Scatter search algorithm for supplier selection and order lot sizing under multiple price discount environment

Supplier selection is one the most important elements of 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. In practical conditions, buyers may face a situation where different types of discount may be offered by candidate suppliers. None of the previous studies have considered different discount schemes simultaneously. In this article a mathematical model is introduced which consider different types of discount (all-unit cost, incremental discount, and total business volume discount) through multi-objective formulation for single item purchasing problem. In addition, constraints such as suppliers’ capacity and demand are taken into consideration in the model. Due to the complexity of the problem a proposed scatter search algorithm (SSA) is presented to solve this problem. Finally several sample problems have been solved by the proposed SSA and the exact (branch and bound) method. The results illustrate slight relative errors to compare with reasonable saving in computational times.