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the strengths of existing suppliers. Ng (2008) presented a weighted LP model for the supplier
selection problem and its objective is to maximize the supplier score. Hong, Park, Jang, and
Rho (2005) developed a mixed integer LP model for the supplier selection problem. The
model determines the optimal number of suppliers and the optimal order quantity so as to
maximize the revenue. A mixed integer non-linear programming model for the multi-
criterion sourcing problem was formulated by Ghodsypour and O’Brien (2001). The model
determines the optimal allocation of products to suppliers so as to minimize the total
purchasing cost. Karpak, Kumcu, and Kasuganti (2001) developed a goal programming
model for the supplier selection problem. The three goals considered in their model are cost,
quality, and delivery reliability. The model determines the optimal order quantity while
satisfying buyer’s demand and supplier’s capacity constraints. Narasimhan, Talluri, and
Mahapatra (2006) proposed a multi-objective programming model for selecting the optimal
suppliers and for determining the optimal order quantity. Wadhwa and Ravindran (2007)
formulated the supplier selection problem as a multi-objective programming model that has
three objectives: price, lead time, and rejects.
Although mathematical programming provides rich modeling capabilities for the
supplier selection problem, solving complex integer and nonlinear programs to obtain exact
solutions generally requires extensive computational efforts and one may need to rely on
state-of-the-art algorithms to efficiently solve practical instances. Moreover, some
mathematical models for the supplier selection problem involve the decision-makers in
determining the relative importance weightings of criteria in advance (e.g., Narasimhan et
al., 2006; Ng, 2008).
2.3 Analytic Hierarchy Process (AHP) and Analytic Network Process (ANP)
AHP, developed by Saaty (Saaty, 1980), is a prominent tool for MCDM. The decision-
maker is asked to give his/her judgment on the relative priority of one attribute (or criterion)
versus another (i.e., pairwise comparison). The subjective judgments are quantified in a
logical manner and used as the basis for reaching a decision. Its core determines the relative
weights of attributes for ranking the decision alternatives (Saaty, 2008).
There are a number of AHP applications for the supplier selection problem. Akarte,
Surendra, Ravi, and Rangaraj (2001) developed a web-based AHP system for evaluating the
casting suppliers with respect to 18 criteria. Muralidharan, Anantharaman, and Deshmukh
(2002) presented an AHP-based model for rating and selecting suppliers with respect to nine
criteria. Chan (2003) proposed an interactive selection model with AHP to aid decision-