Globalization in our modern times is giving rise to a multitude of continual changes and developments in the business environment including regulatory changes, increasing competition intensity, increasingly demanding customers, new information technologies, mergers and acquisitions, among others. The supply chain management (SCM) is the term used to describe the management of materials and information across the entire supply chain, from suppliers to component producers, to final assemblers, to distribution (warehouse and retailers), and ultimately to the consumer. In fact, it often includes after-sales service and returns or recycling as well. Supplier selection and material procurement planning are the most important issues in supply chain management. This function involves evaluation of many factors such as, cost of parts/materials, size of order, quality, and delivery performance. Therefore, this problem is categorized as multi-criteria decision making problems. Different approaches have been applied in order to assess and select the suppliers when suppliers offer discount on the unit price. Price discounts provide a reduction in the price per unit as the number of units purchased increases. Large quantity orders lower the unit cost, but may increase inventory which conflicts with the financial department’s goal of investing fewer dollars in inventories. The introduction of price discounts complicates the determination of the optimal purchasing quantities with minimum cost for an item. It is the task of the purchasing department to evaluate all of the considerations and make profitable buying decisions under different conditions. In real situation, each supplier may apply different methods such as different types of discount schedules and various types of payment in order to increase market share. In this situation, buyers try to select the best supplier by considering all tangible and intangible factors which may be included in this decision problem. Besides in multi-period planning, inventory management may be considered as an important issue for supplier selection in lot sizing decision. A bi-objective model is proposed for multiple item multiple period supplier selection and lot sizing problem. This model includes all-unit discount, and delay in payments which ordinary may be proposed by each supplier. Traditionally, supplier selection should simultaneously take into account numerous heterogeneous criteria, and then is a tedious task for the purchasing decision makers. Under such manner, most studies often formulate such a problem as a Multi-Objective Linear Programming (MOLP) problem, This work applied a mixed integer programming approach to solve the sourcing and order allocation problem with multiple products and multiple suppliers in a supply chain. The decision process is driven by multiple objectives and a set of constraints. We used the weighted sum of objective functions since buyers usually look for a unique decision to follow. The problem is to determine which products to order in which quantities from which suppliers in which periods. Considering the complexity of these models on the one hand, and the ability of genetic algorithms to obtain a set of Pareto- optimal solutions, we apply a genetic algorithm to solve the model. Finally several sample problems have been solved by the proposed GA and the exact (branch and bound) method. The results illustrate slight relative errors to compare with reasonable saving in computational times.
