Mathematical Problems in Engineering

Volume 2017 (2017), Article ID 7430248, 9 pages

https://doi.org/10.1155/2017/7430248

## Supplier Selection by Coupling-Attribute Combinatorial Analysis

School of Management, The State Key Laboratory for Manufacturing System Engineering, Xi’an Jiaotong University, Xi’an, China

Correspondence should be addressed to Xinyu Sun

Received 14 May 2017; Revised 5 September 2017; Accepted 14 September 2017; Published 25 October 2017

Academic Editor: Danielle Morais

Copyright © 2017 Xinyu Sun. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Increasing reliance on outsourcing has made supplier selection a critical success factor for a supply chain/network. In addition to cost, the synergy among product components and supplier selection criteria should be considered holistically during the supplier selection process. This paper shows this synergy using coupled-attribute analysis. The key coupling attributes, including total cost, quality, delivery reliability, and delivery lead time of the final product, are identified and formulated. A max-max model is designed to assist the selection of the optional combination of suppliers. The results are compared with the individual supplier selection. Management insights are also discussed.

#### 1. Introduction

Managing the outsourcing process productively is the key to enhancing competitiveness because for every dollar an industrial company generates, 50 to 90 cents are spent on purchasing [1]. Selecting the right outsourcing suppliers becomes essential in shaping company performance. Supplier selection is the process by which suppliers are reviewed, evaluated, and chosen to become a part of a company’s supply chain [2]. Several reviews have been published recently to summarize research development in this area [3–7].

A company’s primary supply chain goal is to efficiently and effectively provide the required products for its customers. To meet the customer-specified criteria to achieve this aim, a company must choose the best suppliers in order to produce the best finished products. A number of publications have focused on the development of various methodologies to select individual suppliers [3, 7]. Most of these publications have assumed that the best supplier combination is composed of the best suppliers of different parts/components, which are evaluated and selected individually. However, this assumption may not apply to all situations. This paper explains the reasons for this and focuses on the following two issues to be considered when evaluating suppliers.

First, the interdependencies between different products and components can affect the choice of suppliers. Synergies may apply when the suppliers that are selected aggregately for a group of products or components outperform the suppliers that are selected separately for individual products or components. With synergy, both buyers and suppliers can be more profitable. One research direction of this synergy is the combinatorial auction, which considers economies of scale and scope. The basic motivation of utilizing a combinatorial auction is the presence of complementarities among items supplied by different suppliers [8]. The most relevant research to our study is the Giacon et al. [9] study, which proposed a combinatorial optimization model that combines multicriteria value analysis for evaluating the trade-offs among the defined criteria. Nobar and Setak [2] presented two layers of suppliers and studied the correlations between price and quality on supply chain performance. Rothkopf et al. [10] studied simultaneous auctions in which the value of assets to a bidder depended on other assets that the bidder won, and they pointed out that the bid for combinations of assets might be beneficial to total revenue. However, so far, there has not been an attempt to quantify the degree to which the synergies are present among the components and attributes. We fill this gap by offering a max-max model that is designed to facilitate the selection of the optional combination of suppliers. The synergies are identified using coupled-attribute analysis. As the coupling attributes of the parts/components affect the attributes of the finished product, the best supplier combination should be considered as a whole rather than individually. Otherwise, the trade-offs and synergies are overlooked.

Second, the literature pointed out that a different production mode (i.e., made to order (MTO) or made to stock (MTS)) has different supplier selection criteria [11]. The more complicated supply network is the combination of MTO and MTS [11]. The production mode has an impact on the supplier selection, and the existing suppliers can affect the selection of the production mode reciprocally. The supplier with a long delivery time may change the production mode from MTO to MTS since the supplier cannot quickly respond to the market. Thus far, there has been no attempt to investigate the synergies of the suppliers with different lead times on the production mode. This paper calculates the production time under the defined supply structure, the lead time of suppliers, and the production mode. We investigate the effect on the production mode when selecting a supplier using the different experimental scenarios.

We believe that this work contributes to several areas. First, we aim to develop an analytical model considering the synergies among product components and supplier selection criteria under the production mode framework, thus enhancing the effectiveness of supplier selection. This paper integrates combinatorial optimization with coupling attributes of the final product, which is the real objective of the end user. It also investigates the balance between component attributes and its effect on the production mode when selecting a supplier. Second, we apply the model to a real case and show it to be an appropriate methodology for evaluating suppliers. The results let practitioners know the importance of balance between suppliers. We structure the rest of this paper as follows: Section 2 cites the relevant literature. Section 3 gives the supplier combinatorial selection methodology. We apply this methodology to a real case in Section 4; we also provide a scenario analysis and some managerial insights. Finally, we offer some concluding remarks in Section 5.

#### 2. Literature Review

The supplier selection literature contains much research studying selection criteria. Dickson [12] pointed out that cost, quality, and delivery performance are the three most important criteria that should be considered for supplier selection. Weber et al. [13] and Sun et al. [14] confirmed these criteria based on empirical data collected from purchasing managers and Chinese companies, respectively. Lin and Kuo [15] stated the supplier’s product quality is one of the three most frequently used criteria for selection, the others being delivery time and cost [7, 16, 17]. In this paper, we also focus on cost, quality, and delivery performance. In terms of cost, quantity, and business volume, discounts are common topics when a range of products is to be purchased, and linear programming is a common method to deal with the related problems.

Several approaches and techniques have been developed to determine an effective supplier selection process. According to Chai et al. [18] and Ho et al. [7], the most common approaches for this type of supplier selection are analytic hierarchy process [19] and data envelopment analysis [20], which are followed by mathematical programming, linear programming [21], case-based reasoning (CBR), ideal solution [22], analytic network process [23], fuzzy set theory [24], simple multiattribute rating technique (SMART), and genetic algorithm (GA). All these methods consider only suppliers, so some limitation exists in reflecting the harmony of the supplier, demand, and operational policies. Moreover, these methods require additional information or assumptions, such as a joint probability density function, accurate transformation function, and normality assumption.

Much attention has been given to the coordination between procurement and production planning or intervention of suppliers to develop supply chain management systems. Cook et al. [25] have developed a DEA method for supply chains with intervened inputs and outputs. Chen and Yan [26] have proposed DEA approaches with centralized, decentralized, and mixed decision makers. Park et al. [27] have proposed a stochastic simulation-based DEA approach to the vendor selection problem, in which a DMU is assigned as a supply chain instead of an individual vendor. This proposed approach, adopting a stochastic simulation scheme, helped the purchaser choose a proper set of vendors with a holistic perspective. Although these DEA methods are advantageous for assessing structural efficiency, the approaches can handle only simple structures such as a two-echelon model with a buyer and two suppliers and product flows in an assembly perspective. Hlioui et al. [24] have proposed to integrate replenishment, production, quality control, and supplier selection decisions for a manufacturing-oriented supply chain under a combination of mathematical formulation, simulation, and optimization techniques. Asadabadi [28] proposed a method that takes into account customer needs as a determinant factor in finding the best supplier and considers possible changes in the priorities of customer needs as time passes. Chen and Zhang [29] proposed a stochastic framework to determine the optimal production control policy and supplier selection procedure for a three-echelon supply chain. All these studies have shown that supplier selection must not be studied separately from the sole supplier and production system. However, only a few of them include holistic effects of ordered items among the supplier selection criteria. Moreover, they do not consider any production mode strategy for the supply chain management.

#### 3. Coupling Attributes Combinational Analysis

##### 3.1. Formulation of the Problem

We evaluate the impacts of different supplier combinations on the finished product performance and identify the optimal combination with the highest performance level. To facilitate the presentation, we summarize Notation and Symbols Used in Section 3.1.

Suppose that there are types of components and each component has suppliers. possible supplier combinations can be obtained. Let denote the set of all types of components, . Any represents a vector of a supplier combination. The problem of finding the optimal combination can be formulated as , where represents the finished product performance of a supplier combination. The performance is related to the attributes of the suppliers in the combination.

Considering the productivity of supplier combination, the attributes of the final product can be classified as two types: (a) higher values, defined as outputs, which indicate better levels of performance such as product quality, and (b) lower price, defined as inputs, which indicate better levels of performance such as component cost. , defined as the ratio of weighted outputs to weighted inputs, is maximized and minimized to obtain a set of dual productivity scores in each combination [30], as follows:

For each ,where represents evaluation of the supplier combination, and each unit has inputs and outputs of supplier combination. represents the value of the th output; stands for the th input for combination; , signifies the weight given to the th output; and denotes the weight given to the th input. The supplier combination consumes an amount of input and produces an amount of output , which can be incorporated into an efficiency measure, the weighted sum ratio. This definition requires a set of factor weights and , which are the decision variables.

Each supplier combination is assigned the highest possible efficiency score by choosing the optimal weights for the outputs and inputs [31]. The term* combinatorial analysis *is used to describe the mechanism that simultaneously selects a supplier from the supplier list for each component. The supplier’s determination is the problem of finding a maximum allocation with respect to the objective , which is also a maximum function (2) conditional on from 1 to . Therefore, the problem is defined as the* max-max* approach.

Constraints (5) and (6) reveal that at least the threshold of all the inputs and outputs should be satisfied. In retail, for example, the total delivery lead time should not be more than seven days if the retail shop promises that its products will reach its customers no later than seven days after the order confirmation. The problem definition is similar to Charnes et al. [32]. The number of possible solutions of is and the computation scale to solve models (2)–(6) will increase very rapidly if there are many extreme components. However, our objective is to select the most efficient supplier combination , not to rank the combinations. It is very practical to develop a model to find the most efficient combination directly without assessing the performance of the other combinations. Wang and Jiang [33] proposed a mixed integer linear programming model to identify the most efficient decision-making unit. The most efficient supplier combination in models (2)–(4) can be found based on the following model proposed by Wang and Jiang [33]:where are binary variables, only one of which can take a nonzero value of one. The model contains () constraints and () decision variables. It aims at seeking a set of input and output weights to maximize the efficiencies of the whole supplier combinations. Based on model (7), only a mixed linear program needs to be solved.

In this paper, there are two inputs: final product cost and total delivery lead time. In addition, there are two outputs: final product quality and delivery reliability of final product. Cost and quality are key factors in evaluating the performance of finished products, whereas delivery lead time and delivery reliability are key supply chain management performance indicators. Their formulae are given in Section 3.2.

##### 3.2. Computation Method of Coupling Attributes

In this section, we define the inputs and outputs in models (2)–(6) as the coupling criteria. The value of a coupling criterion is affected by all suppliers in a supplier combination. It is evident that the purchasing costs of all components in a supplier combination are added together and become the total cost of the finished product. However, in general, the value functions are nonlinear. We describe the formulae of coupling criteria as follows.

###### 3.2.1. Total Cost

The purchasing cost of the finished product is , where and are the number of components and the number of components needed for a finished product, respectively, and is the unit purchasing price of component .

###### 3.2.2. Final Product Quality

The quality of the finished product is related to its components. We treat the finished product as a system, which may be composed of unreliable components. In order to analyze the system reliability and other related characteristics, we use reliability block diagrams (RBDs). RBDs are widely used in engineering and science for describing the interrelations among components [34]. A system can be classified as series, parallel, or mixed. In a series configuration, a failure in any component results is the failure of the entire system. Let us assume that the components of a computer, such as the motherboard, the hard drive, the power supply, and the processor, are arranged in a series. If the power supply does not work, the computer will not work. In other words, the system only works when all components work. System quality is calculated as , where is the quality of component , in terms of reliability rate.

In a parallel system, at least one of the units must succeed for the system to succeed. Units in parallel are also referred to as redundant units. Redundancy is a very important aspect of system design and reliability in that adding redundancy is one of several methods for improving system reliability. For example, in a computer with a redundant array of independent disks (RAID), there are many hard disks. To put it another way, if disk A, disk B, or any of the disks succeed, then the system succeeds. The system quality is then given by .

While many smaller systems can be accurately represented by either a simple series or parallel configuration, there may be larger systems that involve both series and parallel configurations in the overall system. Such systems can be analyzed by calculating the reliabilities for the individual series and parallel sections, respectively. Then, we combine them in an appropriate manner. Such a methodology is illustrated in the example shown in Figure 1. The system quality is then given by .