll′m). The aim is to interpret how the distribution

costs and the modality utilization are influenced by this condition. The results are presentedin Table 6, Figure 12 and 13.

38

0 10 20 30 4040

50

60

Increase of Captll′m

as a percentage

eT

hous

ands

Total cost and transportation cost

Total CostTrp. Cost

0 10 20 30 400.7

0.8

0.9

Increase of Captll′m

as a percentage

eT

hous

ands

Storage cost

Storage Cost

Figure 12: Scenario 1; operational costs as a result of increasing Captll′m

.

Figure 12 demonstrates that the total cost tends to decrease as we are allowing higher trans-portation capacity (Capt

ll′m). Slower and cheaper modes are utilized more when the trans-

portation capacities are extended (Figure 13). This explains the decreasing transportation costfunction. Transportation via train and sea can be associated with a relatively higher storagecost at intermodal terminals. Due to relatively higher throughput at these terminals, the storagecost increases slightly.

0 10 20 30 40

80

90

100

Increase of Captll′m

as a percentage

Mod

ality

utili

zatio

nin

%

Road utilization

Road

0 10 20 30 400

4

8

Increase of Captll

′m

as a percentage

Mod

ality

utili

zatio

nin

%

Rail and sea utilization

RailSea

Figure 13: Scenario 1; modality utilization as a result of increasing Captll′m

.

Scenario 2: Storage capacities at intermodal terminals

Scenario 2 includes a restriction of allowed storage time at intermodal terminals. The aim is toinvestigate what impact allowed storage time at intermodals (∆) may have on the distributioncosts and the modality utilization.

39

Supply: 265, Demand: 170, Initial inventory: 0, Time periods: 21, Captll′ m

= 5000

settings Instance 1 Instance 2 Instance 3 Instance 4 Instance 5

∆ 0 1 2 3 4Total cost (e) 955,117 954,110 945,584 934,718 930,831Transportation cost(e)

810,709 806,818 801,542 790,397 785,505

Storage cost (e) 144,408 147,292 144,042 144,321 145,326# Shortages 38 22 0 0 0Shortages (%) 0.37 0.2 0 0 0Modality util. (%) 100/0/0 90.8/4.5/4.7 91.0/4.7/4.3 89.0/4.8/6.2 89.1/5.1/5.8Road / Rail /Sea

Table 7: Operational costs and modality utilization’s as an effect of allowed storage time (∆)at intermodal terminals.

0 1 2 3 4700

900

1,100

Unit increase of ∆

eT

hous

ands

Total cost ans transportation cost

Total CostTrp. Cost

0 1 2 3 4140

145

150

Unit increase of ∆

eT

hous

ands

Storage costs

Storage Cost

Figure 14: Scenario 2; operational cost as a result of unit time period increase of ∆.

In the situation where storage at intermodal terminals is not allowed (∆ = 0), we expect a lowutilization of transportation via rail and sea. Figure 15 confirms this expectation. Even thoughthe storage cost tends to fluctuate as we allow longer storage time at intermodal terminals(increasing ∆), the total cost tends to be a decreasing function (see Figure14).

0 1 2 3 480

90

100

Unit increase of ∆

Mod

ality

utili

zatio

nin

%

Road utilization

Road

0 1 2 3 40

4

8

Unit increase of ∆

Mod

ality

utili

zatio

nin

%

Rail and Sea utilization

RailSea

Figure 15: Scenario 2; Modality utilization as a result of unit time period increase of ∆.

40

The reason to this is that slower and cheaper modes are used more and the transportation coststends to decrease. The deviation of the storage costs may depend on the shortages that can beavoided as we increase ∆ and the relatively higher storage costs at intermodal terminals.

Scenario 3: Anticipated demand

The last sensitivity analysis regards scenario 3 where tank containers may be shipped basedon anticipation of demand. The intent is to investigate how λ effects the optimal solution. λrepresents the time required to execute the end-haulage; the last mile for delivery of the tankcontainer that is excluded from the pre-specified planning horizon.

Supply: 273, Demand: 169, Anticipated demand: 27Initial inventory: 0, Time periods: 5, Capt

ll′ m= 5000

settings Instance 1 Instance 2 Instance 3

λ 0 1 2Total cost (e) 528,028 528,152 532,868Transportation cost (e) 523,263 523,300 527,989Storage cost (e) 4765 4852 4879# Shortages 4 4 4Modality util. (% of KM) 56/29/15 56/31/13 56/29/15Road / Rail /Sea

Table 8: Operational costs and modality utilization: effect of unit time period (λ) increase.

Table 8 indicates that the total cost increases as tank containers are required to be deliveredearlier (increasing λ) to storage locations in anticipation of demand to arise.

41

6 Summary and Discussion

The company’s motivation for this project is to study whether or not there is any incentiveto further analyze and develop a mathematical model that supports tactical decisions for flowmanagement of empty tank containers. To this aim, a mixed-integer linear programming (MILP)multi-period optimization model is developed tasked to helping make tactical decisions for theempty tank container allocation problem, or more specifically, for determining the best strategyfor distributing the empty containers through the transportation network of the company. Themodel is used to evaluate the performance of and quantify the trade-offs between the differentcriteria of the empty repositioning problem.

The model is analyzed and developed step by step, and its functionality is demonstrated byconducting experiments on the network from our case study problem. However, this masterthesis has been dealing with only one part of the company’s whole distribution network thatinvolves approximately 40% of the total European market. The case study constitutes threedifferent scenarios of empty tank container allocation. Computational experiments indicates theperformance of the model, suggesting that total cost saving varies between 6.54% and 10.3%(Table 3). The reader is advised to interpret these results with precaution due to the limitationsof the case study, stated in chapter 5. An extensive sensitivity analysis demonstrates the effect ofthe model’s parameters on its performance, separately for each scenario. The main conclusionsfrom these computational experiments are discussed below.

Obviously, there might be many factors that can impact the results presented here, such asdecisions at operational level; transport and service scheduling by the 3PL company and theplanning, manufacturing and purchasing performed by its customers. Also, factors like, taxes,business rules etc. are of great importance to consider in the model. However, these factorsmostly are either out of control or are at operational level, and hence they are out of the scopeof this work. This thesis has been dealing with the decisions at tactical level, namely it advisesthe empty tank container flow management policies over different links and suggests the besttransportation modes thorough the network.

The company’s success depends on the ability to establish and integrate customized logisticsservices to its customers’ supply chains. Logistical service planning in this context is concernedwith the coordination and integration of many key business activities undertaken by a 3PLcompany, from the pick-up process of an empty tank container to its delivery at a customer sitefor loading. The demand of empty tank containers highly depends on unbalanced loaded moveswhich in turn depends on trade patterns across regions in the company’s distribution networkand the inherent nature of customers’ supply chains.

Moreover, upon the company’s request, we have developed 3 different scenarios from our model.Scenario 1 represents the generic model, which includes the basic characteristics of the emptycontainer repositioning problem, previously described in the problem definition, presented inchapter 4. Some considerable conclusion were deducted from the the sensitivity analysis inScenario 1. The computational results indicate that a detailed time discretization of the planninghorizon enhance the accuracy of the results from the model. The total cost tends to increaseas the planning horizon becomes more realistic i.e. the unit time periods approaches real-time (Table 4). On the other hand, the computational requirements of the model increasessubstantially by increasing the number of time periods, making it impossible to further improve

42

the accuracy of the model and the realism of the planning horizon (9). The reader is suggestedto interpret these results as a limitation of the model and one of the main reason why theproposed model only considers planning proposals at an tactical level. Obviously, real-timedecision at an operational level is not to be considered as an expected output from this model.

Additional computational experiments under scenario 1 demonstrate that cost improvementcan be achieved by extending the planning horizon and subsequently via enhancement of themodality utilization. The model suggests that cheaper and slower modes are utilized relativelymore in the earlier part of the planning horizon when the length of the planning horizon hasbeen increased. However, denoting a large amount of stock would result in almost only emptymoves to be carried out via road since demand can then be satisfied without long distancetransports and intermodal shifts (Table 5, Figure 10, Figure 11).

As mentioned previously, in the background section from Chapter 1, many intermodal terminalssuffer from some transportation frequency or capacity limitation. For this reason can intermodalterminals be seen as the bottleneck part of the distribution system. Intuitively, indicates thecomputational experiments that lower limitations of transportation capacities (Capt

ll′m) may

give better empty container distribution plans, see Table 6 from scenario 1.

Scenario 2 represents another possible bottleneck that may occur when the allowed storage time(∆) at an intermodal terminal is limited. During an interview with Hoyer, it was revealed thatintermodal terminals do not only suffer from transportation frequency or capacity limitations.Rather, should the storage time at intermodal terminals also be included in the model. Itwas concluded from the sensitivity analysis that extended allowed storage time at intermodalterminals results in cost savings due to enhanced modality utilization (Figure14).

The third and last extension of the generic model is reflected in Scenario 3, constituting asituation frequently faced by the company. Transport decisions for empty moves are based onnot only known customer order, but also on anticipated demand. The company is frequentlyforced to distribute empty tank containers storage facilities such as depots, cleaning stations andintermodal terminals based on anticipations of future demand to arise in the neighborhood ofthese locations. This is often a difficult task and therefore it requires the company to substituteanticipations of demand by forecasted demand. However, forecasting is out of scope of thiswork. Rather, we proposed a model that is ready to take forecasted demand as an input.Computational experiments under scenario 3 demonstrate that cost saving can be obtained byshortening the estimated time required to execute the end-haulage (λ), see, e.g., Table 8.

43

7 Final Recommendations & Future Research

The company’s motivation was to investigate the possibility of reduction in distribution costs bydetermining the best strategy for distributing the empty containers through the transportationnetwork of the company. On this basis, we have not been dealing with the operational leveleddecisions, market variability, or demand forecasting etc. The proposed model is only lookingat one of the main aspects of the distribution chain, namely the operational/distribution cost.Therefore, the current state analysis emphasizes that there are a lot of aspects that need tobe taken into account when redesigning the distribution chain. Hence, the model is partiallyevaluating a small part of the whole system that comprises a portion of the total market. So, itcan be seen as a relaxation of the real large-scaled problem. This needs to be kept in mind whilereviewing the results. But yet, the model proves that the system can be partially improved,at least in terms of distribution costs. The result from the model/scenarios show a potentialsaving of the total costs.

We are hoping that the research findings will return the company’s favors when implemented.However, considering the complexity of large operations, market variability, and the objectives ofthe various business divisions such as marketing, sales, distribution, planning and purchasing, itis very important for the company to develop a unified and rigorous structure while capturing allthe various synergies, criteria, and trade-offs involved. A crucial recommendation is, therefore,to develop the road map previously discussed in chapter 4. The road map should not onlyfocus on repositioning of empty tank containers. Rather should the planning procedure in aglobal perspective also be presented, including e.g. workforce scheduling, assignment of loadedcontainers, consideration of planning processes at both tactical and at an operational level inorder to facilitate investment decisions regarding future implementation procedures and otherimprovements at Hoyer. Further, the objectives of the various business divisions mentionedabove are also recommended to be included in the road map.

The company, wishes to know whether or not there exists incentives to further investigate anddevelop a mathematical model supporting the planning tactical decisions for flow managementof empty tank containers. The computational experiments show that the model demonstratethat cost and modality improvement can be achieved in the network. For this reason we arguethat there exist incentives for further investigation. However, based on the discussion abovewe recommend the company to first develop the road map and evaluate the models’ priority ina global perspective of the various planning procedures and the activities from other businessactivities within the firm. Based on the limitations of the case study, clearly stated in Chapter5, it seems worthwhile to further investigate the models performance when the shift from thecompany’s older TMS system to ORD has been finalized. In addition, we encourage the companyto consider the various possibilities to extend the model, stated in the end of this chapter.

The model captures many practical applications needed for tank container management in anintermodal distribution network of this topic. A variety of different types of locations areincluded in the distribution network, each for different purposes. To the best of our knowledgeno research has been carried out replicating an intermodal distribution network at the same levelas the proposed model in this work. Cleaning stations allow containers to be both stored andcleaned whereas depots only constitutes storage facilities. Train, port, and rail ship terminalsenable door-to-door transits for intermodal transports. In addition, the model also considerstransportation capacities and storage limitation at intermodal terminals. We also include the

44

frequent occurrence of transportation to be carried out based on anticipated demand ratherthan known orders. However, there are several possibilities for extending the model proposedin this study. We close this work by proposing some possible directions for future research.

• Container purchasing, short and long term leasing. Container purchasing, shortand long term leasing can be modeled to avoid shortages and support decision makersbringing tanks into and out from the system in an optimal course of action.

• Matching of tank container functionalities to the product to be loaded. Thedemand of empty tank containers is characterized by not only the type (volume) andthe condition (dirty/clean), but also by the functionalities of the tank container. In apractical point of view, the tank containers functionalities are matched to the products tobe shipped. Adding these dimensions to the model could, for instance, lead to a reducednumber of tank containers to be shipped to cleaning stations. Cleaning processes are notalways necessary. In the situation where the previous product is the same as the futureproduct to be loaded, cleaning processes may be neglected.

• Regulations for transportation of hazardous goods. Transportation of hazardousgoods is a common practice for any logistic service provider company. To include regula-tions for these sorts of shipments in the model would surely add significant value to thestake holders.

• Cost and capacity dependency of the tank containers dimensions. Cost andcapacity parameters included in the model depend on the tank containers dimensions ina real-life perspective. For instance, the quoted transportation price for trains and vesselsdepends on the length of the tank container. To include such dependencies would alsomake the model more realistic.

• Integrate loaded assignment decisions. To integrate loaded assignment decisionsinto the proposed model is another possible extension. The demand of empty movementsarises from unbalanced loaded movements. It is therefore natural to try to integratethese two types of movement into the same allocation model. However, the companyunder consideration argues that loaded moves depends on customer orders and includingsuch a functionality would not be necessary i.e. the company would never reconsiderloaded moves, rather are they acting on orders. Future research is suggested to verify thisstatement.

• Include the uncertainty of the relevant parameters. The proposed model has beendeveloped under the assumption that the information for decision makers is known forfuture periods i.e. the models are deterministic. However, in this application domain, itis widely known that the variability of the demand and supply have significant impacton the performance of the distribution system. The availability of empty tank containersdepends on previous loaded moves, whereas the demand of empty tank containers dependon customers. One should note that the demand and supply of empty tank containerscannot be derived from loaded moves only. Other factors should also be taken into account,such as repairs of empty tank containers and leasing that occurs in the situation whenadditional empty tank containers are need to fulfill the demand. Another factor is lossesof current customers or gains of a new customer. Further, not only supply and demandhave an uncertain nature. Transit times are generally not constant. This variation maybe identified by weather conditions, congestion or other random events.

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• Time scheduling. The times of departure and arrival, especially via rail and sea, dependon a certain time window or some time schedule. Modeling time dependency would surelymake the model more realistic, but also more complex. For this reason, time windows areoften neglected. To the best of our knowledge, there are only a few research that considertime windows while modeling this particular problem.

• Computational limitations. One drawback of the proposed model may be the compu-tational limitations addressed in the sensitivity analysis. In order to solve the problem forlonger planning horizons a certain time discretization will be needed, resulting in a lossof information. One way of enhancing the computational performance is to use heuris-tic algorithms. However, heuristic methods are unable to find all possible solutions andprovides generally an approximated solution to the problem.

• Analytical hierarchy process (AHP). Finally, our model can be improved by addingseveral criteria, such as customer power, credit performance, and distributor reputation,profit and transit time. Generally, when the objective function have multiple criteria ofdifferent importance or when it consists of conflicting goals, the AHP-method is highlyrecommended. This method will give the possibility of having all goals and criteria in themodel altogether in a meaningful way i.e. this method incorporate multiple preferencesfrom the decision makers. The decision makers does not need to provide a numerical judg-ment. Instead are they asked to do a pairwise comparison of the criteria. Subsequently,normalized weights are calculated for each criterion.

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Appendix A

Table 9: Countries and regions included in Hoyer’s distribution network.

Country Region 1 Regioin 2 Region 3 Region 4AustriaBelgiumBulgariaSwitzerlandCzech RepublicGermany EastDenmark North West SouthSpain Central North-East North-WestFinland North SouthFrance North-West South-East VenissieuxGreat Britain(England) North-East North-West SouthGreat Britain(Scotland)Ireland North SouthItaly Central North-East North-West SouthNetherlandsNorwayPolandPortugal North SouthRussiaSweden North East West SouthSloveniaTurkeyBaltics

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