Dss for Vending

8/6/2019 Dss for Vending

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A DECISION SUPPORT SYSTEM FOR INVENTORY ROUTING

PROBLEM

Stephen C. H. Leung, Ligang Zhou

Department of Management Sciences, City University of Hong Kong, Hong Kong

[email protected], [email protected]

ABSTRACT

In this paper, we develop a decision support system for solving a real inventoryrouting problem about vending machine products. The system helps to make thedecision about everyday products delivery scheduling and also provides the decisionmaker with an opportunity to perform what if analysis. The system was tested witha set of real instances and the results were compared with the company method.

Keyword: Decision support system, routing problem, replenishment decision

INTRODUCTION

Inventory routing problem (IRP) is an important problem in logistics andtransportation. In IRP, the replenishment of inventory for a number of geographicallydispersed customers is controlled by a central decision maker who manages a fleet ofvehicles that makes the deliveries. So, to find an effective vehicle route can helpreduce the transportation costs. Despite the practical significance of this class of

problems, they are challenging NP-hard problems.

In this paper, we discuss a real problem in close relation to IRP. Below, follows a

complete description of this problem. Most soft drinks providers not only supply softdrinks to convenience stores and supermarkets, but also install their own vendingmachines (VM) in shopping malls, schools, hospitals and even remote areas. Thenumber of vending machines has soared dramatically in the past decade because softdrinks providers are attracted by the benefits of these machines: 24-hour availability,low cost of installation and implementation, and little manpower required. This studyis motivated by the problem faced by a beverage company that sells canned softdrinks using vending machines covering Hong Kong Island, the Kowloon peninsulaand the New Territories. Due to the variation in sales volume, some of the vendormachines require much more frequent replenishment, e.g. three times per week, whileothers only need to be replenished once a month. Without a systematic forecast and

decision analysis process, the replenishment policy and delivery plan are mainlybased on the decision-makers experience. This dependency on experience sometimesmakes the refilling process inefficient. Thus, it is important for the company todevelop a systematic decision analysis process.

The companys decision maker has developed a replenishment and delivery methodwhich mainly categorizes the vending machines into different groups based on theirhistorical average demand. Six groups of vending machines are clustered under theallocation system: three visits per week, two visits per week, one visit perweek, one visit per two weeks, one visit per three weeks and one visit permonth. After clustering the six groups, the decision maker has to plan the vehicle

routing every day. The vehicle routing depends on traveling time and vendingmachine location. Normally, the decision maker chooses the nearest vending


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machines, or vending machines that can be reached quickest. The characteristics ofthe current inventory and routing problem for vending machine products aresummarized as follows.

(1) The company has almost 100 vending machines covering Hong Kong Island,the Kowloon peninsula and the New Territories. Some vending machines

can be moved from location to location, but other machines cannot beremoved under contract. The company has two different types of vendingmachines: 18-column and 20-column, with a capacity of 380 and 400 cansrespectively.

(2) Vending machines installed in shopping malls, sports complexes andchurches usually sell more over the weekend. Those in schools and officessell more during weekdays. The daily demand for each vending machine isnot known until the vehicle visits the machine. However, details of the totalnumber of transactions within the interval between the last and current refillare available.

(3) The company owns one vehicle, which has an approximate capacity of 2500

cans. The driver works from Monday to Saturday. He starts working at 9:30am and finishes at 6:30 pm, taking a one-hour lunch-break. The vehicle is

parked and loaded at a warehouse (depot). After loading, the driver canbegin the replenishment from the warehouse. For each visit, the quantity ofproduct replenishment is the maximum level of the vending machine.

(4) Sometime, due to the uncertain inventory level at the vending machine, theremay be insufficient items for replenishment in the vehicle. The vehicle thenhas to return to the depot to refill immediately and wait for the following dayto refill the machine.

(5) A number of popular electronic payment devices have been installed invending machines. Consumers can use a contactless smart card with built-inradio frequency identification (RFID) tag the Octopus card to pay fortheir purchases. However, the Octopus company requires each transaction to

be transferred to its headquarters within seven days, otherwise transactionswill be voided. As a result, some vending machines must be visited at leasttwice per week in order to collect the data, even though replenishment is notnecessary.

Many methods have been used for solving inventory routing problem and itsvariations. Generally, they can be categorized into exact methods and approximatemethods or, heuristics. The first attempt to integrate IRP into a single model may be

found in (Federgruen and Zipkin, 1984). The developed non-linear integerprogramming model analyzed a single period, one warehouse, multi-retailer IRP withuncertain demand. Due to the cost considerations and commodity availability, notevery customer will be selected to be visited every day. An interchange heuristic wasdeveloped to handle the complexity of the IRP. Dror et al. (1985) comparedalgorithms for the IRP defined over a short planning period. In order to reduce the

planning horizon from an annual to a weekly base, the customer set was divided intwo subsets. One includes customers whose inventory must be replenished during thegiven planning period, and the other includes customers whose inventory is onlyreplenished if there is a cost-savings opportunity in doing so. A set of real data from a

propane distribution firm in Pennsylvania was used. Dror and Ball (1987) further

developed a heuristic technique to reduce the long-run average problem to a single- period problem. The heuristic consists of an LP-based generalized assignment


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algorithm modified by the Clarke and Wright (1964) algorithm, and an interchangeprocedure for local improvement. Chien et al. (1989) formulated the IRP as a mixed-integer program and the Lagrangean dual ascent method was used to solve severalsmall instances. They focused on a single day approach without treating each day as acompletely separate entity. The information on each day is passed to the rest days and

used to simulate multiple-day system. The heuristic approach is to select thecustomers to supply the commodity so that the total profit can be maximized on asingle day. Unselected customers with low inventory levels or possibly shortageshave penalties imposed. Moreover, unsatisfied demand today will reflect higherrevenues tomorrow. Using todays information, penalties and revised revenue thenext-day selection can be made as todays procedure. Trudeau and Dror (1992)addressed the issue in SIRP when the actual demand on a route exceeds the capacityof a vehicle. The pre-determined route cannot be completed and hence the vehicle hasto return to the depot to be refilled. Uncompleted route occurrence is referred to asroute failure. Four SIRP stages were defined: selection of the customers whoseinventory must be replenished during the planning period (stage 1), the assignment of

customer to days of planning period (stage 2), the assignment of vehicles to visit acustomer on each day (stage 3), and improvements based on stage 3 (stage 4). Theoverall performance was measured by the number of commodities delivered whileincurring the stock outs and route failures. The Markov decision process is one of theemerging methods used to model SIRP. Campbell et al. (1998) formulated the SIRPas a Markov decision process and proposed approximation methods to find goodsolutions with reasonable computational effort. Christiansen and Nygreen (1998a, b)modeled the inventory pickup and delivery problem with time windows using seatransport.

It is not surprising to see that researchers and practitioners consider IRP withinnovative policies and strategies. Viswanathan and Mathur (1997) studied the IRPwith stationary nested joint replenishment policy (SNJRP), in which replenishment atthe locations is made at constant intervals which are power-of-two multiples of thecommon-base replenishment period for instance, once every week, once every twoweeks and once every four weeks for three different locations. Chan et al. (1998)referred to this replenishment policy as a power-of-two strategy. Chan et al. (1998)addressed the zero inventory ordering (ZIO) policies, under which a customersinventory is replenished if and only if it drops to zero. Without considering thecapacity of the vehicle and the frequency of replenishment at the locations, it wasverified that this policy is optimal: otherwise, ZIO policy may fail to be optimal.

They analyzed ZIO policies and derived asymptotic worst-case bounds on theirperformance.

The main objective of this study is to develop a simple heuristic approach to solve thereal inventory routing problem for vending machine products, under which thereplenishment policy and delivery plan for the following weeks demand can beobtained in advance instead of organizing the trips at time of actual delivery.Moreover, we introduce a decision support system to help the soft drink companymake daily routing schedule and provide information to do good business decision.Using computer simulation, we compare performance of the proposed method and thecompany current method with different performance measures. In addition, with the

proposed solution procedure, the decision maker can easily identify the impact of anychanges in demand, change in vendor machine location and changes in the number of


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electronic payment devices installed.

The organization of this paper is as follows. After this introductory section, a framework of the decision system will be described and a heuristic method for inventoryand distribution planning in vendor machine operations is presented in Section 2. A

set of data from a Hong Kong beverage company is used to test the effectiveness andefficiency of the proposed method and in order to deal with future changes andrequirements, sensitivity analysis is then conducted in Section 3. Finally, ourconclusions and recommendations are given in Section 4.

DECISION SUPPORT SYSTEM

In this study, we develop a special decision support system for the vending machineproducts delivery. The DSS contains user interface, delivery optimization modelbased on a heuristic approach to select the vending machine to be served each day andmixed integer linear programming (MILP) to decide the sequence of vendors to be

visited, database about everyday delivery and vending machine location information.The DSS can help the decision maker not only make everyday delivery scheduling butalso analyze the allocation decision of vending machine for more profit. Thearchitecture of this DSS is shown as Figure 1.

Figure 1. Architecture of decision support system

Trudeau and Dror (1992) stated that the inventory and routing problem consists of atemporal component the time of the replenishment at customers location andspatial component the routing of vehicles travelled. These two components are

interrelated because the routing decision might affect the timing of replenishment:vice versa, the timing of replenishment, which directly affects the inventory level, willimpact on the vehicle routing. Heuristic algorithms are widely used to handle thecomplex inventory and distribution problem with uncertain demand (Federgruen andZipkin, 1984). Christofides (1985) identified that most routing heuristics belong tothe two-phase method: the cluster first-route second method and the route first-clustersecond method. In the cluster first-route second heuristic method, customers areclustered into groups and then efficient routes are designed for each cluster. In theroute first-cluster second heuristic method, a travelling tour is formed amongcustomers and then the tour is divided into different clusters. However, Bienstock etal. (1993) stated that no heuristics in the route-first cluster second heuristics algorithm

can be asymptotically optimal for the stochastic routing problem. In this paper, a

Database

Excel

Selectionof VM

Routingoptimizatio

nReport

DSS

Decision maker Driver


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heuristic approach, cluster-first route-second, is employed. Figure 2 shows the stepsin the framework of the heuristic method for SIRP.

The proposed heuristic algorithm allows us to reduce the long-run average problem toa single period problem. In the first phase, we determine when and how much to

deliver to each customer on each day of the planning period. Then we can identify aset of customers to be served by a single vehicle each day. Campbell et al. (1998)stated that the cost of serving a cluster does not only depend on the geographiclocations of the customers in the cluster, but also on whether the customers in thecluster have compatible inventory capacities and usage rates. The selection ofvending machines in the cluster formation is based on the penalty imposed on eachvending machine. Vendors with the highest penalty are selected for the first routingsection. Vending machines are given penalties on two occasions. As suggested byChien et al. (1989), a penalty will be imposed for not visiting vending machineswhich currently have low inventory levels and which face possible shortages duringthe day. There are four penalties for different sales levels as shown in Table 1.

Table 1. Penalty levels on sales.

Penalty Sales

1 15 20 %

2 20 30 %

3 30 50 %

4 >50 %

The secondly penalty is imposed on vendors using the Octopus device. The Octopusservice provider requires each transaction to be transferred to its headquarters within

seven days, otherwise transactions will be voided. The penalty is made when acertain day has passed after the last replenishment. There are five penalty levels andthese are listed in Table 2.

Furthermore, there are two constraints on the selection of vending machines in theclustering process. One is the time constraint: total replenishing time must not exceedtotal working hours. The other is the capacity constraint: the total number of softdrinks replenished must not exceed the machines capacity. Vending machines must

pass these two constraints to form a cluster.

Table 2. Penalty levels on Octopus.

Penalty level Number of days1 2

2 3

3 4

4 5

5 6


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Figure 2. Flow chart of cluster-first route-second heuristic search method

In the second phase, given that we cluster all customers and know how much todeliver to each customer on each day of the planning period, we determine deliveryroutes visiting customers in the same cluster for each day. To decide the sequence ofvendors to be visited, Clark and Wright (1964) suggested using a savings matrix to

partition customers into different groups. Routes with the highest savings arecombined into a new feasible route in order to minimize the total distance traveled by

the trucks. We propose that the farthest insertion is adopted in order to avoid serioustraffic congestion occurring along main roads in the morning, since large numbers of

yes

yes

yes

Clustering procedure: Calculate the closing

inventory and the number of days since thelast data collection

Input the general information and dailydemand

Sales reachpenalty level?

Assign penalty to specific vendingmachines.

Did data collection

reach penalty level?

no

no

Assign penalty to specific vendingmachines.

List out and sort the vending machinesby penalty.

Was time constraintexceeded?

Add and form a feasible cluster.

Select vending machines from cluster list and formdistance matrix among them selected vending machines.

Assign each vending machine in selected list to thetrip, calculate and insert vending machine with thelargest minimum increase in distance to the trip.

no

The replenishment sequence is formed.Output the results.

yes


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workers move between their homes and their workplace, causing serious congestionin the inner city. If the delivery schedule starts from the farthest vendor, rush hourtraffic congestion can be avoided and hence some travel time saved. Figure 3 shows ascreen shot of the DSS based on this two phase heuristic approach.

Figure 3. Sample screen of DSS

COMPUTATIONAL ANALYSIS

3.1 Performance Measures

In this study, based on our interviews with key operational personnel in the companyand our review of the literature, three major criteria for comparing currentreplenishment and delivery methods with the proposed method are identified.

(1) Average number of visits: In order to increase the operating efficiency asstudied by Trudeau and Dror (1992), the average number of vendingmachines that can be visited per day should be maximized.

(2) Vending machines with stock out (in %): Dror and Ball (1987) stated that thechallenge to the inventory and routing problem is to maintain sufficientcommodity at the customers location. Shortages may result in the loss ofgoodwill as well as revenue. It is important to study the proportion ofvending machines with stock outs.

(3) Total transportation cost: One of the major objectives of the vehicle routingproblem is to minimize total transportation costs.

3.2 Computational Results

The computer simulation was conducted on a set of daily replenishment schedules fortwo years and three months. The two-year period was a warm-up period, which wasestablished afterwards for the purpose of statistical stability. The three-month period(76 days) was used for analysis. Before running the simulation, some assumptions aremade:

(1) Deliveries are carried out by the companys own vehicles, and no out-sourcing is allowed.

(2) The warehouse provides an unlimited supply of soft drinks.(3) The vehicle starts replenishing with a full load of soft drinks.

(4) The vehicle returns to its starting point every day after delivery.(5) If there is more than one vending machine in the same location, this location


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is still considered as having one machine.

Average number of visits

Results in Table 3 show that the number of vending machines to be visited improvesunder the proposed method. The average number of vending machines to be visited

has increased to 10, compared with 7.31 vendors under the company method. Onaverage, two more vending machines can be visited each day if the proposed methodis adopted. Furthermore, the number of vending machines to be visited per day ismore stable under the proposed method, as this has a standard deviation of zero(Figure 4). Under the proposed method the driver is able to allocate evenly thenumber of vending machines to be visited. This compares with the current situationwhere the number of vending machines fluctuates dramatically with a standarddeviation of 2.74.

Table 3. Summary of number of visits under original method and proposed method Total days Mean 1 S.D. 2 Most 3 Least 4Original method 76 7.31 2.74 13 4Proposed method 76 10 0 10 101 Average number of vending machines to be visited2 Standard deviation of number of vending machines to be visited3 The greatest number of vending machines visited in one day4 The smallest number of vending machines visited in one day

Figure 4. Comparison of original method and proposedmethod by number of vendors visited

Vending machines with stock outs

It is shown that using proposed method the number of vending machines with stockouts has decreased, dropping by about 11% (as shown in Table 4). Less vendingmachines experience stock outs when the proposed method is adopted. On average,0.75 vending machines have stock outs each day under the proposed method,compared with 1.66 vendors under the original method. The quality of replenishmentscheduling is therefore significantly improved if the proposed method is adopted.

Table 4. Summary of inventory under original method and proposed method

0

2

4

6

8

1

0

1

2

1

4

1 61

116

21

26

31

36

42

47

52

57

62

67

72

Days

visit

Original method Proposed method

Nu

mberof

Visit

s


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Total visited 1 Without stock outs 2 Stock outs 3 Average stock outs 4Companymethod

555 429 (77%) 126 (23%) 1.66

Proposedmethod

473 416 (88%) 57 (12%) 0.75

1 Total number of vending machines visited2 Number of vending machines without stock outs3 Number of vending machines with stock outs4 Average number of vending machines with stock outs per day

Total transportation cost

Using the delivery schedule given by the soft drinks provider, the farthest insertionheuristic is used. Results in Table 5 show that using farthest insertion the totaldistance and total cost are reduced by 6% when compared with the original method.Therefore, using the farthest insertion, replenishment can be effected while traveling ashorter distance and incurring a lower cost.

Table 5. Summary of transportation cost under original method and proposed method Total distance (km) Cost Distance saved Cost savedOriginal 617.38 $ 1,234

34.88 km (6%) $70 (6%)Farthestinsertion

582.54 $ 1,165

Sensitivity analysis

This paper not only offers a solution to the present inventory and distributionproblem, but also gives insights into possible management changes that can help the

company meet future rapid changes in terms of the three performance measuresdiscussed in the last section. First, we assume a change in the demand ranging from adecrease of 25% to an increase of 50% of current demand. Second, we test the impactof the installation of electronic payment systems. It is assumed the number ofelectronic payment devices installed in the vending machines changes from a decreaseof 25% to an increase of 25% of the current number of devices installed. Third, weexamine the feasibility of a new IT-based transaction method. Sensitivity analysis iscarried out and the results are shown in the following section.

Demand level

Since the competition among vending machines is keen, demand changes

significantly over a period of time. A change in demand often leads to a differentreplenishment schedule being needed. The test on demand level is carried out byvarying the demand for each vending machine. Also, this test aims to find the criticaldemand level at which performance of the distribution system worsens. The resultsare shown in Table 6.


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Table 6. Results of the proposed method with different demand levels

Proposed methodDemand Level

0.75 0.85 1 1.15 1.25 1.5

Vendors with stock outs 7% 9% 12% 16% 19% 26%

Vendors without stock outs 93% 91% 88% 84% 81% 74%

Note: (0.75) - 25% decrease in current demand; (0.85) - 15% decrease in current demand;(1) - current demand(1.15) - 15% increase in current demand; (1.25) - 25% increase in current demand;(1.50) - 50% increase in current demand

In Table 7, results show that the critical demand level is about a 50% increase incurrent demand, under which 26% vending machines experience stock outs. Thedistribution systems performance becomes unacceptable since the frequency of visitscannot cope with daily demand. Suppose the demand level is increased by 50%, andthe working hours per day are increased by 1 hour, from 9 hours to 10 hours. Withthe increase in working hours, around two more vending machines can be visited.

Table 7 shows that if the working hours increase to 10, the number of vendingmachines with stock outs falls to 19%. Hence, if the demand level is increased to150% of current demand, the soft drink provider should consider extending itsworking hours to cope with a serious stock out problem.

Table 7. Results of the proposed method with different working hours

Demand 150% 150%

Working hours (per day) 9 10

Machines with stock outs 26% 19%

Machines without stock outs 74% 81%

Electronic payment system

The Octopus payment system is used by many people in their daily life. Octopusaffords convenience to the customer and increases sales. A test on the number ofOctopus devices is carried out and the results are summarized in Table 8. These showthat when the total number of Octopus devices installed increases, the percentage ofvendors with stock outs increases. The replenishment schedules quality worsenswhen total number of Octopus devices installed increases because more vendorsrequire more visits in order to collect the Octopus data. Thus the driver needs tospend more time on the collection of Octopus data when more Octopus devices areinstalled.

Table 8. Results of proposed method with different number of Octopus devices

Proposed method 0.75 0.85 1 1.15 1.25

Machines with stock outs 11% 12% 12% 12% 16%

Machines without stockouts

89% 88% 88% 88% 84%

Note: (0.75) - 25% decrease in total number of Octopus devices installed; (0.85) - 15% decrease intotal number of Octopus devices installed; (1) - current number of Octopus devices installed; (1.15) -15% increase in total number of Octopus devices installed; (1.25) - 25% increase in total number ofOctopus devices installed

CONCLUSION

In this paper, it is shown that the decision support system is more effective than the


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manual routing system currently adopted by the decision maker for several reasons.When same demand figures are used, the proposed solution is able to (1) increase theaverage number of vendors to be visited by 37%, (2) decrease the number of vendingmachines with stock outs by 11%, and (3) save 6% of transportation costs.

Although the model developed provides a systematic and effective inventorymanagement policy for the vending machine products, it still has some limitations.

1.The distance between vending machines may not be accurate. More data andfurther studies are required to strengthen the validity of the schedule.

2.Seasonal factors and keen competition in the soft drinks industry lead to largefluctuation in daily demand. As a result, daily demand should not beconstant over time. Thus, further study of daily demand is also required

before implementation.

REFERENCES

Bienstock, D., Bramel J. & Simchi-Levi, D. 1993. A probabilistic analysis of tourpartitioning heuristics for the capacitated vehicle routing problem with unsplitdemands. Mathematics of Operations Research, 18, 786-802.

Campell, A., Clarke, L., Kleywegt, A. & Savelsbergh, M. 1998. The inventory routingproblem. In: Crainic TG, Laporte G (eds). Fleet Management and Logistics.Kluwer Academic Publishers, Dordrecht, The Netherlands, 95-113.

Chan, L. M. A., Federgruen, A. & Simchi-Levi, D. 1998. Probabilistic analysis and practical algorithms for inventory-routing models. Operations Research,46(1), 96-106.

Chien, T. W., Balakrishnan, A. & Wong, R. T. 1989. An integrated inventoryallocation and vehicle routing problem. Transportation Science, 23(2), 67-76.

Christiansen, M. & Nygreen, B. 1998a. A method for solving ship routing problemswith inventory constraints.Annals of Operations Research, 81, 357-378.

Christiansen, M. & Nygreen, B. 1998b. Modelling path flows for a combined shiprouting and inventory management problem. Annals of Operations Research,82, 391-412.

Christofides, N. 1985. Vehicle routing. In: Lawler EL, Lenstra JK, Rinnooy Kan AHGand Shmoys DB (eds.). The Traveling SalesmanProblems. John Wiley, NewYork, 431-448.

Clarke, G. & Wright, J. W. 1964. Scheduling of vehicles from a central depot to anumber of delivery points. Operations Research, 12, 568-581.

Dror, M. & Ball, M. 1987. Inventory/routing: reduction from an annual to a short-period problem.Naval Research Logistics, 34, 891-905.Dror, M., Ball, M. & Golden, B. 1985. A computational comparison of algorithms for

the inventory routing problem.Annals of Operations Research, 4, 3-23.Federgruen, A. & Zipkin, P. 1984. A combined vehicle routing and inventory

allocation problem. Operations Research, 32(5), 1019-1037.Trudeau, P. & Dror, M. 1992. Stochastic inventory routing: route design with

stockouts and route failures. Transportation Science, 26(3), 171-184.Viswanathan, S. & Mathur, K. 1997. Integrating routing and inventory decisions in

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