Mathematical Problems in Engineering

Volume 2017 (2017), Article ID 4541914, 9 pages

https://doi.org/10.1155/2017/4541914

## A Multicriteria Decision Model for Supplier Selection in a Food Industry Based on FITradeoff Method

Center for Decision Systems and Information Development (CDSID), Universidade Federal de Pernambuco, Av. Acadêmico Hélio Ramos, s/n, Cidade Universitária, 50740-530 Recife, PE, Brazil

Correspondence should be addressed to Eduarda Asfora Frej

Received 16 May 2017; Revised 9 August 2017; Accepted 6 September 2017; Published 19 October 2017

Academic Editor: Josefa Mula

Copyright © 2017 Eduarda Asfora Frej et al. 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

This article puts forward a decision model for solving a supplier selection problem in a food industry by considering multiple objectives that influence the decision-making process. In times of increasing competitiveness, companies strive hard to improve their profitability, and selection of supply sources may help if an appropriate decision is made through a well-structured decision-making process. Preference modeling is conducted in a flexible and interactive elicitation manner with the decision-maker (DM), aided by FITradeoff method. Partial information is gathered about the DM’s preferences in such a way that less effort is spent on finding a final solution for the problem.

#### 1. Introduction

One of the main decision-making problems faced by organizations is the supplier selection problem. How to select supply sources is a strategic decision for companies, since doing so successfully enables them to reduce their costs and improve profits [1]. Choosing a source of supply is one of the most critical activities of supply chain management, because a wrong choice can lead the supply chain as a whole to suffer losses and thus this would directly affect the performance of the organizations involved. On the other hand, appropriate decisions can reduce purchasing costs, decrease production lead time, increase customer satisfaction, and strengthen the competitiveness of organizations [2].

Companies frequently misunderstand the supplier selection problem as a single-criterion decision-making problem, taking into account only cost factors when making decisions. This approach is inefficient, since there are other quantitative and qualitative factors that should be considered. Tradeoffs between multiple and conflicting objectives have to be made in order to select the best supplier [3].

Several supplier selection problems are addressed in the literature as multiple criteria decision-making problems. Ho et al. [4] review the main MCDM approaches for supplier selection problems between 2000 and 2008. Chai et al. [5] provide a guide to studies on supplier selection with MCDM from 2009 to 2012 based on four aspects: decision problems, decision-makers, decision environments, and decision approaches.

In this context, this article sets out to build a multicriteria decision model to solve a supplier selection problem in a food company by considering a purchasing manager’s preferences in order to select a source of supply for packaging material of a new product that the company is going to start manufacturing. Preference modeling is conducted through a compensatory approach, aided by the Flexible and Interactive Tradeoff method, FITradeoff [6].

The FITradeoff method was developed to elicit criteria weights within the scope of Multiattribute Value Theory [7] in a structured way, based on tradeoffs. The main feature of this new methodology compared to the traditional tradeoff elicitation procedure is that FITradeoff works with partial information about the DM’s preferences and thus it requires less cognitive effort from the DM during the elicitation process [6]. Partial information approaches for MCDM were mainly developed by the fact that the information required by traditional methods can be tedious and time-consuming [8], and the DM may not be willing to give information in the detailed way required [9]. There are several ways of dealing with partial information provided by the DM in the elicitation process. Dominance intensity methods consider the information given by DMs to run linear programming problems so as to build a pairwise dominance matrix and thus rank the alternatives based on incomplete information regarding criteria weights [10–12]. The FITradeoff method works based on the concept of potential optimality in order to choose the best alternative in a determined set of possible actions, based on tradeoff judgments given by DMs. FITradeoff improves the applicability of the traditional tradeoff procedure [6], providing an easier decision-making process. The elicitation is conducted interactively with the DM through a Decision Support System, which provides graphical visualization to help the DM in the analyses of partial results. More details about this MCDM method are provided in Section 3.

This paper is organized as follows: Section 2 presents a brief literature review about MCDM approaches for supplier selection problems; Section 3 explains how the FITradeoff method works for aiding MCDM problems; Section 4 sets out the multiple criteria model for supplier selection and describes the application in a food industry; and finally some conclusions regarding this application are discussed in Section 5.

#### 2. Literature Related to Supplier Selection Problems

Most organizations that produce goods or services, at some point in the process, need some components that they do not produce internally. When such situations happen, a purchasing process must be started. According to Slack et al. [13], despite the variety of purchasing activities inside organizations, five performance objectives should always be taken into account, quality, speed, credibility, flexibility, and price, in order to ensure that suppliers’ systems and performance are in accordance with the objectives of the organization.

The high dependency between organizations regarding the purchasing process makes supplier selection a strategic process for organizations. Organizations seek long-term relationships with their suppliers, based on trust and commitment, so that favorable results can be achieved jointly. Despite the strategic importance of the supplier selection process, many organizations still limit themselves to evaluating the price performance goal as the sole determiner when choosing a supplier. The evaluation of this single criterion, however, is not the most adequate approach, since many other factors must be taken into account for the selection process to be effective [1]. Weber and Current [14] list at least twenty-three criteria that can be considered when it comes to supplier selection problems.

Therefore, it can be observed that supplier selection problems have two main characteristics: they are strategically important and complex. These situations are characterized as problems where at least two alternatives of action are driven by the desire to meet multiple objectives that often conflict with each other, categorized as multicriteria decision problems [15].

In this context, several supplier selection problems in the literature are tackled within a multiple criteria approach, and different MCDM methods are applied to evaluate the alternatives, according to the DM’s preference structure, in the context of the problem [15]. Some of these MCDM approaches to supplier selection problems are discussed below.

Regarding the decision actors of the process, either a unique DM or a group of them may be involved in supplier selection problems. As to selecting a single supplier, Dweiri et al. [16] propose a decision support model to solve a supplier selection problem in the automotive industry in Pakistan based on the Analytic Hierarchy Process (AHP). Within a group decision-making context, Li et al. [17] approached a cloud service supplier selection problem based on AHP and TOPSIS methods.

Supplier selection problems can be present in both certainty and uncertainty environments. An uncertainty environment was approached by Çakır [18] who proposes a supplier selection model involved in a decision process with imprecise and subjective information; in this paper, an algorithm based on Fuzzy Analytic Hierarchical Process (FAHP) and Choquet Fuzzy Integral (CFI) methods is developed. In the same way, Dursun and Karsak [19] propose a fuzzy multicriteria group decision approach for supplier selection based on Quality Function Deployment (QFD) and the Fuzzy Weighted Average (FWA) method for dealing with imprecise and subjective information.

A supplier selection situation can be involved in an environment of risk operations. Xiao et al. [20] propose a decision model to solve a supplier selection problem under operational risks based on integrating a Fuzzy Cognitive Map (FCM) and a fuzzy soft set model with the Analytic Network Process (ANP).

As a result of the growing concern about environmental issues, Hamdam and Cheaitou [21] presented a multicriteria decision problem to deal with green supplier selection based on combining two MCDM methods: fuzzy TOPSIS and AHP. In the same way, Kannan et al. [22] approached Green Supply Chain Management (GSCM) in a multicriteria decision problem to select the best green supplier for a plastics manufacturer in Singapore, using Fuzzy Axiomatic Design (FAD). Another green supplier selection problem was approached by Tsui and Wen [23] within a group decision-making context.

A noncompensatory rationality was considered by Gonçalo and Alencar [24] who proposed a multicriteria decision support model for supplier selection which had two phases: the analysis of suppliers’ products/services that needed to be evaluated using the PROMSORT method and the analysis of suppliers whose products/services are considered crucial using PROMETHEE II. Awasthi et al. [25] presented a multicriteria decision-making approach using the TOPSIS method with partial information.

Therefore, due to their strategic importance for organizations, supplier selection problems need to be modeled carefully, by considering the particular and individual issues related to each specific situation. In this context, this study aims to model a supplier selection problem of packaging material in a food industry within a multiple criteria approach, considering a compensatory rationality for modeling the decision-maker’s preferences with FITradeoff method. This new partial information method was also applied by Henriques de Gusmão and Pereira Medeiros [26] for selecting a strategic information system.

#### 3. FITradeoff Method

The Flexible and Interactive Tradeoff (FITradeoff) method [6] was developed for eliciting scale constants of criteria (for simplicity’s sake, in this paper, sometimes the expression* criteria weight* is used but with meaning of scale constant) within the scope of Multiattribute Value Theory (MAVT), in which alternatives are scored straightforwardly according to the value function in the following equation:

This new method incorporates the axiomatic structure of the traditional tradeoff procedure [7] but improves its applicability for the DM: the information required by FITradeoff is cognitively easier to provide, because this new method works with partial information about the DM’s preferences, searching for potentially optimal alternatives inside a space of weights, by solving linear programming problems (LPP) [6].

Considering a multicriteria decision problem with alternatives and criteria and a DM with a compensatory rationality, the FITradeoff method follows the steps that are described below.

The first step is for the DM to rank the criteria weights. This step is conducted in the same way as in the traditional tradeoff procedure [7]. Thus, considering as the most preferable criteria and as the least preferable criteria, the following relationship is obtained after this step:

After this information has been provided, a preliminary weight space (2) is obtained. Thus, the potential optimality of each alternative will be verified by linear programming problems in order to identify which alternatives are dominated (and thus eliminated from the decision process) and which ones continue in the process as potentially optimal alternatives for the problem. An alternative is potentially optimal if its value in (1) is greater than or equal to the values of all other alternatives for at least one vector of weights inside the weight space [6]; that is, an alternative is potentially optimal if the following inequality is satisfied:

In order to verify the potential optimality of an alternative at this point, the value of is maximized by an LPP model with the objective function in (4) (where the decision variables are the scale constants ) subject to the constraints in (2) and (3) and considering nonnegative and normalized weights.

If the LPP model for alternative has a feasible solution, then is potentially optimal for the problem; otherwise, is eliminated from the decision-making process.

After running the LPP model for all alternatives, if only one alternative is found to be potentially optimal, then a single solution for the problem has been found and the process finishes at this point. Otherwise, the DM proceeds to the next step: he/she starts answering elicitation questions by considering tradeoffs between consequences.

In this next step, the DM compares two fictitious consequences, considering tradeoffs amongst criteria [6]. An interesting point to highlight here is the fact that the comparisons are made based on strict preference statements, unlike what happens in the traditional tradeoff procedure, in which the DM is required to specify the exact point at which two consequences are indifferent for him [7].

The main feature of FITradeoff compared to the traditional tradeoff procedure is the absence of specifying an indifference point (. In FITradeoff, points above () and below () the indifference value can be found, depending on the answeres given by the DM in the elicitation questions. It is cognitively difficult for the DM to specify indifference relations between consequences, so that a high inconsistency rate is observed when applying the traditional tradeoff procedure [27]. Strict preference statements are easier to provide, and thus a reduction in inconsistencies is expected when applying FITradeoff [6].

Therefore, rather than obtaining equations from indifferent statements, FITradeoff works with partial information in the form of inequalities (5) and (6) obtained from strict preference statements given by the DM.

These inequalities, jointly with (2), form the new updated space of weights. At this point, the LPP model is run again with (5) and (6) as new constraints, with a view to finding the new set of potentially optimal alternatives for the problem, based on the updated weight space.

In the FITradeoff method, after the DM gives each answer, a new inequality of type (5) and/or (6) is obtained, such that the weight space is updated and the LPP is run again, thereby seeking to find potentially optimal alternatives. This interactive process goes on until a unique solution is found or until the DM is not willing to give additional information [6].

The elicitation of FITradeoff is conducted with the DM by means of a Decision Support System (DSS). The DSS provides the DM with a graphical visualization of the partial results, so that he/she can better analyze and compare the performances of the current potentially optimal alternatives. At this stage, if these partial results are already sufficient for his/her purposes, the DM has the flexibility to stop the process before the elicitation ends and keeps the partial results. Otherwise, the DM continues answering questions until a unique solution is found or until he/she is no longer able to provide more information. The FITradeoff process is summarized in Figure 1.