Single Item Supplier Selection and Order Allocation Problem with a Quantity Discount and Transportation Costs

In this paper, we address a single item supplier selection, economic lot-sizing, and order assignment problem under quantity discount environment and transportation costs. A mixed-integer nonlinear program (MINP) model is developed with minimization of cost as its objective, while lead-time, the capacity of the supplier and demand of the product are incorporated as constraints. The total cost considered includes annual inventory holding cost, ordering cost, transportation cost and purchase cost. An efficient and effective genetic algorithm (GA) with problem-specific operators is developed and used to solve the proposed MINP model.  The  model is illustrated through a numerical example and the results show that the GA can solve the model in less than a minute. Moreover, the results of the numerical illustration show that the item cost and transportation cost are the deciding factors in selecting suppliers and allocating orders. Keywords: Supplier selection, Economic Order Quantity, Order allocation, Mixed-integer nonlinear programming.