| With globalization and the emergence of the extended enterprise of interdependent organizations, there has been a steady increase in the outsourcing of parts and services. This has led firms to give more importance to the purchasing function and its associated decisions. One of those decisions which impacts all firms'areas is the supplier selection. Since the 1950s, several works have addressed this decision by treating different aspects and instances. In this paper, we extend previous survey papers by presenting a literature review that covers the entire purchasing process, considers both parts and services outsourcing activities, and covers internet-based procurement environments such as electronic marketplaces auctions. In view of its complexity, we will focus especially on the final selection stage that consists of determining the best mixture of vendors and allocating orders among them so as to satisfy different purchasing requirements. 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. |