Supplier selection with multiple criteria in volume discount environments

Supplier selection is a multi-criteria decision making problem which includes both qualitative and quantitative factors. In order to select the best suppliers it is necessary to make a trade-off between these tangible and intangible factors some of which may conflict. When business volume discounts exist, this problem becomes more complicated as, in these circumstances, buyer should decide about two problems: which suppliers are the best and how much should be purchased from each selected supplier. In this article an integrated approach of analytical hierarchy process improved by rough sets theory and multi-objective mixed integer programming is proposed to simultaneously determine the number of suppliers to employ and the order quantity allocated to these suppliers in the case of multiple sourcing, multiple products, with multiple criteria and with supplier's capacity constraints. In this context, suppliers offer price discounts on total business volume, not on the quantity or variety of products purchased from them. A solution methodology is presented to solve the multi-objective model, and the model is illustrated using two numerical examples.