Supply chain design and multilevel planning—An industrial case

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Computers and Chemical Engineering 32 (2008) 2643–2663

Supply chain design and multilevel planning—An industrial case

Rui Sousa a, Nilay Shah a,∗, Lazaros G. Papageorgiou b

a Centre for Process Systems Engineering, Imperial College London, London SW7 2AZ, UKb Centre for Process Systems Engineering, Department of Chemical Engineering, University College London (UCL),

Torrington Place, London WCE 7JE, UK

Received 21 May 2007; received in revised form 17 September 2007; accepted 17 September 2007Available online 21 September 2007

bstract

In this paper we address a case study, inspired by a real agrochemicals supply chain, with two main objectives, structured in two stages. In the firsttage we redesign the global supply chain network and optimise the production and distribution plan considering a time horizon of 1 year, providingdecision support tool for long term investments and strategies. The output decisions from the first stage, mainly the supply chain configuration

nd allocation decisions, are the input parameters for the second stage where a short term operational model is used to test the accuracy of theerived design and plan. The outputs of this stage are detailed production and distribution plans and an assessment of the customer service level.

At the operational level, failure to meet on time the demand fulfilment targets established at the planning stage is usually caused by allocationf too many products/customers to the same resource in the first stage, especially to those surrounding the system bottlenecks. This introduces
dle periods in the planning of the bottleneck resources, preventing the whole system from operating at its maximum capacity. An analytical
ethodology was developed to use the information gathered in the second step to improve the supply chain design and plan by enforcing a moreistributed allocation of products/customers to the available resources in each time period.

2007 Elsevier Ltd. All rights reserved.

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eywords: Supply chain planning; Multi-level integration; Enterprise optimisa

. Introduction

In Supply chain optimisation “. . . it is often difficult to effectarge improvements simply by changing logistics and transac-ional processes; fundamental changes at the process and plantevel and at the interfaces between the different constituents ofhe value-chain from product discovery to manufacture and dis-ribution are often required” (Shah, 2005). Furthermore, “. . .[theupply chain concept] implies that a system view is taken ratherhan a functional or a hierarchical one” (Papageorgiou, 2006).xperience shows that benefits are achieved by adopting holisticpproaches that include and integrate all the participants in theupply chain rather than addressing each of them separately.

Many typical supply chains in the pharmaceutical and agro-hemical industries have production that spans several countries
nd product markets that are global. This opens the possibilityo explore differences in (Shah, 2005):
∗ Corresponding author. Tel.: +44 20 7594 6621; fax: +44 20 7594 6606.E-mail address: [email protected] (N. Shah).

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098-1354/$ – see front matter © 2007 Elsevier Ltd. All rights reserved.oi:10.1016/j.compchemeng.2007.09.005

regional production and transportation costs;tax rates over income and duty structure;exchange rate variation;manufacturing and network complexity and efficiency (e.g.single vs. multi sourcing, distribution through several possiblechannels);prices paid by final customers.

The product portfolio of these companies is usually very largeue to all the possible formulations (excipient, concentration,ixture of several AI’s) and packaging (liquid, powder, tablets,

apsules etc) available to process the AI, which is translated intohigh number of SKU’s. Most of the manufacturing consists ofatch processes in multipurpose assets, resulting in the need foroth campaign planning at individual sites and global networkoordination. For this reason, it is also difficult, if not impossible,o separate the supply chains of individual product families, as
hese always share common resources.
An Enterprise Wide Optimisation (EWO) approachGrossmann (2005)) applied to one of these companies results, ineneral, in a large scale mixed integer linear programming model

mailto:[email protected]

dx.doi.org/10.1016/j.compchemeng.2007.09.005

2644 R. Sousa et al. / Computers and Chemical

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MILP) that is hard to solve by direct application of commercialolvers (Fig. 1). Hierarchical planning using aggregated modelss always a possibility, however as pointed out by Grossmann2005) this frequently results in an optimistic plan which is hardo accomplish at the scheduling level. The situation becomesven more complex if we take into account the fragmented naturef the orders placed by customers. These tend to be large in num-er and individually low in volume, as in some cases customersre not willing to keep significant stocks of the final product,aking supply chain responsiveness a key issue on top of theultilevel planning integration difficulties. This leads to a large

umber of opportunities for supply-chain improvement.In this work we aim to address the multilevel planning inte-

ration problem relevant to pharmaceutical and agrochemicalupply chains, characterised by the management of a large prod-ct portfolio and an extensive, widely distributed manufacturingetwork over long time horizons (Section 3). This is referred toy several authors (e.g. Grossmann, 2005; Shah, 2005) as onemportant and still open issue for which little work has beenublished.

. Literature review

Hierarchical solution approaches use aggregated models orther relaxed versions of the original problem, with a lower levelf detail (information) in order to reduce the size of the modeleing solved in each step. Multilevel planning approaches areimilar processes where the hierarchy is generally established inerms of time, which is particularly adequate when accurate datas not available for the later time periods of the horizon. However,n optimum solution provided by an aggregated model it is notlways the best (or even feasible) at a more detailed operationalevel. A major challenge in complex multisite problems is toevelop planning approaches that are consistent with detailedroduction scheduling at each site and distribution across sites.

It is therefore necessary to develop aggregated models thatrovide good plans by themselves, balancing operational costsnd setting realistic targets for each node in the supply chaint the scheduling level without reducing the levels of resourcesage.

Shah (1998) and more recently Grossmann (2005) identifyultilevel planning integration as one of the challenges left in

he upper levels of multiscale process system engineering, forhich no satisfactory general approach has been purposed.
There is a relevant body of literature addressing planning
cheduling integration in single manufacturing sites or smallroups of manufacturing facilities but there is little work withinhe global supply chain scope. This is partially explained by

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Engineering 32 (2008) 2643–2663

he fact that supply chain planning problems address strate-ic decisions, such as product and customer allocation, designnd investment decisions, aggregate inventory profiles, etc, thatffect the system over a long term scale, so detailed short termlanning of individual sites is not relevant as detailed operationalata (e.g. orders) may not be available.

However, it is our belief that there are cases where supplyhain design and strategic planning should not be performedeparately from short term scheduling, or the adopted solutionay prove inefficient at the operational level. Section 3 presentscase study addressing redesign and strategic planning of an

grochemicals supply chain, characterised by an annual seasonalemand cycle, with predictable, stable long- run demand levels.

In our case study, we investigate the feasibility of the derivedlan at the operational level and whether the manufacturingapacity established at the planning level is adequate.

.1. Relevant factors in multilevel integration

The makespans for activities at the planning level are usu-lly predicted to be shorter than at the scheduling level wheredle times appear. Raaymakers and Fransoo (2000) identify theeasons for this:

workload (relation between resource utilisation rate and num-ber of parallel lines of the same resource);number of parallel lines per resource type;number of processing steps in the manufacturing path of eachproduct;overlap of processing steps.

In Raaymakers, Bertrand, and Fransoo (2000), the authorsssess the performance of “workload rules” used to estimaterder acceptance and due dates in a pharmaceutical, multipur-ose, plant with a hierarchical planning methodology. At thepper level, the site planner estimate the delivery date of orders tonal customers and workload allocated to each of the three pro-uction departments. Generally, customer orders are known overshorter horizon than the throughput times of each product. Due

o the lack of accurate information and need for quick responseso customers, the first level in the hierarchy is an aggregate,mpirical plan, elaborated using current orders, demand fore-asts, current inventory levels and empirical workload limits forach of the three manufacturing departments using informationathered in the past experiences. This plan is then implementedt a more detailed level and adjustments are made to the originallan to make both of them consistent. Each department then hasscheduler responsible for the translation of the upper level plan

or his area into a detailed schedule. If the set of jobs allocated isnfeasible for the given time horizon, then he negotiates changesith the site planners. The authors registered a very significantisparity between the number of orders allocated at the planningevel and the orders effectively accepted for manufacture.

Raaymakers et al. develop a methodology to provide the phar-aceutical company with a tool to generate an aggregate planith a higher realization rate at the operational level. The general

dea is to develop a formula to estimate the makespan of each set

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f jobs (orders) and then use the value for long-term planningevel (Raaymakers, Bertrand, & Fransoo, 2001). The authorstart by establishing a lower bound (LB) for the makespan ofach job set, given by the processing step duration taking place inhe resource with the highest quotient between the workload andumber of parallel lines (assigned as the bottleneck). The rela-ive deviation between the actual makespan (Cmax) and the loweround is designated as the “Interaction Margin” (IM) betweenobs (Raaymakers & Fransoo, 2000):IM = Cmax−LB

LB The IM isssumed to be a function of a set of parameters related to theesource configuration and the aggregate properties of the set ofobs being executed; hence if enough information is gathered onhe influence of these factors in the IM, it is possible to build aormula, by regression analysis, to estimate the makespan of aiven set of jobs performed in a particular plant.

In Raaymakers and Fransoo (2000) a factorial set of tests iset up to investigate the influence on the IM of the number ofarallel lines per resource, number of manufacturing steps perob and overlap of processing steps, both in terms of the averagealue and standard deviation. The main results obtained were:

The average number of parallel resources reduces the IM asit provides greater flexibility. The standard deviation of thisparameter has only a slight influence in the IM.The average number of processing steps significantly affectsthe IM, but job sets with the same average number but differentdistributions were found to perform at the same level.The IM increases with higher standard deviations of the pro-cessing times within the job set.Processing step overlapping influences the IM in two oppo-site ways: on the one hand higher overlapping increases thecomplexity of the manufacturing process and hence the inter-action between jobs, on the other hand, the total processingtime of each job decreases for higher overlapping levels.For lower values of the average workload per resource, the IMlevels are always low; for high values of this parameter, theresulting IM tends to increase although it may also assumelow values.

A key contribution of this work is the observation that if aeasible schedule is found with no idle time on the bottleneckesources, the total makespan for the job set will be equal to theower bound or, in other words, if conditions are created thatllow the bottleneck resources to operate at full capacity for asong as possible, the upper limit on the overall production ratesill be very similar at both the planning and scheduling levelsnd equal to the physical capacity of these resources.

The authors consider all the processing steps as being no-waitperations as the intermediate products are unstable. For caseshere intermediate storage is possible, this will introduce extraexibility in the system.

.2. Rolling horizon methods

Wilkinson, Shah, and Pantelides (1995) introduce an aggre-ated procedure to tackle large MILP scheduling models derivedrom the application of the Resource Task Network (RTN)

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Engineering 32 (2008) 2643–2663 2645

pproach (Pantelides, 1994). The time horizon is divided intonumber of Aggregated Time Periods (ATP’s) each containingoriginal time periods. The formulation is derived by applyingformal aggregation operator to the constraints of the originaletailed RTN formulation for each ATP.

Bassett et al. (1996) develop an aggregated algorithm for sin-le site scheduling models based on the RTN approach. An upperevel, multi-period, planning problem is obtained by summingariables and constraints over time periods and replacing theespective sums by new (aggregate) variables. The feasibility ofhe upper level plan is then tested with a lower level scheduling

odel, run for every time period of the first level. If any of theubproblems set by the first level model proves to be infeasiblet the scheduling level, then the corresponding time period isodelled in detail at the aggregate level. Dimitriadis, Shah, andantelides (1997) use this principle and the aggregated formu-

ation described in Wilkinson et al. (1995) to develop a rollingorizon algorithm applied to the RTN approach. This is a single-evel, iterative, heuristic, approach that at each iteration solvesmodel with a much lower number of variables than the orig-

nal problem, where part of the time horizon is progressivelyodelled in detail and the remainder approximately.There is no guarantee of feasibility of the detailed models

ssociated with part of the horizon. The authors identify twoauses for infeasibility:

Inability to fulfil the necessary production requirements (dueto fixing some variables estimated in previous iterations).Incompatibilities at the border of detailed and aggregated timeperiods.

The first effect is avoided by considering soft orders insteadf hard ones; the second is solved by extending the detailed timelocks in order to accommodate the longest task if this startedt the last time interval of the detailed time block.

As in Wilkinson et al. (1995), the accuracy and result qualityf the Rolling Horizon method also increases with number ofTP’s, however this also means solving a larger sized subprob-

em in each iteration.Here, we described the rolling horizon method applied to the

TN approach, however the concept is broader than this and haseen applied to derive other solution algorithms, e.g. in mul-istage stochastic modelling (Balasubramanian & Grossmann,004; Guillen, Badell, Espuna, & Puigjaner, 2006).

.3. Sequential approaches in multilevel planning

We have already referred to the popularity of hierarchi-al methodologies either as global approaches to large supplyhain problems that span over long time horizons (sequentialpproaches) or in the solution algorithm of the large MILP’sesulting from single stage approaches for these problems.he general methodology consists of running an upper level
ggregated model to estimate some long-term strategic decisionariables that are then fixed for a lower level detailed model withreduced number of variables or even decomposable into several
ndependent sub-problems. The whole process involves, to a cer-

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ain extent, some multilevel planning integration to be successfuln order to obtain feasible lower level models and a reducedumber of iterations, “In general, the effectiveness of decompo-ition approaches depends strongly on the accuracy with whichhe master problem approximates the original. The tighter thiselaxation the fewer iterations between master problem and sub-roblem will be required to obtain the optimal solution to theriginal problem” (Papageorgiou & Pantelides, 1996b).

Papageorgiou and Pantelides (1996a) develop a single-evel model for simultaneous campaign planning and detailedcheduling of batch/semicontinuous plants by means of a State-ask network (STN) (Kondili, Pantelides, Sargent, 1993; Shah,antelides, & Sargent, 1993). Within each campaign, a cyclicchedule is considered to make the human resources manage-ent easier. There are no fixed demand levels to fulfil, instead

t is assumed that there is a market for all the production ofhe plant, independently of its composition. Two integral frame-orks are built, campaign planning and detailed scheduling, with

he latter embedded in the former one. The upper level frame-ork addresses the total number of campaigns along the timeorizon, number of cycles within each campaign (i.e. campaignuration), material balances at the start and end of each campaignnd external events, such as receipt or shipment of materials, thatre only allowed to take place between campaigns. The intra-ampaign scheduling framework follows the STN formulationor periodic scheduling (Shah et al., 1993), with inclusion ofrequency-dependent cleaning constraints. The model requires aigorous decomposition procedure (Papageorgiou & Pantelides,996b) for its solution.

Zhu and Majozi (2001) proposed a two level decomposi-ion strategy for multipurpose batch plants. In the upper level,he planning model is solved for the optimal allocation of raw

aterials to individual processes, and at the lower level, the rawaterial targets obtained at the planning level are incorporated

nto the models for individual processes and then solved inde-endently. If the scheduling model fails to meet the targets set byhe planning model, it is revised with the shortfalls informationathered in the scheduling stage. In extreme cases, dependingn the system, these could lead to very low resource utilisations.

Erdirik-Dogan and Grossmann (2006) describe a simulta-eous planning and scheduling with a hierarchical, iterative,pproach similar to that of Papageorgiou and Pantelides (1996b);owever this time applied to single-stage multiproduct plants,sing a continuous time description. The upper level model,n aggregated version of the original model, is concerned withetermining the products to be produced in each week, pro-uction levels and inventory profiles. This is a relaxation ofhe original model, where the detailed sequencing of tasks isgnored, so its solution will be an upper bound to the originalroblem. At the lower level, the original model has a reducedariable space as the decision variables concerning the prod-cts not chosen to be produced are set to zero. The solutionf the lower level subproblem constitutes a lower bound. If the
ifference between the upper and lower bounds is within theermination criteria, the algorithm stops, otherwise integer andogic cuts are added to the upper level plan to eliminate therevious set of decision variable values and the cycle is repeated.
Engineering 32 (2008) 2643–2663

Most of the sequential approaches in the literature do not usehe information gathered at the lower level to directly improvehe upper level of planning. The iterative procedure leads ton optimum solution in a finite number of steps as the possibleombinations of values for the first stage decisions are also finite;owever large problems may present a very large number ofossible combinations.

. Problem statement

Product X (PX) is a chemical compound used as an activengredient (AI) in several commercial herbicides. PY is chem-cally similar to PX, and its uses are nearly identical to thoseroposed for PX. They are produced by a multinational agro-hemicals company.

The most basic products of these families of herbicides haveeen in the market for many years. They are mature productshat have already passed the peak demand in their life cycle andace ever increasing competition from more sophisticated andffective products, hence their added value is now very low. Onhe other hand they remain attractive due to their low costs, son order to keep being competitive they should arrive to the finalustomer at a very low price.

A factor that has been putting enormous pressure on the lowost strategy for these products is the price of raw materials.he manufacturing methods are robust and very well establishednd do not leave any margin for improvement for cost cuttingurposes, so the product management team turned to supplyhain optimisation as a way of controlling and even reducingosts while improving service levels.

.1. Project description

The product management team distinguishes two subsystemsithin the global supply chain, linked by the AI production site,hich are the basis to define the modelling approach:

US network – in this region, the team is responsible forthe operation in all the stages in the chain, from AI pro-duction in the US factory to distribution to small groups ofindividual final customers. This involves the management ofa network of public warehouses and bulk liquid terminalsscattered throughout the regions where final customers con-centrate. All the AI and is produced in the US factory, in theUS. The produced AI may then follow one of three paths:• Shipment to formulation sites around the world, either

directly or through an export terminal.• Shipment to worldwide and US AI customers.• Formulation into final products in the US factory formula-

tion lines.Bulk liquid products are shipped to US customers

directly from the US factory or through a network of bulkliquid terminals. Packed products reach the domestic con-
sumers by one of two existing channels with the possibilityof setting up a third one:
• Direct shipment from the US factory.• Through a network of public warehouses.

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• Shipment in bulk to local packaging sites. From here thepacked products maybe delivered directly to the final cus-tomers or through the network of public warehouses.

Worldwide formulation network – the company possessesseveral formulation sites worldwide that process the AI’sreceived from the US factory into final products through afew simple manufacturing steps. From here, the final prod-ucts are distributed to customers worldwide, which may alsobe supplied directly from the AI manufacturing/formulationsite in the US. Each country is viewed as an individualcustomer.

The global objective of the project is to redesign the world-ide formulation and US distribution networks while providingtemplate plan for the company’s annual activity cycle (as her-icides are products that follow a seasonal demand profile). Inhe US, the main decisions are which storage facilities and localackaging sites to establish in the country and how to distributeroduction through the different manufacturing resources. Forhe rest of the world the main decisions address production
llocation through the several sites and main product flows tonal market areas. The company is receptive to solutions whereustomers in a given region of the world are supplied fromormulation sites in other areas.
Fig. 2. Supply cha

Engineering 32 (2008) 2643–2663 2647

The objective is reformulated as:

Redesign and assess the worldwide formulation and USdistribution networks and provide a template plan for the com-pany’s annual activity cycle that sets feasible objectives atthe scheduling level without reducing production and salesvolume and keeping the inventory at the possible minimumlevels.

A two-stage approach is used.

.1.1. First stageIn the first stage we develop a high level planning model with a

yclic time horizon of one year (discretised into twelve months),ncluding all the nodes in the US and worldwide networks asescribed above (Fig. 2). The model has an aggregate view ofhe manufacturing resources. The outputs are:

Design decisions – which manufacturing and storage facilitiesto open and their locations.Strategic decisions – production allocation to the manufac-
turing resources and in the case of the US network, allocationof customers to distribution centres and exports plan from theAI manufacturing site to the rest of the world, predicted saleslevels at each customer/customer region.
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Operational decisions – product campaign map for each man-ufacturing site for the whole year, stock profiles in eachlocation with storage facilities.

.1.2. Second stageIn the second stage, a detailed operational model is built for

ach month, with a time resolution of one day to assess theeasibility of the upper level plan at the operational level. Theesign and strategic decisions determined in the first stage thatstablish the supply chain configuration work as sets of inputarameters in the second stage model. The US manufacturingites are described in detail and individual orders are considered.

The outputs are a detailed production and distribution planor the US network, while accomplishing the export plan estab-ished in the first level. The second stage outputs also providenformation on how to improve the accuracy of the upper levellanning.

In this article we focus on the second stage of the project.

. Mathematical formulation

.1. First stage model—medium term planning

ndexessites – all kinds of nodes in the SC (except customers):formulation, packaging or storage;products – all kinds of materials in the SC: AI, formu-lated, packaged;customers – in the US customer zones are consideredindividually; outside the US each country is consideredas a single customer;time periods (12 × 1 month);manufacturing resource types;storage types (bulk liquid 1, bulk liquid 2, packed).

The same product composition may have different identitiesccording to its packaging. Manufacturing and storage facilitiesn the same location in the US network are considered to beifferent sites (i.e. different values of s are assigned to each ofhem).

etsW set of worldwide formulation sites (except US);US set of packaging sites in the US;m set of manufacturing sites (S − SI);I set of bulk terminals and public warehouses in the US;1 US factory;c set of sites that can supply customer c;f set of site (s, s′) combinations with allowed, unidirec-

tional, flows between them;W set of customers outside the US (worldwide);US set of customers in the US;i set of intermediate products that cannot be sold as final

products;s set of products that can be manufactured in site

s ∈ (S − SI);g set of products that require storage type g;

SMM

Engineering 32 (2008) 2643–2663

s set of available manufacturing resources in sites ∈ (S − SI);

p set of resources used to manufacture product p.

ecision (binary 0/1) variablespst equal to 1 if product p is manufactured in site s in time

period t, 0 otherwise;Ss equal to 1 if site s is chosen to be open, 0 otherwise;Cpsct equal to 1 if product p to customer c is supplied from

site s in time period t, 0 otherwise;

perational (continuous, positive) variablesnet profit value (NPV);

Rpst amount of product p produced in site s in time periodt;

Vpst inventory of product p in site s ∈ SI in time period t;pss′t amount of product p transferred from site s to site s′ in

time period t;Cpsct amount of product p shipped from site s to customer c

in time period t;pct unfulfilled demand of product p at costumer c in time

period t.

Parameters:

ostsTss′/CTCsc transportation costs between site s and

site/customer s′/c;Pps production costs of product p in site s;Ips Inventory handling costs of product p in site s;Upc unfulfilled demand costs;Ss cost of opening site s.

anufacturingAsrt available resource r capacity in site s in time period t;Dpr manufacturing requirements of product p on resource

r;Asg storage capacity of type g in location s;OTps changeover time – cleaning period before starting pro-

duction of product p in site s.

roductCpp′ units of product p′ required per unit of product p (com-

position);Ypr accumulated process yield, per resource;YYp global process yield;Fpr production rate correction factor.

arketingpct demand forecasts of product p in customer c;pc market value of final products (customer products);Sps internal transfer price factor of product p produced in

site s;Rs tax rates at location s.

calarsax maximum production rates;in minimum production rates.

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The model considers that each proposed location for productormulation/packaging/storage has the same probability (open-ng cost) to be chosen, independently of whether it is or notlready in operation, in order to prevent the natural bias towardshe actual configuration. The allocation of products to sites isllowed to change over the entire time horizon, although a for-ulation with fixed allocation throughout the entire period may

lso be used.

.1.1. Design constraintsConstraint (1) limits the manufactured amounts of each prod-

ct in the sites where it has been allocated. Max is an arbitrarilyhosen large number and Min is a minimum production levelhat has to be accomplished if the site is chosen to manufac-ure product p. If the product is not allocated to a certain site, Xps is 0 and manufacture does not take place. Each products not assigned to a site unless the site is open (2). Constraints3.1) and (3.2) state that the resource utilisation at a given siteannot exceed the available capacity of each resource as wells that manufacture can only take place if the site is open. Noingle sourcing policy is required by the company; however theodel may be easily modified to include this feature for both

roduction and customer allocation.

in Xpst ≤ PRpst ≤ Max Xpst ∀p, t, s ∈ Sm (1)

pst ≤ XSs ∀p, s ∈ Sm (2)

∑p ∈ Ps∩Rp

MDprPRpstPFpr

PYpr

≤ MAsrt XSs−∑

p ∈ Rp

(XpsCOTps) ∀t, s ∈ (S − Si), r ∈ Rs

(3.1)

n alternative approach is to allow the model to decide when tohut down a certain resource for maintenance. In order to do so,wo new parameters and a set of binary variables are defined:Mrss the nominal capacity of each manufacturing resource, MRrs

he capacity reduction during maintenance periods and XMrst ishe equal to 1 if maintenance of resource r on site s takes placeuring period t;

∑p ∈ Ps∩Rs

MDprPRpstPFpr

PYpr

≤ (MsrXSs − MRrsXMrst)

−∑

p ∈ Pm

(XpsCOTps) ∀t, s ∈ (S − SI ), r ∈ Rs (3.2)

he model considers the occurrence of two maintenance peri-ds per year on each resource which will only take place if the
orresponding site is open (constraint (3.3)):
t

XMrts = 2XSs ∀s ∈ (S − SI ), r ∈ Rs (3.3)

Engineering 32 (2008) 2643–2663 2649

.1.2. Mass balances (flow and inventory constraints)Constraints (4)–(7) express the mass balances at the main site,

he US factory ((4) and (5)) and the packing sites in the US ((6)nd (7)). Eqs. (4) and (6) state that the raw material flow to sitesas to be equal to the manufacturing requirements since, at thelanning level, it is assumed that manufacturing sites in the USannot hold any inventory. Constraints (5) and (7) state that allhe production has to flow to other locations: storage facilities,

anufacturing sites or final customers.

US factory

Fp,s,s,t =∑

p′ ∈ Ps

(PRp′,s,tPCp′p

PYYp′

)∀p, s ∈ S1, t (4)

∑s′

Fp,s,s′,t +∑

c

FCp,s,c,t = PRp,s,t ∀p ∈ Ps, s ∈ S1, t (5)

Packing sites in the US

Fp,s′,s,t =∑

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(PRp′stPCp′p

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(6)

∑s′ ∈ Si

Fpss′t +∑

c ∈ CUS

FCpsct = PRpst ∀s ∈ SUS, p ∈ Ps, t (7)

Constraint (8) establishes that the incoming flows of raw mate-rials to formulation sites in a certain time period have to beused in the production of final/intermediate products on thosesites in the same time period. Constraint (9) is the inventorybalance for formulation sites.

Storage sites in the US are described by relations (10) and(11). The first one establishes the upper limit on the amount ofproduct that can be stored by each storage category; the secondone expresses a simple inventory balance.

Inventory constraints link all the time periods in the wholehorizon. As referred to the introduction, the goal of this modelis to recreate and optimize the annual cycle of the company’sactivity, starting in T1 and finishing in T12. In order to expressthis, the time set in the MILP model is defined so that thefollowing relations are enforced:

IVp,s,t−1 = IVp,s,t′ ∀p, s, t = T1, t′ = T12,

IVp,s,t′+1 = IVp,s,t ∀p, s, t = T1, t′ = T12

i.e. a sustainable supply chain is established and inventoriesare not drawn down over the annual cycle.

=∑

p′ ∈ Ps

PRp′stPCp′pPYYp′

∀s ∈ SW, s′′ ∈ S1, p ∈ (P − Ps), t

(8)

2 mical

4

ud

s

X

4

tp

U

4

tisc

or

F

P

4

i


IVpst = IVps,t−1 + PRpst +∑

s′ ∈ SW :s′ /= s

(Fps′st − Fpss′t)

−∑

c ∈ CW

FCpsct −∑

p′ ∈ Ps

PRp′stPCp′pPYYp′

∀s ∈ SW, Ps, t

(9)

Storage sites in the US∑p ∈ PG

IVpst ≤ IAsgXSs ∀s ∈ SI, g, t (10)

IVpst = IVps,t−1 + Fp,s1,s,t +∑

s′ ∈ SUS

Fps′st

+∑s′ ∈ Si

(Fps′st − Fpss′t) −∑

c ∈ CUS

FCpsct ∀s ∈ SI, Ps, t

(11)

.1.3. Sales constraintsConstraint (12) establishes an upper limit on the total prod-

ct flow to each final customer/country, equal to the forecastedemand. Constraint (13) imposes a minimum production rate:∑∈ Sc

FCpsct ≤ Dpct ∀p, c, t (12)

Cpsct0.2Dpct ≤ FCpsct ≤ XCpsctDpct ∀p, c, t (13)

.1.4. Unfulfilled demandUnfulfilled demand is calculated as the difference between

he demand forecasts and the total predicted sales (i.e. finalroducts shipped to customers):

pct = Dpct −∑

s

FCpsct ∀p, c, t (14)

.1.5. Forbidden flows/productionEq. (15.1) states that each site cannot supply other loca-

ions with products that it does not produce/store. Eq. (15.2)s not strictly necessary for the model however it reinforces con-traint (15.1) and reduces the number of variables that must bealculated.

φs ∈ S1 = TRs

⎡⎣ ∑

p,t,c ∈ CUS

FCpsct(Vpc − CTCsc) +p,t

+∑

p,t,c ∈ CW

FCpsctVSps +∑

p,t,s′ ∈ SW

Fp

φs ∈ SW = TRs

⎡⎣ ∑

p,t,c ∈ CW

FCpsctVSps +∑

p,t,s′ ∈

−∑

p,t,s′ ∈ SW

Fps′st(VSps′ + CTs′

Engineering 32 (2008) 2643–2663

The degree of design flexibility decreases with the numberf forbidden flow constraints, i.e. the final solution will be moreestricted to a pre-defined configuration.

pss′t = 0 ∀s, s′, p ∈ (P − Ps′ ), t (15.1)

Rpst = 0 ∀s ∈ (S − SI ), p ∈ (P − Ps1), t (15.2)

.1.6. Objective functionAs mentioned before, the objective of the model is the max-

misation of the Net Profit Value (NPV) of the whole network.

Revenues

Π =∑psct

(FCpsctVpc) (16.1)

Production costs

KP =∑

p,t,s ∈ (S−SI )

(PRpstCPps) (16.2)

Inventory costs

KI =∑

p,t,s ∈ (SI∪SW)

(IVpstCIps) (16.3)

Transportation costs

KT =∑pss′t

(FCpss′tCTss′ ) +∑psct

(FCpsctCTCsc) (16.4)

Investment costs

KY =∑

s ∈ (SI∪SW)

XSsCSs (16.5)

Gross profit

Θ =∏

−KP − KI − KT − KY

Tax costsThe tax cost calculation for each location expresses the inher-

ent relationships between the several nodes.Tax costs at US factory

∑,s′ ∈ SI

Fp,s,s′,t1.3VSps +∑

p,t,s′ ∈ SUS

Fp,s,s′,t1.09VSps

,s,s′,tVSps −∑

t,p ∈ PS

PRpstCPps

⎤⎦ (16.5)

Tax costs at formulation sites worldwide

∑
SW
Fpss′tVSps −p,t,s′ ∈ S1

Fp,s′,s,t(VSp,s′ + CTs′,s)

s) −∑

t,p ∈ Ps

PRpstCPps

⎤⎦ (16.6)

mical

VSp

S1

Fp

CTs′

ps) −

4

au

Z

4

4

tUmfipm

ftsnoshmma

•

•

•

•••

•

••

4

i


Tax costs at packing sites in the US

φs ∈ SUS=TRs

⎡⎣ ∑

p,t,c ∈ CUS

FCpsct(Vpc − CTCcs) +∑

p,t,s′ ∈ SI

Fpss′t

Tax costs at storage locations in the US

φs ∈ SUS = TRs

⎡⎣ ∑

p,t,c ∈ CUS

FCpsct(Vpc − CTCcs) +∑

p,t,s′ ∈ SI,s′′ ∈

−∑

p,t,s′ ∈ SI,s′′ ∈ S1

Fps′st(1.3VSp,s′′ + CTs′′,s′ +

Tax costs at the company hubs

φhub = TRhub

⎡⎣ ∑

p,t,s ∈ (S1∪SW),c ∈ CW

FCpsct(Vpc − CTCcs − VS

Φ =∑s ∈ S1

φS1 +∑

s ∈ SW

φSW +∑

s ∈ SUS

φSUS +∑s ∈ SI

φSI +∑hub

φhub

(16.10)

.1.7. Net profit valueThe terms in the objective function (OF) are the gross profit

nd tax costs (NPV). A penalty term is added to account fornfulfilled demand.

= Θ − Φ −∑pct

UpctCUpc (17)

.2. Second stage model—operational scheduling

.2.1. Model features and assumptionsThe second stage model is similar to the one developed in

he first stage; however, at this point we aim to describe theS network in greater detail. We now distinguish the differentanufacturing lines for each resource at each site and use aner time resolution. This allows the derivation of a detailedroduction and distribution plan for the US network in eachonth.Information about product flows between the US factory and

ormulation sites and customers worldwide is transferred fromhe first stage model through a new set of parameters. The secondtage model has an aggregated view of these flows, i.e. there is
o detailed plan for exports as long as the total flow at the endf the time horizon is equal to what was determined in the firsttage for the same month (orders which are soft in time andard in quantity). As for the US network, customer orders areodelled as soft in time and amount in order to guarantee theodel feasibility (see Section 2.2). The following features and
ssumptions are part of the second stage model:

fmb

Iio

Engineering 32 (2008) 2643–2663 2651

s −∑

p,t,s′ ∈ S1

Fp,s′,s,t(1.09VSp,s′ + CTs′,s) −∑

t,p ∈ Ps

PRpstCPps

⎤⎦

(16.7)

ss′t(1.3VSps′′ + CTs′′,s′ ) −∑

pt,s′ ∈ S1

Fp,s′,s,t(1.3VSp,s′ + CTs′,s)

s) −∑

t,p ∈ Ps

IVpstCIps

⎤⎦ (16.8)

KYhub

⎤⎦ (16.9)

Consideration of transportation times between the nodes ofthe supply chain.Bulk liquid product transportation lot sizes should be multi-ples of 25 t, with −12.5 t of tolerance (i.e. each transportationvehicle has to be minimum 50% full).Bulk liquid product customers in the US are divided intogroups (by geographical location) for bulk shipments plan-ning purposes.Inclusion of changeover operations.Existence of an export terminal at the US factory.The total of export flows to worldwide locations (either man-ufacturing sites or customers) has to be equal to the valuesdetermined in the first stage model for the same time periodunder consideration in the second stage model.Upper limits on demand levels by US customers are set tothe same value as the fulfilled demand, distributed through adiscrete number of orders. These orders are soft in time andquantity.No upper limit on resources for transportation tasks.Opening and closing inventories in each storage locationenforced to the same values as determined by the first stagemodel.

.2.2. FormulationThe short term scheduling model uses the same sets of

ndexes, parameters and variables as the design stage model. Aew new elements, listed below, are now introduced to allowodelling of individual orders and transfer of information

etween the first and second level of planning.

ndexparallel production lines of the same resource type;order identification index;

2 mical Engineering 32 (2008) 2643–2663

ljk

SI

C

PM

α

B

TLD

I

I

F

F

XX

X

DX

X

X

nffi(ttstafl

4a

Fs

otipdhAirr(ct

p

p

IXi

−

4sttc


transportation lot size;customer area (for bulk liquid products transportation);time periods of the second stage model.

etsrs set of parallel production lines within each site s and

resource type r;j set of customers within customer area j.

arametersAsri available capacity in production line i of resource type

r in site s;ss′/αsc time taken to transport products between site s and

site/customer s′/c;pco amount of product p ordered by customer c under order

o;Oo time at which order o is placed;Sl capacity of lot size l;PMps maximum daily production capacity of product p in site

s;VIps first stage decision – inventory level of product p at

location s at the start of the time horizon;VFps first stage decision – inventory level of product p at

location s at the end of the time horizon;1ps first stage decision – product p flow to formulation sites

s worldwide;C1pc first stage decision – product p flow to customer c

worldwide;Ss first stage decision – site opening;ps first stage decision – product allocation to manufactur-

ing site s;Cpsc first stage decision – product p supplied to customer c

from site s.

ecision (binary 0/1) variablesRpsrik equals 1 if product p manufacture is allocated to line i

of resource type r in site s in time period t, 0 otherwise;Vpsrik changeover variables. Equals 1 if product p will start

being manufactured in line i of resource type r in sites in time period t, 0 otherwise;

Lpsklj equals 1 if the flow of product p leaving site s at time tto customer area j is equal to LSl, 0 otherwise.

The first stage decision variables XSs, Xpst, and XCpsct areow fixed to the values determined in the network design stageor each month, becoming second stage parameters. Each of therst stage decisions mentioned above is valid for one monthi.e. one time period of the first stage model) which correspondso the time horizon of each second stage model (see Fig. 3 forhe information transfer process). Since the time periods in theecond stage are much shorter (than in the design model), theransportation time between sites (αss′ ) is no longer negligiblend should be accounted for by constraints involving product
ows between sites.
.2.2.1. Production scheduling constraints. As mentionedbove, in the second stage model we are looking into the events

o

F

ig. 3. Information transfer between the first and the second stages. (1) Firsttage model; (2) second stage model.

n a short time scale, making this a scheduling type problem. Athis level it becomes necessary to plan the resource utilisationn detail. Each production line can be occupied by at most oneroduct during each time period (constraint (18)). Between pro-uction of two different products in a line, a changeover periodas to take place; this is expressed by constraints (19) and (20).t the moment, in the US factory, all cleaning operations are

ndependent of the sequence of products using each particularesource. The occurrence of a changeover event, XVpsrik = 1, iseflected in the resource availability term in the capacity balanceconstraint (24)). A changeover takes place if a product is allo-ated to manufacturing line i in site s in time period k but not inime period k − 1:∑∈ Rp

XRpsrik ≤ 1 ∀s ∈ (S − SI − SW), r ∈ Rs, i ∈ Irs, k (18)

∑∈ Rp

XVpsrik ≤ 1 ∀s ∈ (S − SI − SW), r ∈ Rs, i ∈ Irs, k (19)

XVpsrik ≥ XRpsrik − XRpsrik−1

∀p ∈ Ps, s ∈ (S − SI − SW), r ∈ (Rs ∩ Rp), i ∈ Irs, k (20)

n order to avoid the occurrence of spurious decisions (XR orV equal to 1 without being meaningful) a small penalty term

s included in the OF:

0.5∑psrik

(XRpsrik + XVpsrik)

.2.2.2. Order delivery/sales constraints. Constraint (21)tates that each customer can only be supplied from the siteso which it was allocated in the first stage (XCpsc = 1). At anyime period, the total amount of each product delivered to eachustomer cannot be higher than the accumulated value of orders
f that product placed by that customer (constraint (22)):
Cpsck ≤ Max XCpsc ∀p, s ∈ ((S − SW) ∩ Sc), c ∈ CUS, k

(21)

mical

4pstfrtma

P

4

srwfpttpfs

ceb

watmoi(

F

A

I

plhhspiif

I

I

atfmstt

I

I


∑s ∈ ((S−SW)∩Sc),k′≤k

FCpsck′−αcs≤

∑o:TOo≤k

Bpco

∀p ∈ Pb, c ∈ CUS, k (22)

.2.2.3. Production constraints. Constraint (23) transfers theroduction allocation decisions from the first to the secondtage model. The capacity balance (constraint (24)) assumeshe same form as constraint (3) in the first stage model exceptor the changeover term, which accounts for the reduction in theesource availability. It is assumed that a half-day is necessaryo perform the changeover operation. Resource capacity is only

ade available for those products allocated to that particularsset in each time period (XRpsrik = 1):

Rpsk ≤ Max Xps ∀p, s ∈ (S − SW − SI), k (23)

MDprPRpskPFpr

PYpr

≤ XSs

∑i ∈ Irs

MAsri(XRpsrik − 0.5XVpsrik)

∀p ∈ Ps, s ∈ (S − SI − SW), r ∈ (Rs ∩ Rp) (24)

.2.2.4. Flow/mass balance constraints.4.2.2.4.1. US factory. The factory possesses capacity to

tore up to three days’ worth of production, at maximumates, of intermediate products. These intermediate storage unitsere not considered in the first stage due to the scale dif-

erence between the residence time in them and each timeeriod at the planning level. However, at the scheduling level,he ability to store intermediate products plays an impor-ant role. By introducing an extra degree of freedom, it isossible to develop a second stage production plan that per-orms closer to the global service levels predicted in the firsttage.

Shipments to foreign destinations (either formulation sites orustomers) may be made directly from the factory or through anxport terminal located at the US factory, where inventory maye kept.

Constraint (25) establishes the mass balance for internal flowsithin the US factory. Constraint (26) is the inventory bal-

nce at the US factory. Stock variations between consecutiveime periods are due to production events taking place in the

anufacturing site (product inlet), and outward flows, either tother locations or within the factory (product outlets). For clar-ty, we segregate the internal flows using a different constraint25):

∑
pss′k =
p′

PRp′skPCp′pPYYp′

∀p, s ∈ S1, s′ ∈ S1, k (25)

IVpsk = IVps,k−1 + PRpsk −∑s′

Fpss′k −∑

c

FCpsck

∀p, s ∈ S1, k (26)

p

o

Engineering 32 (2008) 2643–2663 2653

lternatively, constraints (25) and (26) could be condensed in

Vpsk = IVps,k−1 + PRpsk −∑s′ /∈S1

Fpss′k −∑

c

FCpsck

−∑p′

PRp′skPCp′pPYYp′

∀p, s ∈ S1, k

4.2.2.4.2. Packing sites US. As in the first stage model, theacking sites in the US perform the operations of packing andabelling of bulk products coming from the US factory. Fromere, the final products are distributed to the company’s ware-ouse network or directly to final customers in the US. Packagingites have capacity to store the equivalent of up to three days ofroduction of both bulk and packed products. Constraint (27)s the mass/inventory balance for these sites and constraint (28)mposes an upper limit on the storage of products in the USactory and the packaging sites:

Vpsk = IVpsk−1 +∑

s′ ∈ S1

Fps′s,k−αs′,s + PRpsk

−∑

p′ ∈ Ps

(PRp′skPCpp′

PYYp′

)−

∑s′ ∈ SI

Fpss′k

−∑

c ∈ CUS

FCpsck ∀s ∈ SUS, p, k (27)

Vpsk ≤ 3DPMps ∀s ∈ (SUS ∪ S1), p, k (28)

4.2.2.4.3. Storage sites US. Constraint (29) is the mass bal-nce, considering transportation times between locations, for allhe storage. The mass balance for the export terminal in the USactory, SET, is expressed in constraint (30). The second stageodel imposes an upper limit on the inventory kept in storage

ites, whose constraint has exactly the same formulation as inhe first stage model. Constraint (31) is the capacity balance forhe storage sites.

Vpsk = IVps,k−1 +∑

s′ ∈ (SUS∪S1)

Fps′sk−αs′s

+∑s′ ∈ SI

(Fps′sk−αs′s − Fpss′k)

−∑

c ∈ CUS

FCpsck ∀s ∈ SI, p ∈ Ps, k > 1 (29)

Vpsk = IVps,k−1 +∑

s′ ∈ S1

Fps′s,k−αs′,s −∑

c ∈ CW

FCpsck

−∑

s′ ∈ SW

Fpss′k ∀s = SET, p ∈ Ps, k (30)

∑
∈ Pg
IVpsk ≤ IAsgXSs ∀s ∈ SI, g, k (31)

4.2.2.4.4. Inventory Boundary Constraints. In order tobtain a feasible global production plan, in each second stage

2 mical

mmm

I

I

4esmttep

k

k

4ucramgucu∑

∑

4in

4rTam

Vpc

∑


odel the inventory levels at the beginning and end of eachonth must have the same value as determined in the first stageodel (constraints (31) and (32), respectively):

Vpsk = IVIps +∑

s′ ∈ (SUS∪S1)

Fps′s,k−αs′s

+∑s′ ∈ SI

(Fps′s,k−αs′s − Fpss′k)

−∑

c ∈ CUS

FCpsck ∀p ∈ Ps, s ∈ SI, k = 1 (32)

Vpsk = IVFps ∀p ∈ Ps, s ∈ SI, k = 30 (33)

.2.2.5. Formulation sites and customers worldwide. Productxports for formulation sites and customers worldwide arehipped directly from the US factory or through the export ter-inal (SET) (constraints (33) and (34)). As mentioned before,

hese are modelled as soft orders in time but hard in quantity, sohe summation of all product flows along the time horizon mustqual the value calculated in the first stage for the same timeeriod.

∑,s′ ∈ (S1∪SET)

Fpssk = F1ps ∀p, s ∈ SW (34)

∑,s ∈ (S1∪SET)

FCpsck = FC1pc ∀p, c ∈ CW (35)

.2.2.6. Sizing of transportation lots for liquid products. Liq-id products have to be transported in tanks, meaning that theorresponding flows can only assume values in a semicontinuousange, multiples of tank capacity, with a tolerance of −50%. It isssumed that each truck leaving the manufacturing/storage siteay deliver the same product to all customers in the same geo-

raphical area j. Constraint (36) ensures that each lot can onlyse one determined number of trucks for its transport, whileonstraint (37) imposes an upper and lower limit to the capacitysage of those trucks:

l

XLsklj ≤ 1 ∀s ∈ (S − SW), k, j (36)

ΓUS =∑

p,c ∈ CUS

⎡⎣0.75

l

LSlXLsklj − Cap50% ≤∑c ∈ Cj

FCpsck ≤∑

l

LSlXLsklj (37)

.2.2.7. Integrality and non-negativity constraints. The modelncludes integrality constraints for the binary variables and non-egativity relations for the continuous variables.

4

fi

Engineering 32 (2008) 2643–2663

.2.2.8. Objective function. In the second stage model, only theevenues and costs of the US network operation are considered.he NPV is formulated in a very similar way to constraints (16)nd (17), however, at this stage, a penalty term is included toinimise the delays in fulfilling the orders placed by customers.

Revenues

ΠUS =∑

ps,c ∈ CUS,k

(FCpsckVpc) (38.1)

Production costs

KPUS =∑

p,k,s ∈ (S1∪SUS)

(PRpskCPps) (38.2)

Inventory costs

KIUS =∑

p,k,s ∈ SI

(IVpskCIps) (38.3)

Transportation costs

KTUS =∑

p,s ∈ (S−SW),s′ ∈ (S−SW),k

(FCpss′kCTss′ )

+∑

p,s ∈ (S−SW),c ∈ CUS,k

(FCpsckCTCsc) (38.4)

Gross profit

ΘUS = ΠUS − KPUS − KIUS − KTUS

Tax costsThe tax cost calculation for each location expresses the inher-

ent financial structure of the company. As for the other termsof the objective function, we only account for the costs for thenodes in the US network. The calculations are performed in thesame way as expressed in Eqs. (16.5), (16.7) and (16.8) (USfactory, packaging and storage sites, respectively):

ΦUS = φS1 +∑

s ∈ SUS

φSUS +∑s ∈ SI

φSI (38.8)

Penalty term for delays in order deliveriesThe penalty term is proportional to the delay and amount

due to fully fulfil the orders placed by customers:

k

⎛⎝ ∑

o:TOo≤k

Bpco −∑

s ∈ (S−SW)

k−αsc+24h∑k′=1

FCpsck′

⎞⎠

⎤⎦ (38.9)

Net profit value for US network with penalty term

ZUS = ΘUS − ΦUS − ΓUS (39)

.2.3. Information transferThe procedure for the transfer of information between the

rst and second stages is explained in Fig. 3.

R. Sousa et al. / Computers and Chemical Engineering 32 (2008) 2643–2663 2655

Table 1US sales (10−1 tonnes/month) and AI production (%) per month

T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 Average total

68 47 49 60 65 66 67 71 71 75 43 50 61.0

P3 221 326 475 526 572 508 569 469 343 244 192 187 4632P6 115 246 352 485 461 447 456 329 282 209 169 112 3662P7 232 255 314 397 406 303 145 178 342 183 59 183 2997P8 59 198 288 155 265 297 277 166 202 139 107 62 2214P9 21 115 108 53 81 99 82 73 98 53 79 37 899P12 146 199 268 225 256 193 191 239 187 58 75 63 2100P13 79 108 174 95 100 77 92 107 72 15 39 35 994P17 154 194 282 328 348 353 339 279 214 375 285 187 3337P18 1795 2565 3514 3738 3669 2926 2544 2590 2712 2146 1560 1522 31281P20 217 161 242 277 290 294 282 233 383 468 360 315 3522P21 317 478 489 808 843 841 808 659 463 274 281 274 6536P 310P 604

5

moo5aUtsiioc

a

5

(nfisnro

TS

V

22 288 409 559 549 442 29723 310 451 622 758 717 626

. Global integration methodology

So far, we have only addressed the feed forward integrationethodology, i.e. utilisation of first stage information in the sec-

nd stage. For several reasons, as mentioned in the introductionf this paper and detailed for this particular case study in Section.1, the targets set by the planning stage tend to be too optimisticnd are often impossible to accomplish at the scheduling level.sually, the feasibility of the models at this stage is ensured at

he expense of (the predicted) customer service level. In our two-tage approach, information from the scheduling level is used tomprove the accuracy of the planning model. Overall, we aim tomprove the maximum feasible service level predicted in the sec-nd stage without significant losses in the profits of the supplyhain.

The following concepts and metrics are used in the discussion
nd evaluation of the quality of the integration results:
OTIF (%): On time and in full – proportion of the orders deliv-ered in the due date. For global OTIF’s, i.e. addressing sets of

p

o

able 2ales delivered on time and in full (OTIF, % in value) per product and globally per m

alues below the 90% target are highlighted in white. The average annual values are

427 521 357 275 267 4701677 534 224 271 264 6058

different products, the parameter is based in the order valuesrather than quantities.AI production (%): AI production – second stage averageresource utilisation in the production of active ingredients as apercentage of the maximum capacity.

.1. Results without feedback integration

The results presented in this section refer to the base casecase 1) of the planning stage. The second stage model uses theetwork structure, allocation decisions, sales and inventory pro-les calculated in the first stage. Tables 1 and 2 show the USales and respective OTIF levels predicted by the detailed plan-ing model. The second stage model results are an average of theesults obtained using two different sets of randomly generatedrders.

The global deviation between the two stages, with respect toroduction levels, is evident in Fig. 4.

The first stage model predicted an average resource utilisationf ∼66% while the second stage predicted a value of ∼61%; as

onth for the base case

shown in the last column.

2656 R. Sousa et al. / Computers and Chemical Engineering 32 (2008) 2643–2663

Ff

faOnodtrM

trtR

utwtatt

Fm

itgopappt

bpwnlo

TS

V

ig. 4. Resource utilisation (AI production) predicted by the two stage modelsor the base case.

or the US sales gross revenues, the values were MM$ 156.9nd MM$ 147.3 respectively, representing a difference of 6%.nly the orders delivered on time were accounted for the USetwork gross revenues in the second stage. In general, the valuef orders delivered on time is very similar to the total valueelivered in the whole time horizon (∼1% difference), a signhat manufacturing facilities are the bottleneck of the networkather than the distribution circuit. Worldwide exports totalled

M$ 95.3 in both stages.Table 2 shows that product families P8/P9 and P12/P13 have

he worst service levels. Each of these families uses at least oneesource that is operating at its maximum capacity most of theime (see results in chapter 5), R8/R9 (in the case of P8/P9) and7 (in the case of P12/P13).

The first stage model has an aggregated view of the man-facturing resources. It provides an estimate of how much ofhe total time capacity will be allocated to each task (product)ithout concerns about their temporal sequence. Naturally, bot-

leneck resources will be more affected by the introduction ofccurate modelling of the changeover events, as the productionargets set in the first stage leave no spare capacity for these toake place.

5

d

able 3ales delivered on time and in full (OTIF, % in value) per product and globally per mo

alues below the 90% target are highlighted in white. The average annual values are

ig. 5. Resource utilisation (AI production) predicted by the two stage modelsanipulating the resource capacity in the first stage.

Direct manipulation (reduction) of the bottleneck resourcesn the first stage provides a better OTIF value in comparison withhe base case, 96 vs. 93% (Table 3 and Fig. 5), however the USross sales revenues are 3% lower corresponding to a reductionf MM$ 4.4 This is not a good solution from the company’serspective, as the objective is always to maximise sales. Also,s in the base case, the deviation between the production targetsredicted by the two models is very significant for those timeeriods when the first model establishes higher AI productionargets.

The aggregate formulation is useful in determining the realottlenecks, i.e. the ones that will set the maximum, physicallyossible, output rates from the manufacturing nodes in the net-ork. Simply constraining these resources in the first stage mayot be the best approach to simultaneously achieve a good multi-evel integration and extract the maximum production potentialf the network.

.2. Integration methodology

At the scheduling level, when task sequencing is planned inetail, it may not be possible for bottleneck resources to work at

nth when manipulating the resource capacity of the manufacturing bottlenecks

shown in the last column.

R. Sousa et al. / Computers and Chemical

Fig. 6. Example of multiproduct production in shared resources. Pxrm: pre-treated raw material for product x; Px: product x bulk; Pxp: product x packed.

frd

d

s“fcr

sIgp

g

•

Fo

•

panaotesieinit

tsaofshoctvo

itdsdut

Fig. 7. First stage model output: campaign planning per resource.

ull capacity. The cause for this may not be due to the bottleneckesources themselves but due to the production stages up andownstream of them instead. Below, we show how this happens.

Consider a generic multipurpose plant with the productioniagram shown in Fig. 6.

Four products are manufactured in this plant. All the recipestart with a mixing stage performed in a single stirred vesselMixer”. From here, the pre-treated raw materials are fed to aormulation unit, in the case of P1 and P2, or to a blender, in thease of P3 and P4. After completion of the second step in theecipe, all products are conveyed to the packaging lines.

Figs. 7 and 8 show a possible campaign and productioncheduling output from the first and second stages respectively.n fact, changeover events are just one out of several of the inte-ration difficulties, as even without considering them, we haveroblems in the second stage.

At the aggregate level, for each time period, each task in a
iven resource is allowed to take place as long as (Fig. 7):
the capacity limit is not violated;

ig. 8. Second stage output: production scheduling. Note that no changeoverperations are considered in the Gantt chart.

sTrtdsaif

otiets

Engineering 32 (2008) 2643–2663 2657

there are enough raw materials available either from existingstocks (at the beginning of the time period) or produced atsome point during that time period.

At the scheduling level, when the sequence of tasks takinglace at each resource is planned in detail, the second condition,relaxed version of the second stage mass balance constraints, iso longer valid. Each task can only take place if there are enoughvailable raw materials from existing stocks at the beginningf the time horizon or through past production. Fig. 8 showshe ability of the second stage model to achieve the targetsstablished in the first stage. In the illustrative example, theecond stage requires up to 15% extra manufacturing capac-ty (or time), to produce the same amount of finished products,ven considering the existence of small storage units for thentermediate products. On top of this inherent limitation, theumber of changeover tasks (not considered in Fig. 8) tends toncrease, especially for those resources closer to the front end ofhe manufacturing process, decreasing the resource availability.

Note that, so far, we have been addressing and discussinghe problem of achieving the same production levels in bothtages of planning, without worrying about the effects on thebility of delivering orders on time. In the first stage, we arenly concerned that the right amount of final products is readyor delivery at the end of each time period while in the secondtage the manufacture should be more distributed along the timeorizon in order to fulfil orders by their due date without the needf building up significant stocks. This will of course bring a newomplexity to the integration problem. At the scheduling level,he production rates will not always be equal to the maximumalue as the customers will require more of a continuous flowf final products rather than large instantaneous batches.

From Figs. 7 and 8, it is evident that the complexity of thentegration problem will increase with the number of manufac-ured products in each resource in each time period and willecrease with the number of parallel independent lines of theame resource, since this arrangement allows processing severalifferent products at the same time. The aggregated capacity val-es used in the first stage model is equal to the total capacity ofhe individual lines.

The maximum production throughput of any manufacturingystem is constrained by the capacity of the bottleneck resources.he previous approach of constraining the availability of these

esources in the first stage model is not advisable, as it preventshe company from using the full potential of the network andoes not tackle the sequencing problem described above. Anyensible approach for this problem should create conditions thatllow the bottleneck resources to work at their maximum capac-ty, i.e. the resources up and downstream should not be the causeor idle periods on the bottleneck equipment.

In the first stage model, we attributed costs to inventory in thebjective function, to account for holding and handling opera-ions as well as working capital costs. In order to minimise the
nventory levels, the model predicts many small campaigns forach product along the 12 months time horizon, in order to main-ain the supply to final customers without needing to build upignificant stock levels. Although this may be seen an ideal plan,

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t brings many problems at the scheduling level, especially of theort described in Figs. 7 and 8. So, for the scheduling problem, itould be better to have fewer and longer campaigns in the first

tage as the complexity of integration problem increases withhe number of products manufactured in each time period.

We develop an analytical methodology to reflect on the firsttage model the impact on the second stage model that manymall campaigns, instead of fewer longer campaigns for eachroduct along the time horizon would have. The capacity balancen the first stage model (constraint (3.1)) is split into two blocksccording to the site and resource it refers to. The first blocktays the same as before while the second one is modified tonclude a penalty factor that decreases the availability of thoseesources upstream and downstream of the bottlenecks everyime the number of allocated products exceeds the number ofarallel lines for that resource (Eq. (40)):

∑p ∈ Ps∩Rp

MDprPRpstPFpr

PYpr

≤ MAsrtXSsΨsrt

∀t, s ∈ (S − Si), r ∈ (Rs ∩ Rhsr) (40)

hsr is the set of resources up and downstream of the bottle-ecks that are conditioning their operation, either in the AIanufacturing site or in the packaging sites.It is not possible to say what would be the best formulation for

he penalty factors but we know that Ψ srt should increase withhe number of lines and decrease with the number of products.he analysis of the second stage model outputs for the base caseuggests the following procedure: where Isr is the number ofvailable parallel lines for a particular resource:

Ψ ′srt =

⎧⎪⎪⎪⎨⎪⎪⎪⎩

1 if∑

p ∈ Rp

Xpst ≤ Isr

Isr∑p ∈ Rp

Xpst

if∑

p ∈ Rp

Xpst > Isr

∀t, s ∈ (S − Si), r ∈ (Rs ∩ Rhsr) (41)

n (41) Ψ ′srt is not a linear function of Xpst. However, we want to

odel the fist stage as an MILP, so we use

srt = 1 + Asr

⎛⎝1 −

∑p ∈ Rp

Xpst

⎞⎠

sr is a parameter, with a value between 0 and 1, that reflects theumber of parallel lines available for a particular resource in aiven site. The formulation of Ψ srt ensures that the maximumapacity will be available if only one product is allocated tohe resource. If no products are allocated the available capacitys higher than the real value, but in this case the constraint isrrelevant. We use the following regression to estimate initialeference values for Asr:

′ ∼ ∑
Ψsrt = −Asr
p ∈ Rp

Xpst + (1 + Asr),

Ψ ′srt

∼=∑

p ∈ Rp

Xpst ∈ [1, 3] (42)ips

Engineering 32 (2008) 2643–2663

his leads to

Isr = 1 → Asr [0.3,0.5];Isr = 2 → Asr [0.1,0.2].

The exact value depends on the maximum number of productshat can use each particular resource and how close to the limit itperates, in accordance with the outputs of stage two. If, after theecond run of the stage two models, a family of products basedn a specific bottleneck resource, has an OTIF of 100% but anbsolute sales value lower than in the base case, it means thatsr for the resources around the bottleneck may be decreased.

Finally, the analysis of the second stage outputs revealedhat when a customer is allocated to be supplied exclusivelyrom manufacturing sites, i.e. no distribution centres are associ-ted with that customer, the predicted service level is very lowalthough it would have provided good results at the planningevel).

An extra constraint is added to the first stage model, to enforcehe allocation of each customer/product to at least one distribu-ion centre:∑∈ (SI∩Ps)

XCpsct ≥ 1 ∀p ∈ Sc, c ∈ CUS, t (43)

.2.1. End-effectShah (1998) reports the downside of end-effects of some

equential multilevel integration approaches. This is defined ashe impossibility of extending the duration of a batch size out-ide the boundaries of a detailed time block, when these areptimised separately from the rest of the global time horizonas defined in the upper level stage). In this case, this is not anssue as the manufacturing tasks are continuous, so for a givenrocessing rate (<ratemax) the amount produced is proportionalo the processing time. However, an analogue effect concern-ng intermediate storage in the AI manufacturing and packagingeeds to be tackled. At the upper level, intermediate storage isot taken into account, but at the scheduling level it plays anmportant role. In real operations, the beginning of each months not different from any other point in time so intermediate stor-ge levels are expected to have values above zero. To preventhis, constraints (26), (27) and (30) are circular in time, i.e. therst time period (Ti) follows after the last one (Tf): Tf + 1 = Ti.his insures that no inventory build-up or depletion takes place

n the US factory or in the packaging sites, apart from what wasstablished in the first stage model. In order to maintain a conser-ative approach, opening inventories of intermediate products in1 and SUS are not allowed to be too high, so:

Vpst ≤ DPMps ∀s ∈ (SUS ∪ S1), p ∈ Pint., t = T30

. Results

From Figs. 4 and 5, it becomes clear that the multilevelntegration quality, measured by the difference between the AIroduction levels predicted by the two stage models and theecond stage order OTIF value, decreases for higher produc-

mical Engineering 32 (2008) 2643–2663 2659

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ion rates in the first stage. For levels below 60% the differenceetween the two curves is not significant. In the base case, we didot force any particular production distribution along the timeorizon, so the rate values oscillate within a 42% range as thisinimises the product inventory for a seasonal demand cycle.he downside of this plan is that at the scheduling stage, it isot possible to achieve the resource utilization rates predictedy the first stage model for the busiest months. The second stageodels are independent for each month and production levels

re not allowed to exceed the targets set by the first stage so thiseans that if we lose the opportunity to fulfil some orders in

he months when the supply chain is under greater pressure, weill not be able to recover them later on, when there is spareanufacturing capacity.In this section, we manipulate three factors to achieve the best

ntegration between the two levels:

Capacity correction factors for the first level, Ψ srt.Imposition of maximum allowed S1.R1 utilisation levels inthe first stage.Imposition of minimum demand coverage levels in the firststage by inventory stocks (Cov).

∑∈ SI

IVpst ≥ Cov∑

s,c ∈ CUS

FCpsct (44)

he third item in the list does not help the integration processith respect to the production levels of the second stage, but it

llows better service levels for the customers.

.1. Effect of capacity correction in the first stage model

Fig. 9 shows the global integration between the two stagessing capacity correction in the first stage. The fist stage predictsn average AI production rate of 66% while the second stage
eaches 63.6% (base case 65.6% vs. 61%, respectively). Theorresponding OTIF, according to Table 4, is 95.2% (93.7% inhe base case) and the US sales revenues are MM$ 2.25 higherhan in the base case (an improvement of 1.5%). From Fig. 9
avie

able 4TIF values per product for the second stage model with resource capacity manipula

T1 T2 T3 T4 T5 T6 T7

94 98 97 96 96 97 96

3 100 100 100 93 100 97 1006 73 97 92 100 100 94 937 65 92 98 100 95 97 998 82 100 100 94 52 77 909 2 100 100 95 56 56 4812 99 100 94 79 98 98 9313 94 74 85 50 99 99 7917 100 100 100 100 100 100 10018 100 100 100 100 100 100 10020 97 96 100 97 97 96 9821 100 100 85 99 99 100 9822 96 100 100 100 100 100 10023 98 98 100 100 95 100 96

ig. 9. Resource utilisation (AI production) predicted by the two stage modelssing capacity correction factors in the first stage model (case 2).

nd Table 4 it is clear that the difference between the two levelss lower than in the base case.

A detailed analysis of the second stage outputs revealed that1.R15 was too constrained in the first stage, as the OTIF forroducts P17 and P18 was 100% but the sales levels were lowerhan in the base case. Lowering the value of AS1,R16, the AIroduction rates are 66.3 and 62% for the first and second stages,espectively, with an OTIF of 94.9% and an improvement in theS sales revenues of MM$ 3.45, corresponding to 2.4% of thease case.

As mentioned above, the introduction of capacity correctionactors in the first stage model generates fewer and longer cam-aigns for each product and, as result, the inventory levels tendo be higher (Fig. 10). The impact on inventory related costs andorldwide sales is analysed in Section 6.2.The order OTIF values improved for all the products com-

ared to the base case. P6 and P12 in particular are now withinhe objective range (>90%). P13, P8 and P9 have better annual
verages; however the last two products still exhibit very lowalues in some months. With respect to sales revenues, the crit-cal products P6 to P13 registered an average increase of 7%xcept for P9, for which the rise was 20%.
tion in the first stage

T8 T9 T10 T11 T12 Average total

96 97 87 98 93 95

100 100 78 100 100 9790 95 100 100 80 9389 100 99 100 83 9361 100 92 100 35 8254 100 79 88 4 6598 92 50 100 100 9294 58 21 100 100 79

100 100 100 100 100 100100 100 100 100 100 100

96 97 82 97 97 96100 100 71 89 100 95100 100 91 100 96 99100 98 78 89 96 96


Fr

6i

rsri

i

nsut

tasics

s(sri

TC

A

BC

CCCC

Fig. 11. Resource utilisation (AI production) predicted by the two stage models(case 3) and comparison with the base case.

FrAc

dp

fbeen constrained to lower values. Demand levels increase fromJanuary to May, so if the AI production capacity is limited to alower value, it is necessary to build up some stocks to supply

ig. 10. US sales and stock value profiles for the second stage model withesource capacity manipulation (case 2) and comparison with the base case.

.2. Influence of the three factors in multilevelntegration—global impact

So far we have focused on the impact of manipulatingesource capacity availability at the first level. Figs. 9 and 10how that the method provides a better agreement between theesults of the two stages, although at the expense of highernventory levels.

Table 5 defines the characteristics of each approach discussedn this section.

The following set of figures shows the global impact on theetwork when combining resource capacity manipulation, impo-ition of minimum sales coverage by product inventories and anpper limit on the global network production rate (measured byhe AI production levels).

Fig. 11 shows the combined effect of the three factors men-ioned above on the quality of the integration. Case 3 exhibitsn average AI production of 64.3% and 62.9% for the first andecond stage models respectively. The global order OTIF values 97.5% with an increase in US sales revenues of MM$ 5.75,orresponding to 3.9% of the base case value. The increase inales values is evident in Fig. 13.

Fig. 10 shows that capacity manipulation by itself causes aignificant increase in the inventory levels for months T4 to T6April to June) and T11/T12 (November/December). Fig. 12
hows how the imposition of minimum sales coverage andestriction of AI production in the first level account for increasesn inventory levels for the rest of the time horizon. Fig. 13
able 5haracteristics of each approach discussed in the results section

pproach Resource manipulation Minimum salescoverage (%)

Maximum AIproductionlevels (%)

ase case – – –ase 1 Bottleneck constriction

1st stage– –

ase 2 Yes – –ase 3 Yes 10 70ase 4 Yes 10 65ase 5 Yes 10 75

c

Ft

ig. 12. US sales and stock value profiles for the second stage model withesource capacity manipulation, minimum sales coverage and upper limit in theI production in the first stage model (case 3) and comparison with the base

ase.

isplays the inventory profiles for three different values of AIroduction restriction.

From January to June, the inventory levels are slightly higheror those cases where the AI production in the first stage has

ustomers during those months when demands are higher.

ig. 13. Inventory profiles for three different levels AI production restriction inhe first stage: 70% (case 3), 65% (case 4) and 75% (case 5).

R. Sousa et al. / Computers and Chemical Engineering 32 (2008) 2643–2663 2661

Table 6Global results for the different approaches

AI production US sales revenues WW exports Invent. costs Neta (Valueb M$)

First stage(%)

Secondstage (%)

First tosecond (%)

Valueb

MM$Relativedifferencec

(%)

OTIF(%)

Valueb


(%)

Valueb


(%)

Base c 65.6 61.0 4.6 147.2 – 93.7 95.3 – 0.55 – –Case 1 63.8 59.6 4.2 −4.42 −3.0 95.6 −1.1 −1.1 0.08 15 −5Case 2 66.1 63.6 2.5 2.25 1.5 95.2 0.61 0.6 0.24 43 2.62Case 3 64.3 62.8 1.5 5.75 3.9 97.5 −0.2 −0.2 0.5 91 5.05Case 4 62.9 60.5 2.4 4.34 3.0 97.0 −3 −3.1 0.5 91 0.84Case 5 65.2 63 2.2 5.24 3.6 96.7 1.15 1.2 0.41 75 5.98

a Net difference to base case = US sales value + WW exports − inventory costs valub Base case: absolute value; cases 1–5: difference to base case.c Relative difference to the base case.

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umT

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PPPPPPPPPPPPP

T

ig. 14. Worldwide sales profile for the base case and for the two bestpproaches.

Table 6 shows the detailed results description for each case.esides the performance metrics for the US, it also includes the

esults for the worldwide network and the impact of the three
easures on inventory related costs.For the base case and case 1, where no resource manipu-
ation around the bottlenecks is performed, the AI productionifference is about 95% higher than for the remaining cases,

i

ru

able 7TIF values per product for the second stage model for case 3

T1 T2 T3 T4 T5 T6 T7 T8

92.8 99 98.8 97.4 98.3 98.8 97.1 95.4

3 100 100 100 100 100 98 95 996 100 93 97 100 94 100 100 797 35 100 100 94 99 100 100 998 100 100 100 54 93 100 100 749 1 100 100 86 82 88 97 5712 99 99 99 98 97 98 92 9813 96 97 89 82 91 90 69 8917 100 100 100 100 100 100 100 10018 100 100 100 100 100 100 100 10020 95 94 100 97 99 98 98 9721 100 100 98 100 100 100 100 10022 100 98 100 100 100 100 100 10023 93 100 95 99 96 96 96 96

he last column shows the increase in the US sales revenues relatively to the base ca

e.

nd corresponds to about 16.5 days/year of S1.R1 operation ataximum capacity, or 25 days/year at 65% of the maximum

apacity. The OTIF for cases 3–5 is consistently higher than inhe base case and is accompanied by an increase in US saleselivered on time. Worldwide sales in case 3 are slightly lowerhan in the base case (−0.2%) and inventory costs are signifi-antly higher but the net gains compensate this. In case 4, theI production is clearly too restricted in the base case causing

ignificant reductions in the worldwide sales levels (Fig. 14).nventory related costs are decoupled into working capital costs∼80%) and inventory storage costs (∼20%).

.3. Influence of the three factors in multilevelntegration—impact on individual products

The analysis of the impact of the three factors on individ-al products is restricted to the two cases whose results areore advantageous from a planning perspective—cases 3 and 5.ables 7 and 8 show the order OTIF value and US sales revenue

ncreases for these cases, for each product, per time period.Case 3 (Table 7) presents a significant overall improvement

elative to the base case (Table 2), and especially for those prod-cts using the manufacturing resources where the capacity was

T9 T10 T11 T12 Average total US salesincrease (%)

96.9 97.2 99 99 97.5

100 99 100 100 99 3100 100 100 100 97 7100 97 100 99 94 −281 100 92 97 91 1457 100 100 97 80 1399 84 100 100 97 1071 52 100 100 85 18

100 100 100 100 100 −6100 100 100 100 100 0

96 97 96 96 97 34100 100 100 100 100 7

99 99 96 96 99 −9100 97 96 96 97 5

se.


Table 8OTIF values per product for the second stage model for case 5

T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 Average total US salesincrease (%)

92.1 99 98.3 96.85 98.7 95.6 96.2 96 96.5 95.4 98.7 98.2 96.7

P3 100 100 100 98 100 100 100 100 100 98 100 100 100 3P6 64 95 97 100 100 90 87 100 83 100 100 91 92 6P7 55 99 100 92 100 90 94 93 100 97 100 100 93 17P8 100 100 100 42 100 79 91 65 92 100 92 92 88 −7P9 1 100 100 100 100 54 100 87 70 100 74 79 80 20P12 95 99 99 95 98 96 98 87 99 84 100 100 96 9P13 84 97 70 80 96 75 84 72 64 61 100 100 82 10P17 100 100 100 100 100 100 100 100 100 100 100 100 100 −6P18 100 100 100 100 100 100 100 100 100 100 100 100 100 0P20 98 99 100 97 97 97 97 95 97 96 97 96 97 31P21 100 99 100 100 99 100 95 100 100 84 100 100 98 5P 100P 100

T se ca

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22 96 100 100 100 100 99 10023 94 95 97 99 88 97 86

he last column shows the increase in the US sales revenues relatively to the ba

anipulated in the first stage (P8/P9 and P12/P3). OTIF valuesre from 7 up to 21% higher (absolute value) than in the basease. This improvement is also accompanied by a rise in the USales revenues for these products. The same analysis applies toase 5 and Table 8, although the figures are not as good as inase 3. Nevertheless, P9 and P13 still have a low OTIF value inome months. The supply chain performance is worst in months1 and T10. These are not periods with very high demand levels

rom US customers; however it is during these periods that theystem builds up stocks for the busiest months in the northernemisphere, while the southern hemisphere reaches its peak inemand early in the year. The same ideas explain the largesteviation in the worldwide sales that happens in month T1 atlesser extent in month T6 (Fig. 14) although the total sales

olume is very similar between the base case and cases 3 and 5Table 6).

.4. Model performance

The model statistics and performance for case 3 are presentedor reference only. The scope of the paper is the introduction ofhe integration methodology which in turn is still in an early stagef development. At this stage, no algorithms were developedo improve the solution performance. All the tests were run innix based machines with 2 GB RAM and 1.8 GHx, Pentium Vrocessors, running CPLEX 10.0 from ILOG.

The first stage model has ∼117,000 continuous variables,67,300 binary variables and uses ∼550 sec of CPU to solve.he large number of binary variables is due to the XCpsct set used

n constraints, however, since no single sourcing conditions arenforced, the solution time is still very low.

The second stage models have ∼4600 continuous variablesnd ∼6372 binary ones. Solution times are highly dependentn the production levels (given by the AI production resourcesage) and the number of active bottlenecks for the particular
eriod of each second stage model. These range between 250 sf CPU for time period T1 (AI production equal to 58% ofaximum capacity) to 3700 s for T8 (AI production equal to
7% of maximum capacity).

rc

a

97 96 100 96 99 −199 90 93 96 94 −1

se.

. Comments

As discussed before, multilevel planning integration poseseveral challenges; in particular there is an inherent difficultyn ensuring the same production levels across the whole tempo-al planning hierarchy as the aggregated formulations used inhe higher levels do not take into account the proper sequence ofasks when deciding resource utilisation in each aggregated timeeriod. At the lower level, this causes the occurrence of idle peri-ds for some resources, which may be critical if these resourcesere planned to operate at full capacity in the upper level, lead-

ng to gaps between achievable production at both levels. Theroblem becomes worse as the number of different productssing the same resource in each time period in the first or upperevel increases. The existence of intermediate product storagenits helps in mitigating this effect however these are generallyery limited in capacity. On the one hand, running fewer andonger campaigns for each product reduces the complexity ofhe integration process; however it also results in higher stocksnd associated costs. On the other hand, higher inventory levelselp in providing a better service to final customers (measured,n this work, by the percentage of order value delivered on time).

The detailed analysis of the problem and the methodologyeveloped in the second part of this case study, reduced theap between the models without the need of decreasing (andctually increasing) the total production outputs of the network.his makes the upper level model a more reliable and realistic

ool for long term planning.Apart from the imposition of minimum sales coverage by

roduct inventories, the measures used to improve the inte-ration process directly affect the production decisions ratherhan the inventory levels, however, in line with what has beeniscussed, they naturally raise the inventory levels, since theumber of campaigns decreases and the global production lev-ls are in 70–75% of the AI production capacity. However this
ise only happens where strictly necessary, as inventory relatedosts are still part of the first stage objective function.
Resource capacity manipulation as presented in this worklso provides a natural, organised way of distributing production

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Wof multipurpose plant-operation. Computers & Chemical Engineering, 19,


peration by all available resources rather than centralising themn a single one, which would make scheduling more difficult forhe local planner.

Another approach was investigated, where the integration andesponsiveness problems were tackled by direct manipulation ofhe inventory variables. This produced inconsistent results, evenf the system was allowed to operate with large stock values.t is our belief that to tackle this class of problems, managershould focus their strategy on production planning rather thann inventory policies.

eferences

assett, M. H., Doyle 111, F. J., Kudva, G. K., Pekny, J. F., Reklaitis, G. V.,Subrahmanyam, S., Zentner, M. G., & Miller, D. L. (1996). Perspectiveson model-based integration of process operations. Computers & ChemicalEngineering, 20, 821.

alasubramanian, J., & Grossmann, I. E. (2004). Approximation to multistagestochastic optimization in multiperiod batch plant scheduling under demanduncertainty. Industrial & Engineering Chemistry Research, 43, 3695–3713.

imitriadis, A. D., Shah, N., & Pantelides, C. C. (1997). RTN-based rollinghorizon algorithms for medium term scheduling of multipurpose plants.Computers & Chemical Engineering, 21, S1061–S1066.

rdirik-Dogan, M. E., & Grossmann, I. E. (2006). A decomposition method forthe simultaneous planning and scheduling of single-stage continuous multi-product plants. Industrial & Engineering Chemistry Research, 45, 299–315.

rossmann, I. (2005). Enterprise-wide optimization: A new frontier in processsystems engineering. AIChE Journal, 51, 1846–1857.

uillen, G., Badell, M., Espuna, A., & Puigjaner, L. (2006). Simultaneous opti-mization of process operations enhance the integrated planning/scheduling
of and financial decisions to chemical supply chains. Computers & ChemicalEngineering, 30, 421–436.
ondili, E., Pantelides, C. C., & Sargent, R. W. H. (1993). A general algo-rithm for short-term scheduling of batch operations. Part I – Mathematicalformulation. Computers & Chemical Engineering, 17, 211.

Z

Engineering 32 (2008) 2643–2663 2663

apageorgiou, L. G., & Pantelides, C. C. (1996a). Optimal campaign planningscheduling of multipurpose batch semicontinuous plants. 1. Mathemat-ical formulation. Industrial & Engineering Chemistry Research, 35,488–509.

apageorgiou, L. G., & Pantelides, C. C. (1996b). Optimal campaign planningscheduling of multipurpose batch semicontinuous plants. 2. A mathematicaldecomposition approach. Industrial & Engineering Chemistry Research, 35,510–529.

apageorgiou, L. G. (2006). Supply chain management and optimisation. In L.Puigjaner & G. Heyen (Eds.), Computer-aided process ABD product design(pp. 621–641). Wiley–VCH.

aaymakers, W. H. M., & Fransoo, J. C. (2000). Identification of aggregateresource and job set characteristics for predicting job set makespan inbatch process industries. International Journal of Production Economics,68, 137–149.

aaymakers, W. H. M., Bertrand, J. W. M., & Fransoo, J. C. (2000). Theperformance of workload rules for order acceptance in batch chemical man-ufacturing. Journal of Intelligent Manufacturing, 11, 217–228.

aaymakers, W. H. M., Bertrand, J. W. M., & Fransoo, J. C. (2001). Makespanestimation in batch process industries using aggregate resource and jobset characteristics. International Journal of Production Economics, 70,145–161.

hah, N., Pantelides, C. C., & Sargent, R. W. H. (1993). A general algorithm forshort-term scheduling of batch-operations. 2. Computational issues. Com-puters & Chemical Engineering, 17, 229–244.

hah, N. (1998). Single and multisite planning and scheduling: current statusand future challenges. In Pekny, J.F., & Blau, G.E. (Eds.), Proceedings ofthe third international conference on foundations of computer-aided processoperations, 94(320), 75–90.

hah, N. (2005). Process industry supply chains: Advances and challenges.Computers & Chemical Engineering, 29, 1225–1235.

ilkinson, S. J., Shah, N., & Pantelides, C. C. (1995). Aggregate modeling

S583–S588.hu, X. X., & Majozi, T. (2001). Novel continuous time MILP formulation for

multipurpose batch plants. 2. Integrated planning and scheduling. Industrial& Engineering Chemistry Research, 40, 5621–5634.

Supply chain design and multilevel planning—An industrial case

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