Comparison between two distribution networks in a leading chemical company: multi distribution layers and hub-and-spoke strategy

Comparison between two distribution networks in a leading

chemical company: multi distribution layers and

hub-and-spoke strategy

Navilah A. Syamlan

(S2829967)

Master Thesis of Technology and Operations Management

Faculty of Economics and Business, University of Groningen

July 2016

Abstract

This thesis assists a pilot project of a specific leading chemical company in choosing the most optimal distribution route strategy between the current and the proposed network strategy in terms of total cost minimization. The current network setup, which is the direct shipment, consists of multiple distribution layers that the products can be shipped more than one time according to the pulled or pushed demands by the downstream warehouses of the subsequent layers. The comparison between direct distribution from origin to destination and hub-and-spoke system is done by building the mathematical model and solved by using Xpress-Mosel. The results suggest that for the case involving 47 nodes, single allocation has no advantage to the cost minimization. Meanwhile, the transportation cost is proven has impacted linearly to the total cost performance.

Keywords: MILP, network design, production and distribution, direct shipment, multiple distribution

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2.2 The Research set-Up ... 8

2.2.1 The current network set-up ... 8

2.2.2 The proposed network set-up (hub and spoke strategy) ... 9

3 Model Formulation ... 10

3.1 Current Network Set-Up: ... 10

3.2 Proposed Network Set-Up ... 13

4 Computational Results ... 15

5 Conclusion ... 20

References... 21

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REFACE

The challenges I experienced during writing my thesis are considerably tough for me as I come from different background of bachelor degree at the first place when decided to study this master subject. Unlike with the other classmates, they already have a strong fundamental of management tools and skills. Thus, I needed to make extra efforts to cope with the gaps. Also, when building my thesis, I have learned many things to improve my knowledges in terms of operations management. Model building and coding in optimization software are the most valuable skills that I am grateful for. Hopefully, it can be useful when I work in specific company in the future. Actually, one of the difficulties I encountered was the large instances of the scope requested by the company. The network involves the route within EMEA countries, thus, the data range is considerably tremendous.

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Supply chain network serves some integrated echelons in whole chain (Thomas and Griffin, 1996; Sabri and Beamon, 2000; Altiparmak et.al., 2006). To be more specific, it includes numerous stages of suppliers, manufacturers, and distributors that deliver the finished goods to the targeted customers in sequence (Erenguc et. al., 1999). Among the chains, the movement of products and flow of information exchanges can be reversed between suppliers and manufacturers, manufacturers and distributors, distributors and retailers, and until end-customers. According to Thomas and Griffin (1996), in the past, organizations focused their efforts on making effective decisions within a facility, thus, the complexity of the decisions was reduced since each component was treated independently of the others. However, this affects the cost performance as ignoring those components dependencies can be costly. As a result, firms are moving toward more coordinated and integrated design and control of all of their components, rather than focusing on decoupled decision making processes. This leads obviously to lower cost performance and higher service level in delivering goods and services to the customer. Thus, designing the optimal performance of the supply chain network comprehensively has been an interesting topic for researchers during these years.

Actually, the attention of the network level can be decoupled by closely echelon level flows, such as producers-distributors; suppliers-producers-distributors; producers-distributors-customers; or even covering the whole network from suppliers until customers. In vendor-buyer coordination, supply chain network can be more complex when applied to one vendor-multi buyer, i.e. one buyer has several business units expanded in the world wide. Gelderman and Semeijn (2006) explain one of examples related to such coordination problem. A certain company network operates several business units throughout the world, which leads it to becoming a decentralized company. The fact of its business practice is that the most of the raw materials can only be bought internationally while the rest of them are bought locally. In addition, certain raw materials are needed in different plants world-wide, and could be delivered by local suppliers. In fact, these opportunities problems offer many room of improvements and such coordination issues are required to be integrally solved to improve their network performance.

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distributors that the decisions have to be acquired simultaneously. Jang et.al (2002) determine such important decisions, i.e. (1) defining the number and locations of manufacturing plants and intermediate inventory warehouse; (2) selecting the distribution channel; and (3) identifying the most profitable transportation amount within the facilities chain. Similarly, Jayaraman and Pirkul (2001) also discuss about the simultaneous decisions in network classification, such as: (1) manufacturing and distribution center locations; (2) specification of plant and warehouse capacities; and (3) distribution systems. Whereas, Thomas and Griffin (1996) emphasize the operational extent that the vehicle routing and machine scheduling are needed to be solved simultaneously. Eventually, all the problems are intended to be cleared up so that the total expenditure cost can be decreased.

Those specified decisions to support in achieving in the well-integrated system in supply chain network are assessed and classified into three categories, i.e. strategical, tactical, and operational. Lee and Kim (2002) summarized the time horizons of three decisions impacting the network performance, strategic level has the longest period time consideration, while contrarily operational discusses the shortest term decisions even until less than hourly. Besides these two, the lasting effect of the tactical breaks in the middle of both of them.

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What is the optimal route from which production sites the products should be produced and to which distribution

centers the products should be transferred in order to reach minimum total cost?

The theoretical contributions of this research are (1) building mathematical model of multi distribution layers in point-to-point delivery strategy in form of Mixed Integer Linear Programming (MILP); (2) giving a recommendation of the most profitable approach by comparing performance of between two model networks that are optimized by exact solver

In order to answer the research question, the report is organized as follows: in section 2 the theoretical background is described. The proposed methodology including mathematical formulation is provided in the next section, which is section 3, then followed by the computational in the section 4. Finally, conclusions and summaries are then given.

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The projects which involve decisions in productions-distribution network strategy have been researched frequently within past decades. Those researches can be categorized into the planning horizon, the type of data (deterministic or stochastic), the chosen objective function, the methodology they performed, and other supply chain characteristics (Melo et. al., 2009). The literature review is narrowed to the single period with cost minimization objective according to the core of the research.

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network. Similar with their previous model, the limitations of the model are based on the supply capacity or storage capacity of each facility. They still use Langrangian relaxation combined with heuristic procedure to solve their new algorithm. In the same way, Amiri (2006) studies the two echelon level distribution network that covers plants until customers route with similar solution method. However, on the other hand, he extends the constraint by allowing multiple levels of capacity level of each facility. Tsiakis and Papageorgiou (2008) also discuss the two echelon environment by including more complete constraints related to the financial and production constraints. They solve the formulation by implementing in GAMS and CPLEX solver.

Differently, Lee and Kim (2002) prefer to perform hybrid analytic - simulation approach to solve their model with capacity constraints. It is done by adapting the situation in the real system especially the production phase, thus, also considering all the uncertainties occurring in the factory. On the other hand, Syam (2002) extend the focus of facility location model by including more logistical components, hence, all related parameters to the logistical cost components such as holding and ordering cost are covered in the model building. The aim is to minimize the physical distribution cost. Meanwhile, Lin et. al. (2006) figure slightly different framework out involving the consolidation centers (CC) which allows the larger shipments for single product to the multiple distribution centers (DC). They define the numbers and location of the CC and DC and also the routing strategy between plants and DCs either through the consolidation centers or direct in order to obtain the least total cost. In addition, Wu et. al. (2002) study the multi depot location routing problem and divide it into two sub-problems, i.e. the location-allocation problem, and the general vehicle routing problem, then solve it by using heuristic method.

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In addition, the other sort of distribution network, i.e. hub and spoke approach has been researched in the past years. Such network strategy comes into consideration to encounter the challenges especially related to the economies of scale faced by the managers and eventually to optimize the supply network design performance. The hubs are such selected facilities which are assigned as a transition and connecting all the nodes within the network (Campbell, 1994; Alumur & Kara, 2008). Hence, the shipments retrieved from the origins must travel through the hub first as a center facility then move to the destinations. More than as a transition, the hubs also have an impact on the route from origin to the hub that consolidates all the products from the same factory to the different distribution centers. Additionally, in the hub, they are combined with the amounts from different factories to the same distribution centers (Alumur & Kara, 2008).

The hubs itself can be chosen among the exist locations within the system then the remaining nodes are each connected to the one of the hubs (Klincewicz, 1991). Regarding the amount of the selected hubs, a hub location problem consists of single allocation and multiple allocation hub problems. Campbell (1994) states that if each node of demand is assigned to a single hub then it is considered as single allocation, otherwise, multiple allocation has obviously more than one selected hub. The problem of determining the optimal hub location to serve the allocation of demands of each node to the hub is then called hub location problem (Alumur & Kara, 2008). Also, O’kelly (1987) emphasizes that determining the location of hub facilities is essential to the hub and spoke network as it influences the total transportation cost eventually. Finally, this research will develop current business process’ performance to the single allocation of the hub and spoke network. It will be then simulated and compared to the current network.

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This paper discusses and compares two performances in order to support the company in choosing the optimal routing distribution strategy within EMEA (Europe, the Middle East and Africa) countries. The structure features multiple commodities with deterministic demands and unlimited capacity of warehouses in single period time frame.

2.2.1 The current network set-up

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process which the products are transported from producers to the downstream warehouses then delivered to the customers. However, this research covers the path dispatching from the factory only until the distribution centers in order to meet the demand of the customers which are already accounted in the total demand of warehouses (Fig. 2.1). Nevertheless, they allow the products travelling more than one time, so that the transportation continued to other downstream warehouses in other layer. For example, in layer 1, the products are produced in plants. Then, they are retrieved form the plant to the DC 1 in layer 2 and have already travelled once. If there are requested demand from DC 2 and can be fulfilled by the stock of DC 1, then the demand is accounted to the demand of layer 3 and the products need to travel for the second time. The network limits the distribution level until the fifth layer.

2.2.2 The proposed network set-up (hub and spoke strategy)

Furthermore, the company also raises a proposed network setup which introducing a central stock point, called as a hub, between manufactures and warehouses (Fig. 2.2). The hub location problem in this study refers to the single allocation problem, only one hub will be selected among the candidates which proposed by the manager.

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Fig. 2.2. The proposed network setup.

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The proposed mathematical models here follow the mixed integer linear programming (MILP) model with single period and deterministic type of data. Before building the two models, the assumptions must be stated to clarify the limitations of the model:

- Unlimited holding capacity of each warehouse – as the company mainly uses a third party warehouses.

- Each product has the same production cost within each production site.

- The transportation cost does not have any dependencies to the weight of transportation.

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is only applied to production site facility. Thus, the model is considered as capacitated manufacturing site facility and uncapacitated warehouse facility. Finally, the model is extended to the concept of multi distribution layers.

The following notations are used in the following model:

i,j locations’ index i = 1,…,I

p products’ index r = 1,…,P

l layers’ index l = 1,…,5 The parameters are:

Apjl Customer demand of each product p of warehouse j in layer l.

Bpjl Demand for each product p which is either pulled or pushed by the downstream warehouse j

in layer l.

Ci maximum production capacity of plant i.

Pi Average production cost of plant i.

Hpj Holding cost of product p warehouse j.

Tij Average unit transportation cost from i to j.

Lpi Required minimum batch size to transport product p from plant i to DC j (only in layer 1).

The decision variables are:

Xpijl Transported amount of product p from location i to location j in layer l.

Zpi Binary variable whether the product p is produced in plant i.

Spjl Inventory level of product p in warehouse j in layer l.

12 Min Z1 = ∑ ∑ 𝑋𝑝 𝑖 𝑝𝑖𝑗1. 𝑃𝑖 + ∑ ∑𝑖∈𝐼 𝑗∈𝐽∑𝑝∈𝑃∑_{𝑙=1 𝑝𝑖𝑗𝑙}4 𝑋 . 𝑇𝑖𝑗 + ∑ ∑ ∑𝑝 𝑗 𝑙=25 𝐻𝑝𝑗 . 𝑆𝑝𝑗𝑙 (1) subject to: ∑ ∑ 𝑋𝑝 𝑗 _{𝑝𝑖𝑗1} ≤ 𝐶𝑖 , ∀𝑖 (2) ∑ 𝑋𝑗 𝑝𝑖𝑗1 ≥ 𝐿𝑝𝑖 . 𝑍𝑝𝑖, ∀ 𝑖, 𝑝 (3) ∑ 𝑋𝑖 𝑝𝑖𝑗1≥ ∑5𝑙=2(𝐴_𝑝𝑗𝑙+ 𝐵𝑝𝑗𝑙) , ∀𝑗, 𝑝 (4) ∑ 𝑋𝑖 𝑝𝑖𝑗𝑙 ≥ 𝐴𝑝𝑗𝑙+ 𝐵𝑝𝑗𝑙 , ∀𝑗, 𝑝, 𝑙 ∈ 1. .4 (5) ∑ ∑𝑝 𝑖∈𝐽𝑋_{𝑝𝑖𝑗𝑙}− ∑ ∑𝑝 𝑘∈𝐽𝑋_{𝑝𝑗𝑘(𝑙+1)}− ∑ 𝑆_{𝑝 𝑝𝑗(𝑙+1)} = 0 , ∀𝑗, 𝑙 ∈ 1. .4 (6) 𝑋𝑝𝑖𝑗𝑙 ≥ 0 , ∀𝑝, 𝑖, 𝑗, 𝑙 ∈ 1. .4 (7) 𝑆𝑝𝑗𝑙 ≥ 0, ∀𝑝, 𝑗, 𝑙 ∈ 2. .5 (8) 𝑍_𝑝𝑖 ∈ {0,1} , ∀ 𝑝, 𝑖 (9) Referring to the objective function (1), this original model aims to minimize the total cost, which incurred from production cost, transportation cost, and holding cost, in order to travel some amount of product flows which are determined to satisfy all the demands. Constraint (2) implies that all the produced amount from certain factory is ensured to be all transferred to the intended DCs. It refers to the variable 𝑋𝑝𝑖𝑗1 and must be less than maximum supply capacity of each production site. No

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Additional assumptions for the proposed model is all transported amount to the hub must satisfy exactly to the demands of the destinations, i.e. downstream DC so that zero inventory inside the hub along the time period. The below formulation follows uncapacitated facilities problem setting. As seen in Fig. 2.2. a central facility which is known as a hub is positioned in between of flows of origins and destinations. Compared to the previous model, mostly, some modifications are performed in building the proposed model to cope with the hub-and-spoke network system. There are slight alterations in the list of indices and parameters, and vast differences in the decision variables as well as the objective function and the constraints.

The indices are:

i,k locations’ index i = 1,…,I

j hub candidates’ index j = 1,…,J

p products’ index p = 1,…,P The parameters are:

dpk Demand of each product p of each warehouse k.

epj Demand of each product p of each hub candidate j.

Pi Average production cost of plant i.

Tpij Average unit transportation cost of each product p from plant i to hub j

Tpjk Average unit transportation cost of each product p from hub j to warehouse k.

The decision variables are:

Yij Binary variable whether the plant i is connected to hub j.

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In regards of the above terms, the model is then formulated as follow (refers to the model built by Daskin, 2013): Min Z1 = ∑ ∑ (𝑑𝑝 𝑖 𝑝𝑘+ 𝑒𝑝𝑗) . 𝑃𝑖 + ∑𝑖∈𝐼∑𝑗∈𝐽∑𝑝∈𝑃∑𝑘∈𝐾𝑇𝑝𝑖𝑗 . 𝑏𝑝𝑗. 𝑌𝑖𝑗+ ∑𝑖∈𝐼∑𝑗∈𝐽∑𝑝∈𝑃∑𝑘∈𝐾𝑇𝑝𝑖𝑗 . 𝑎𝑝𝑘. 𝑌𝑖𝑗 + ∑ ∑𝑖∈𝐼 𝑗∈𝐽∑𝑝∈𝑃∑𝑘∈𝐾𝑇𝑝𝑗𝑘 . 𝑎𝑝𝑘. 𝑌𝑖𝑗 (10) subject to: ∑ 𝑌𝑗 𝑖𝑗 = 1 , ∀𝑖 (11) ∑ 𝑊𝑗 𝑗 = 1 (12) 𝑌_𝑖𝑗 − 𝑊_𝑗 ≤ 0, ∀𝑖, 𝑗 (13) 𝑊_𝑗 ∈ {0,1} , ∀𝑗 (14) 𝑌_𝑖𝑗 ∈ {0,1} , ∀𝑖, 𝑗 (15)

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The two set of models described above are then solved by implementing in the Xpress-Mosel software, one of the solvers which can solve the problems related optimization using MILP model. Initially, the original data is considerably rich since the network involves the route within EMEA countries to transfer various kinds of commodities. The number of commodities involved in general are larger than 30000 items that can be produced in 20 types of production sites and distributed to around 47 distribution centers. As the methodology chosen at the first place using exact solver, it turned out that the solver cannot accommodate such data range. The system needs to incorporate around hundreds of thousands of variables, which proceeds longer calculation time or CPU time and requires considerable memory size. Eventually the simulation is forced to stop due to the insufficient memory capacity.

Therefore, before the simulation process can be done, the data range needs to be reduced first. The numbers of plants and DCs still remain the same, only the demands are adjusted to be quite sufficient according to the memory size requirement of the software. The simulation only covers the demand which larger than around 50% of the total demand orderly which eventually generates the amount of layers trimmed off to only three in total. All the data parameters included in the software are presented in the appendices. Finally, the simulation is indicated to find the optimal solution with gap 0.0% by the default and reasonable CPU time.

Fig. 4.1 The optimal route of some location networks in current setting Table 4.2. Some of satisfied demands of each warehouse in each layer

Item Demand Layer DC 2 DC 1 Plant

Item AA 1651 2 - GLE SMK

Item BB 2582 2 - SMK UMB

Item CC 7558 3 DNV UMB MMA

Item DD 1261 3 DNV UMB MMA

Item EE 1132 3 CTL UMB MMA

Item FF 2537 2 - DSI J11

Item GG 3904 2 - DSI J11

Item HH 1028 2 PWA J11

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Fig. 4.3. The network of single hub allocation – Hub Case 1

Meanwhile, the Hub Case 1 (Fig. 4.3), which is according to the proposed model, states that a hub is selected among the four candidates out of existing locations. They are “MMA”, “GOH”, “N01”, “SMK”. The node of GOH is then selected as the best hub than the other three locations. Such locations, which are not assigned as a hub, still have the same functions as of other DCs. Fig. 4.4. shows the comparison results acquired from the two models, however, the additional model is also presented. The Hub Case 1 results in increasing the total cost than the initial setting. On the other hand, the additional model or called Hub Case 2 accesses if there are no statement of hub candidates which means omitting the set of index j in proposed model in section 3.2. As a consequence, if the candidates are not predetermined, the cost is more decreased than the Hub Case 1. It implies that the solver has more space and is not restricted to the only hub candidates when choosing the most profitable hub. Instead of GOH, the DC of MHE is chosen as the most optimal hub among all the exist nodes, so that GOH becomes the non-hub nodes in this network case. Both DCs are located in Europe continent. However, it is still indeed more expensive than the Multi-Layers Case.

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connected using hub and spoke system than when they are directly connected.” Basically, the purpose of implementing hub route strategy is to minimize the maximum distance route. Depending on the amount of the nodes, the number of selected hubs can vary for each problem. For this case involving more than 30 nodes, there is only one assigned hub for all the non-hub nodes, some might have shorter distance to the destination if using direct connection. It impacts to the increasing transportation cost for several routes. Therefore, more than one hub allocation can be wiser by assigning each nodes to the nearest hub among the certain hubs. The products movement from hub to hub generates the advantage in term of transportation cost. Compared to the link cost between a hub and another non-hub nodes or spokes, the cost rate for inter-hub flow connection is usually cheaper (Campbell, 1994).

Fig. 4.4. Total cost (€) comparison of three cases

Additionally, all these cases then are resolved with different values of production cost and transportation cost parameters. The cost parameters of production cost and transportation cost are redefined by ±10 % of the initial values respectively. The results shown in Fig. 4.5, 4.6, and 4.7 indicates that changes on production cost do not have any significant influences to original total cost, while modifications on the transportation cost impact the final results linearly to the changes value of the cost. It is proven that decreasing the transportation cost can also decline total cost performance.

1.48E+09

1.04E+13

1.63E+11

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Fig. 4.5. Production and transportation costs impacting the total cost performance of Multi-Layers Case model

Fig. 4.6. Production and transportation costs impacting the total cost performance of Hub Case 1 model 1.00000E+09 1.10000E+09 1.20000E+09 1.30000E+09 1.40000E+09 1.50000E+09 1.60000E+09 1.70000E+09 PC 90%,TC 100% PC 110%, TC 100% PC 100%,TC 90% PC&TC 90% PC 100%,TC 110% PC&TC 110%

Multi-Layers Case

Total Cost (€) Base

8.00000E+12 8.50000E+12 9.00000E+12 9.50000E+12 1.00000E+13 1.05000E+13 1.10000E+13 1.15000E+13 PC 90%,TC 100% PC 110%,TC 100% PC 100%,TC90% PC&TC 90% PC 100%,TC110% PC&TC110%

Hub Case 1

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Fig. 4.7. Production and transportation costs impacting the total cost performance of Hub Case 2 model

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This paper has studied the comparison of two network performances between direct shipment in multi-layer distributions and single hub allocation. Strategical decision level has been discussed into the model building that determines plant locations of each product to be produced and distribution strategy route in multiple distribution layers. Then, the simulation using exact solver are performed. The scope of research is not trivial to the certain region, but covering the distribution track within EMEA countries. The simulation deals with the overwhelmed data range which at the first place the process cannot be succeeded. Thus, the data is needed to be reduced in order to meet the research time.

As a result of this research, the single hub allocation problem does not generate positive impact to the total cost minimization compared to the original total cost of current setting. The involved distribution centers are not in few numbers, there are 47 DCs in total. Hence, the problem can barely be solved effectively with only one hub connected to all the remaining nodes. Klincewicz (1991) also studies the p-hub median problem in less than 50 nodes and he does not perform single hub allocation system, otherwise several trials for 2, 4, and 10 hubs problem are executed. Also, the discount factor

1.00000E+11 1.10000E+11 1.20000E+11 1.30000E+11 1.40000E+11 1.50000E+11 1.60000E+11 1.70000E+11 1.80000E+11 PC 90%,TC 100% PC 110%,TC 100% PC 100%,TC90% PC&TC 90% PC 100%,TC110% PC&TC110%

Hub Case 2

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is applied to the cost rate of inter-hub in multiple hub allocation problem which can lead to the minimized transportation cost.

All in all, future research could be addressed to the study of multiple hub allocation and discussed further in the network comparison. Also, the transportation cost can be modified with the multiplier cost constraint which is in accordance to the shipment size, since the freight cost is totally dependent on the weight of transportation. The more number of products being transported, the cheaper the transportation cost will be. The transportation cost is also proven can affect positively to the decreasing of the total cost performance. By applying multiplier transportation cost to the problem of multiple hub allocation, hopefully, it will result in more preferred total cost performance. In addition, the company should improve their data organization such as incorporating the cost parameters into the main document. It aims to achieve user friendly data, so that, the data collection can be easily done.

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Altiparmak, F., Gen, M., Lin, L., Paksoy, T., 2006. A genetic algorithm approach for multi-objective optimization of supply chain networks. Computers and Industrial Engineering 51, 196-215. Alumur, S., & Kara, B. Y. (2008). Network hub location problems: The state of the art. European

Journal of Operational Research, 190(1), 1–21. http://doi.org/10.1016/j.ejor.2007.06.008

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Campbell, J. F. (1994). Integer programming formulations of discrete hub location problems.

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http://doi.org/10.1016/0377-2217(94)90318-2

Gelderman, C. J., & Semeijn, J. (2006). Managing the global supply base through purchasing portfolio management. Journal of Purchasing and Supply Management, 12(4), 209–217. http://doi.org/10.1016/j.pursup.2006.10.002

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(n.d.). Retrieved April 6, 2016, from

http://warrington.ufl.edu/departments/isom/docs/vakharia/1999_EJOR.pdf

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Jayaraman, V., & Pirkul, H. (2001). Planning and coordination of production and distribution facilities for multiple commodities. European Journal of Operational Research, 133(2), 394–408. http://doi.org/10.1016/S0377-2217(00)00033-3

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Research, 53(1), 25–37. http://doi.org/10.1016/0377-2217(91)90090-I

Lee, Y. H., & Kim, S. H. (2002). Production–distribution planning in supply chain considering capacity constraints. Computers & Industrial Engineering, 43(1-2), 169–190.

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Lin, J.-R., Nozick, L. K., & Turnquist, M. A. (2006). Strategic design of distribution systems with economies of scale in transportation. Annals of Operations Research, 144(1), 161–180.

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A

Table 1.

Supply capacity per production site (liters/day)

AZO 11080498 BNA 14525089 COR 13616685 CST 12971940 DSI 43433116 ESS 14816475 GRO 9143441 J01 9836042 J11 7219363 MHE 20054143 MMA 28205687 MTA 49415826 PRD 8045621 PWA 47560836 SLH 46059722 SMK 100017923 UMB 40428806 W11 7270310 W21 25715485 WPV 14878422 Table 2.

Unit production cost per factory in average (€/BuOM*) AZO 1.21 BNA 1.24 COR 1.24 CST 1.27 DSI 1.17 ESS 1.22 GRO 1.20 J01 1.17 J11 1.19 MHE 1.20 MMA 1.20 MTA 1.34 PRD 1.23 PWA 1.19 SLH 1.21 SMK 1.18 UMB 1.18 W11 1.21 W21 1.20 WPV 1.22

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Table 3

Transportation cost between location (€/BuOM). For every unfeasible route, the big M value is inserted as 10000. Not all the data are shown due to the excessive amount of data, below is only for display purpose.

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Table 4

27

Table 5

Batch size requirement of each product for dispatching from plant (BuOM). For some products, they are not restricted to the minimum batch size. In that case, value of 1 is used. Not all the data are shown due to the excessive amount of data, below is only for display purpose.

Item Batch Size

28

Table 6

Demand data of each product per distribution center for each layer. Not all the data are shown due to the excessive amount of data, below is only for display purpose.

Item DC Layer Demand