An improved model for supplier selection under capacity constraint and multiple criteria

Ghodsypour and O'Brien [2001. The total cost of logistics in supplier selection, under conditions of multiple sourcing, multiple criteria and capacity constraint. International Journal of Production Economics 73(1), 15–27] study multiple sourcing problem with multiple criteria and capacitated suppliers. Considering the buyer's quality requirements as a constraint, they develop a mixed integer non-linear programming model to find the least-cost cyclic ordering policy for the buyer. They propose to solve the model by enumerating over all possible supplier combinations. Although the problem is interesting and their analysis is correct, we point out two issues with their assumptions, namely, capacitated suppliers and cyclic ordering policy. We discuss two different capacitated supplier settings: (i) long-run average annual capacity, and (ii) exact annual capacity. First, under long-run average annual capacity assumption we propose a model which provides the same or a better solution and is much easier to solve than their model. Then, we discuss how to modify our and their models to handle exact annual capacity assumption.