## Journal of Industrial Engineering and Management Science

Vol: 2018    Issue: 1

Published In:   January 2019

### A Decision-Making Approach for Supplier Selection in the Presence of Supply Risk

Article No: 1    Page: 1-14    doi: https://doi.org/10.13052/jiems2446-1822.2018.001

 1 2 3 4 5 6 7 8

A Decision-Making Approach for Supplier Selection in the Presence of Supply Risk

Z. Khojasteh-Ghamari and T. Irohara

Faculty of Science and Technology, Sophia University, Tokyo, Japan

Email: khojaste.z@gmail.com; Irohara@sophia.ac.jp

Received 15 August 2017; Accepted 26 December 2017;
Publication 17 January 2018

## Abstract

In order to deal with the various kind of risks in a supply chain, we need to have different approaches. In this study, we propose a mathematical programming model to manage the supply risk considering multi layer feature of the supply chain. The aim of this model is managing the supply chain risk by controlling the selection of suppliers. By having this approach, we aim to lower the risk of supplier disruption. We examine various datasets to observe the behaviour of the proposed model in different data sizes through the several steps. Analysing the results of different datasets, we show the trend of objective value by increasing data sizes. Besides, we analyse the increasing ratio of cost within different steps of the model. Finally, we discuss the effect of our proposed approach on the total cost.

## Keywords

• Supply chain risk
• Mathematical programming model
• Supplier selection
• Multi sourcing

## 1 Introduction

In today’s global marketplace, firms are relying more on their supply chains to remain competitive [1]. In the past, supply chain managers mainly focused on reducing costs, and apparently, this was the only main objective of the studies; but recently, they have begun to give importance to supply chain continuity and resiliency which have significant impacts on costs as well. Hence, conventional reactive planning has given way to proactive planning in Supply Chain Risk Management (SCRM) [2]. Proactive planning is preparing to avoid risky situations before disruption happens. However, a reactive approach is the response to the disruption outcomes, after it occurs.

## 2 Problem Statement

In this model, we propose an optimization approach to manage the Supply Chain Risk (SCR). The objective of this model is minimizing the total cost including purchasing cost and initial contract cost.

The problem is based on the selection from many suppliers for many manufacturers. Each candidate supplier has different purchasing cost. Moreover, we add more criterion to the supplier selection. We avoid selection of suppliers which have the same sub-suppliers. This strategy is controlling the disruptions in the lower tier supply chain. Figure 1 illustrates a simple view from the relationship between manufacturers, suppliers and sub-suppliers. As shown in Figure 1, supplier 1 and supplier 2 can not be selected together in our model. The reason is that they are sharing the same sub-supplier (sub-supplier 2). Similarly, suppliers 2 and 3 can not be selected together, since they have a shared sub-supplier which in this case it is sub-supplier 3. The purpose of considering these criteria is the cases that a sub-supplier is disrupted. Then, all the suppliers which get parts from that particular sub-supplier will be affected as they can not receive supplies from that disrupted sub-supplier. As a consequence, they all will have the same problem and can not deliever the parts to the above tier. Our idea is avoiding the selection of supplier which are getting parts from the same sub-suppliers to prevent this problem.

Figure 1 Relation between manufacturer, suppliers and, sub-suppliers.

In this study, we propose an extended approach to double sourcing. The purpose is to control supplier selection by considering their lower tier suppliers.

The following notations are defined for formulating our proposed model:

 Indexes: i index of suppliers j index of manufacturers q index of sub-suppliers
 Parameters: p i Unit purchasing cost of supplier i hi Initial contract cost with supplier i ci Capacity of supplier i dj Demand of manufacturer j M Big number siq $:\left\{\begin{array}{l}=\text{1},\text{\hspace{0.17em}}\text{if}\text{\hspace{0.17em}}q\text{\hspace{0.17em}}\text{is}\text{\hspace{0.17em}}\text{the}\text{\hspace{0.17em}}\text{sub-supplier}\text{\hspace{0.17em}}\text{of}\text{\hspace{0.17em}}\text{supplier}\text{\hspace{0.17em}}i,\\ =\text{\hspace{0.17em}}\text{0},\text{\hspace{0.17em}}\text{Otherwise};\end{array}\text{\hspace{0.17em}}$ k minimum order from each supplier
 Decision variables: y ij Quantity to be transferred from supplier i to manufacturer j aij $:\left\{\begin{array}{l}=\text{1},\text{\hspace{0.17em}}\text{if}\text{\hspace{0.17em}}\text{supplier}\text{\hspace{0.17em}}i\text{\hspace{0.17em}}\text{is}\text{\hspace{0.17em}}\text{selected}\text{\hspace{0.17em}}\text{for}\text{\hspace{0.17em}}\text{manufacturer}\text{\hspace{0.17em}}j,\\ =\text{\hspace{0.17em}}\text{0},\text{\hspace{0.17em}}\text{Otherwise};\end{array}\text{\hspace{0.17em}}$
$Minimizing Cost∑i∈I∑j∈Jpi*yij+∑i∈I∑j∈Jhi*aij (1)$

subject to

$yij≥0∀i∈I,∀j∈J (2)∑jyij≤ci∀i∈I (3)∑iyij≥dj∀j∈J (4)∑iaij≥2∀j∈J (5)∑iaij*siq≤1∀j∈J,∀q∈Q (6)yij≥k*aij∀i∈I,∀j∈J (7)yij≥aij∀i∈I,∀j∈J (8)yij≤M*aij∀i∈I,∀j∈J (9)$

Equation (1) is the only objective function in our proposed model, it is minimizing the total cost; which includes initial contract cost with each supplier and unit purchasing cost of each supplier. We consider a primary contract cost for each supplier. This parameter will be considered only once, regardless of the amount of orders from the supplier. Constraint (2) is applying the non-negativity feature of the decision variable. Constraint (3) serves as the capacity constraint for each supplier. This constraint is for the cases that due to the low cost of a supplier, there are too many requests from it. By considering the capacity of each supplier, we limit the number of requests from it. Constraint (4) specifies that for each manufacturer, the total number of supplies to be received should be equal or more than its demand. In the other words, this constraint indicates the necessity of demand satisfaction. In this model, since the objective function is minimizing the total cost, the number of requested items from suppliers will be exactly equal to the demand of manufacturers and not more. Constraint (5) specifies that the number of selected suppliers for each manufacturer should be equal or more than two. This constraint is representing the concept of double sourcing. It means that for each manufacturer at least two suppliers should be selected. In this case, if one of the suppliers will be disrupted, at least there is the other one which can provide the supplies and therefore, the disruption in entire SC will not happen. Constraint (6) prevents the selection of the suppliers which have the same sub-suppliers. So, our SCRM model controls suppliers according to the second tier suppliers. This is beneficial for the case that a sub-supplier is disrupted and if both suppliers of our model receive their primary materials from that sub-supplier, then both the suppliers will confront disruption and eventually all the SC network will face supply problem. Constraint (7) specifies the minimum number of order from each supplier which makes the model more realistic. If we relax this constraint, then the result would be only a single unit of order. Finally, Constraints (8) and (9) define the relationship between binary and integer decision variables.

## 3 Numerical Examples

In this section, in order to show the validity of the above-mentioned optimization approach, we tested several datasets. We solve the model using Gurobi Optimizer Version 6.5.0 mathematical programming solution software. All experiments were run on a personal computer with an Intel (R) Core (TM) i7-6700 CPU (3.40 GHz) and 16.0 GB of RAM. All the runs solved in about 1 second.

### 3.1 Experimental Results

In this section, as sample, we selected 10 datasets which their information is shown in Table 1. These datasets were different in terms of their size. The size of datasets is randomly generated. Dataset number 1 has only 3 candidate suppliers, 1 manufacturer, and 4 sub-suppliers. Dataset number 2 is slightly bigger than dataset number 1, with 5 candidate suppliers and 6 sub-suppliers. From dataset number 3 to number 10, number of suppliers and sub-suppliers increase. The unit purchasing cost of suppliers and the initial contract cost assigned randomly between the span of 93 and 105 by keeping the average cost the same in all the datasets. Table 2 shows the results after running the program. Changing the size of datasets did not have any effect on the time of running the program. In all these datasets, we could see the optimal results in about one second. The results are the selection of two suppliers for each manufacturer. We set the demand of manufacturer to 100. As the model is double sourcing, the result will be two selected suppliers for each manufacturer. We call the first selected supplier with the lowest cost as “primary” and the second lowest price supplier as “secondary”. Assigning 90 over 100 of demand to primary supplier and the rest of 10 to the secondary supplier.

Table 1 Information of parameters in 10 datasets

 Dataset Number of Suppliers Number of Manufacturers Number of Sub-suppliers 1 3 1 4 2 5 1 6 3 7 1 8 4 9 2 11 5 10 2 12 6 12 2 13 7 13 3 14 8 14 3 15 9 15 3 15 10 17 3 18

Table 2 Results of 10 datasets

 Dataset Purchasing Price from Primary Supplier hi of Primary Supplier Number of Orders from Primary Supplier Purchasing Price fromSecondary Supplier hi ofSecondary Supplier Number of Orders fromSecondary Supplier Total Price 1 105 200 90 107 200 10 10920 2 104 199 90 108 201 10 10840 3 102 197 90 107 200 10 10647 4 101 196 90 106 199 10 10545 5 100 195 90 106 199 10 10454 6 97 192 90 105 198 10 10170 7 96 191 90 105 198 10 10079 8 96 191 90 104 197 10 10068 9 94 189 90 104 197 10 9886 10 93 188 90 104 197 10 9795

After running the program of the selected sample datasets, we had the minimum feasible objective value for each dataset. The objective value includes the total purchasing costs and the initial contract costs from the two suppliers. The observation from the selected datasets is presented in Table 1. Moreover, Figure 2 shows the results of the selected sample datasets which by adding the number of candidate suppliers, the amount of total cost either decreases or stays the same value. We can interpret this tendency as follows. As we know by adding the number of suppliers, the SC network will be bigger. Consequently, the supplier selection will be more flexible. Apparently, there is a direct relationship between the number of suppliers and number of sub suppliers. When there is a limited number of candidate suppliers, then the selection will be limited. Once the number of suppliers increases, number of sub suppliers grows as well. Knowing that supplier selection of this model is selecting two suppliers which are not sharing the same sub supplier. By adding the number of candidate suppliers, the number of sub suppliers increases as well. Therefore, the supplier selection in this model will be more flexible. Thus, the model will have more options to select with broad cost options, and finally, the total cost will be lower. As it is shown in Figure 2, in general, by increasing the number of candidate suppliers, the amount of total cost decreases.

Figure 2 Total cost variation by adding suppliers.

Table 3 Cost variation within three steps of SCRM

 Dataset Total Cost Before Step 1 Total Cost AfterStep 1 Total Cost AfterStep 2 Total Cost AfterStep 3 Increasing Rate ofStep 1 Increasing Rate of Step 2 Increasing Rate of Step 3 1 10700 10902 10906 10920 0.0189 0.0004 0.0013 2 10599 10804 10806 10840 0.0193 0.0002 0.0032 3 10397 10602 10602 10647 0.0197 0.0000 0.0043 4 10296 10500 10504 10545 0.0198 0.0004 0.0040 5 10195 10400 10402 10454 0.0201 0.0002 0.0051 6 9892 10098 10098 10170 0.0208 0.0000 0.0073 7 9791 9998 10000 10079 0.0211 0.0002 0.0081 8 9791 9996 9996 10068 0.0209 0.0000 0.0074 9 9589 9796 9798 9886 0.0216 0.0002 0.0092 10 9488 9696 9698 9795 0.0219 0.0002 0.0102

Figure 3 Increasing ration of the total cost while applying SCRM in 3 steps.

### 3.2 Cost Variation

Moreover, we break down the model into three steps. Step one is adding double sourcing constraint (Constraint 5). Step two is adding constraint number 6 which assigns as the two selected suppliers should not share the same sub supplier. Our motivation to consider disruption in multi layer supply chain is a paper analysing Toyota industry’s problem after tsunami occurred in 2011 [17]. This paper focuses on a case of supply disruption of the automotive microcontroller units supplied to Toyota via its first tier suppliers. As we know Toyota stopped production for sometimes after the big tsunami in 2011 in Japan, since some functions were missing in the supply chain coordination mechanism of Toyota Production System. It was because there was a close interaction between the successive layers of its multi-layered supplier network. This case analysis implied that not only the first tier suppliers but also their sub suppliers (second tier supplier) need to be controlled. The strategy to control the second tier supplier is applied in step 2 of the proposed model. Step three includes the constraint number 7, while parameter “k” is set to 10. The results of numerical examples show that the most percentage of increasing is in step 1, then in step 3 and the least is in step 2. Step 1 includes the major increasing, mostly because of the initial contract cost parameter(hi). Table 3 shows the objective value of 10 datasets and its variation in three above-mentioned steps. Following the table, Figure 3 depicts the increasing ratio of the cost in three steps following the same data in Table 3. As it is shown in Figure 3, the constraint that we considered for sub-suppliers (Constraint 6), has the least (Around 1%) of affect in total increasing rate of cost.

## 4 Conclusion

In this paper, we proposed an optimization approach for managing supply chain risk. After reviewing the state of art in SCRM, we selected multiple sourcing strategy as one of the SCRM strategies. We applied double sourcing as the base of SCRM strategy in our model. Moreover, we avoided the risky situations when both suppliers have the single point for disruption. In the proposed model, we restricted the supplier selection by considering the risk in second tier suppliers. We examined the model by various datasets. We examined ten datasets with different data sizes. The results of the sample datasets showed the variation of total cost by adding candidate suppliers. Besides, we considered the model with three steps of implementation of SCRM methods and we noticed that the main increase in total cost occurs after the first step.

In our future work, we aim to add the demand risk of manufacturer to the current model. Moreover, by considering more criteria, we plan to design more robust SC. The proposed model can be extended to multi objective function by considering more important parameters and strategies of SCRM.

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## Biographies

Zohreh Khojasteh-Ghamari received the B.Sc. in Information Technology (IT) Engineering from Tabriz, Iran in 2009. She received MS in Computer Science from Ca’ Foscari University of Venice, Italy in 2014. Currently, she is a Ph.D. candidate in graduate school of green science and engineering, Sophia University, Tokyo, Japan.

Takashi Irohara received the B.E., M.E., and Doctor of Engineering degrees from Waseda University, Japan, in 1993, 1995, and 1998, respectively. Since 2010, he has been working as a professor at the Department of Information and Communication Sciences, Faculty of Science and Technology, Sophia University, Japan. He has published over 60 reviewed journal papers in the area of facility logistics (order picking, inbound/outbound truck scheduling in the warehouse, facility layout problem, material handling), supply chain management (inventory control, transportation, and vehicle routing problem), production scheduling and humanitarian relief logistics. He served as a board member of Japan Industrial Management Association, Japanese Material Handling Society and APIEMS (Asia Pacific Industrial Engineering and Management Systems Conference).