A multi-objective supplier selection model under stochastic demand conditions

doi:10.1016/j.ijpe.2006.03.001

International Journal of Production Economics

Volume 105, Issue 1, January 2007, Pages 150-159

https://doi.org/10.1016/j.ijpe.2006.03.001 Get rights and content

Abstract

Supplier selection is a typical multi-criteria decision problem attracting great attention recently. Cost, quality, delivery and flexibility are generally involved in the supplier selection decision making. In this paper, a measurement of supplier flexibility is extended to consider demand quantity and timing uncertainties comprehensively. A multi-objective supplier selection model is developed under stochastic demand conditions. Stochastic supplier selection is determined with simultaneous consideration of the total cost, the quality rejection rate, the late delivery rate and the flexibility rate, involving constraints of demand satisfaction and capacity. Using a problem specific genetic algorithm, computational results are presented.

Introduction

In the last several decades, the supplier (or vendor) selection problem has gained great attention in business literature and practices. It may be the most important decision made in the purchasing process (e.g. Weber et al., 1991, Nydick and Hill, 1992, Mobolurin, 1995). The supplier selection problem was defined as which supplier(s) should be selected and how much order quantity should be assigned to each supplier selected (Weber and Current, 1993).

Supplier selection is a typical multi-criteria decision problem. Twenty three selection criteria were identified in the vendor selection process (Dickson, 1966). The coverage of these 23 criteria was investigated in the literature published from 1966 to 1990, and it was found that price, delivery and quality were the most discussed factors (Weber et al., 1991). The importance of selection criteria was studied and the ranking was found to be quality, service, price and delivery (Wilson, 1994). The gap between the perception and the actual practice of selection criteria was investigated, in which price, quality, delivery and flexibility were the criteria studied (Verma and Pullman, 1998). The investigation revealed that flexibility attracted considerable attention in recent studies.

While earlier studies on flexibility focused on manufacturing flexibility, recent attention turned to that of supply chain (e.g. Vickery et al., 1999, Das and Abdel-Malek, 2003, Lummus et al., 2003, Wadhwa and Rao, 2004, Pujawan, 2004). Pujawan presented a framework for assessing the flexibility of a supply chain including the flexibility of product delivery system, production system, product development and supply system (Pujawan, 2004). It was put forward that the flexibility of the entire supply chain was a result of the flexibility of the supply chain components and their interrelationships (Lummus et al., 2003). Therefore, suppliers are supposed to provide enough flexibility to appropriately adjust their supply processes as demand conditions change, and thus to contribute to the flexibility of supply chains. A key problem is how to measure the flexibility of a supplier. A measurement was developed for supply chain flexibility between a supplier–buyer pair with consideration of demand quantity and timing reduction uncertainties (Das and Abdel-Malek, 2003). In this work, the measurement of supplier flexibility is extended to consider the uncertainty when the demand quantity is randomly raised.

A multi-objective supplier selection model was built under deterministic demand conditions assuming known and fixed demand quantity and timing, optimizing cost, quality and delivery (Weber and Current, 1993). Another extension in this paper is the development of a multi-objective supplier selection model under stochastic demand conditions with constraints of demand satisfaction and capacity, optimizing cost, quality, delivery and in addition flexibility.

The rest of the paper is organized as follows. Stochastic demand conditions and supplier flexibility are illustrated in Section 2. Model development is performed in Section 3. Genetic algorithm application is introduced in Section 4. A numerical example and computational results are reported in Section 5. Conclusions are finally drawn in Section 6.

Section snippets

Stochastic demand conditions and supplier flexibility

It was found that demand quantity and timing uncertainties were the two most common changes which occurred in supply chains and were often the causes of buyer–supplier grievance (Das and Abdel-Malek, 2003). Stochastic demand conditions are assumed to be modelled based on the available statistical data as follows:

D represents a stochastic demand quantity satisfying a normal distribution, $μ_{D}$ , $σ_{D}$ and $Φ (D)$ are the mean, the standard deviation and the probability density function of D; T represents

Model development

Notations for model development are as follows. $x_{i}$ is the order splitting ratio for supplier i; $y_{i}$ is the binary variable indicating whether supplier i is selected; $p_{i}, q_{i}, l_{i}, f_{i}$ are, respectively, the net purchasing price, the quality rejection rate, the late delivery rate and the flexibility rate of supplier i, $i = 1, \dots, n$ .

A multi-objective stochastic supplier selection model is developed as follows with constraints of demand satisfaction and capacity, optimizing cost, quality, delivery and

Genetic algorithm application

The developed multi-objective stochastic supplier selection model is a typical non-linear mixed integer combinatorial optimization problem. It involves 0–1 variables $y_{i}$ , continuous variables $x_{i}$ , non-linear cost function $Z_{1}$ and linear quality, delivery and flexibility functions $Z_{2}$ , $Z_{3}$ , $Z_{4}$ , equality constraint $\sum_{i = 1}^{n} x_{i} = 1$ and inequality constraints $x_{i} D ⩽ C_{i}$ , $i = 1, \dots, n$ .

Heuristic search methods, such as local search, simulated annealing, tabu search, or genetic algorithm, are often used to find optimal

Computational results

A numerical example is presented in Table 2, modified from the case study in the work of Das and Abdel-Malek (2003), including stochastic demand conditions and supplier data, in which $f_{i}$ is calculated through Eq. (2) (setting $W_{D} = 0.6, W_{T} = 0.4, a = 0.4, b = 0.3, c = 0.4, d = 0.3$ ). They are: $f_{1} = 56.80 %$ , $f_{2} = 62.07 %$ , $f_{3} = 55.08 %$ , $f_{4} = 56.40 %$ , i.e. $S_{2}$ is the most flexible supplier while $S_{3}$ is the least flexible one.

Computational results using the problem specific genetic algorithm are documented in Table 3. Five

Conclusions

This paper studies the supplier selection problem under stochastic demand conditions. Based on the work of Das and Abdel-Malek (2003), this paper extends the measurement of supplier flexibility to consider demand quantity reduction/increase uncertainties and demand timing reduction uncertainty. Additionally, this work extends the development of a multi-objective supplier selection model under stochastic demand quantity and timing conditions with constraints of demand satisfaction and capacity,

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A multi-objective supplier selection model under stochastic demand conditions

Abstract

Introduction

Section snippets

Stochastic demand conditions and supplier flexibility

Model development

Genetic algorithm application

Computational results

Conclusions

International Journal of Production Economics

International Journal of Management Science

European Journal of Operational Research

European Journal of Operational Research

European Journal of Operational Research

An analysis of vendor selection systems and decisions

Journal of Purchasing