A new normalized goal programming model for multi-objective problems: A case of supplier selection and order allocationby O. Jadidi, S. Zolfaghari, S. Cavalieri

International Journal of Production Economics


Solving a multi-objective mixed-model assembly line sequencing problem by a fuzzy goal programming approach

Babak Javadi, Alireza Rahimi-Vahed, Masoud Rabbani, Mostafa Dangchi

Computation of a multi-choice goal programming problem

Kanan K. Patro, M.M. Acharya, M.P. Biswal, Srikumar Acharya


A new normalized goal programming model for multi-objective problems: A case of supplier selection and order allocation

O. Jadidi a, S. Zolfaghari b,n, S. Cavalieri c a Department of Business Administration, Bergamo University, Via Dei Caniana 2, Bergamo BG, Italy b Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, ON, Canada M5B 2K3 c Department of Engineering, University of Bergamo, Viale Marconi 5, Dalmine BG, Italy a r t i c l e i n f o

Article history:

Received 19 February 2013

Accepted 6 October 2013

Available online 15 October 2013


Multi-objective supplier selection

Normalized goal programming

Compromise programming


Weighted goal programming

Min–max goal programming

Weighted max–min model a b s t r a c t

This paper models the problem of supplier selection as a multi-objective optimization problem (MOOP) where minimization of price, rejects and lead-time are considered as three objectives. The paper considers two different cases: (1) the crisp MOOP in which the goals of objectives are predetermined; and (2) the fuzzy MOOP in which the weights of objectives are predetermined. In both cases, the aim is to achieve some levels of consistency among different objectives. To do so, a normalized goal programming approach is developed and tested for both cases. In order to compare the effectiveness of the proposed method, a comparative analysis is presented which includes weighted goal programming, compromise programming, TOPSIS, weighted objectives, min–max goal programming and weighted max–min models. An illustrative example reveals that our proposed model is able to achieve the desirable consistency among all objectives. & 2013 Elsevier B.V. All rights reserved. 1. Introduction

In a purchasing department, one of the most important tasks is the selection of the right suppliers as it can meaningfully decrease the cost of purchasing and improve corporate competitiveness (Willis et al., 1993; Dobler et al., 1990; Xia and Wu, 2007). The literature shows that the cost of component parts and raw materials in manufacturing industries can equal up to 70% of the product cost (Ghodsypour and O’Brien, 1998). As carefully discussed by Aissaoui et al. (2007), purchasing decisions have six stages: (1) ‘make or buy’; (2) supplier selection; (3) contract negotiation; (4) design collaboration; (5) procurement; and (6) sourcing analysis. Stages 2, 5 and 6 are entirely the responsibility of purchasing departments (Aissaoui et al., 2007). In Stage 2, a set of suppliers are pre-evaluated and selected according to some criteria. For instance, only those suppliers may be pre-approved who have access to the needed technology for producing a product that meets the buyer's requirements. After Stage 2, the question that how much and who (from the set of pre-approved suppliers) should provide the buyer with the products arises. The literature shows that in order to answer this question, the problem can be formulated as a mathematical programming model to further assess the suppliers according to some important factors such as price, quality, delivery, market demand, and suppliers' capacity.

Decision makers (DMs) who may come from different roles (such as senior managers, production managers, and purchase managers), usually gather to evaluate suppliers (Demirtas and Ustun, 2008;

Jolai et al., 2011). Studies that answer this question (or address lot sizing) fall under Stage 5, so does our study in this paper.

The supplier selection in its nature is a multi-criteria decisionmaking (MCDM) problem since some conflicting criteria have influence on evaluation and selection of suppliers (Dickson, 1966; Aissaoui et al., 2007). By sending a questionnaire to 273 purchasing agents and managers in the United States and Canada,

Dickson (1966) identified and ranked 23 criteria for supplier selection problems (SSP). The top six criteria were respectively quality, delivery, performance history, warranty policy, production facilities and capacity, and price. The existence of various criteria with different importance contributes to the added complexity of

SSP (Wang and Yang, 2009). However in practice, the importance of those criteria may change from one industry to another. In the studies that have employed mathematical programming for SSP, price, defects and lead-time are widely used as the top three criteria influencing supplier selection (Roa and Kiser, 1980; Weber and Current, 1993; Ghodsypour and O’Brien, 1998; Kumar et al., 2004, 2006; Wadhwa and Ravindran, 2007; Amid et al., 2006, 2009, 2011). The reason for choosing these three criteria from the top six list presented by Dickson (1966) is mainly because they are readily quantifiable. Other criteria that appear in the top six list include performance history and warranty policy, which are

Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ijpe

Int. J. Production Economics 0925-5273/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ijpe.2013.10.005 n Corresponding author. Tel.: þ1 416 979 5000x7735; fax: þ1 416 979 5265.

E-mail address: zolfaghari@ryerson.ca (S. Zolfaghari).

Int. J. Production Economics 148 (2014) 158–165 primarily qualitative measures. In this paper, we also consider price, defects and lead-time as the objective of our model while the capacity of production facilities is considered as a constraint.

There exist two kinds of SSP: single- and multiple-sourcing scenarios. In the first scenario, almost all suppliers are capable of meeting the buyer's needs, and therefore, the buyer needs to select the best supplier. In the second kind, limitations on quality, capacity, price, delivery, etc. force the buyer to purchase the same item from more than one supplier. Applying multiple-sourcing scenario is a practical way for ensuring the reliability of a manufacturer's supply stream (Aissaoui et al., 2007). In multiplesourcing scenario, a buyer needs to make a decision on how much should be purchased from which supplier. DMs or managers usually make a decision analytically or intuitively (Simon, 1987;