Solving inventory lot-sizing with supplier selection under alternative quantity discounts and vehicle capacity

Abstract

In this paper, we present a multi-product and multi-period inventory lot-sizing problem with supplier selection under alternative quantity discounts and vehicle capacity. Each supplier offers quantity discounts (all-units and incremental discounts) to motivate the buyer for purchasing large quantity. In addition, we consider that the capacity each vehicle of the supplier transport the products to the decision maker (buyer). The objectives are to minimise total costs, where the costs include purchase cost of the products, ordering cost for the suppliers, transportation cost for the suppliers and holding cost of the remaining inventory in each period. The problem is formulated as a mixed integer linear programming (MILP) model. Finally, a numerical example is provided to illustrate the solution procedure. The MILP model can provide a satisfactory solution with a very short elapsed runtime. The results, the buyer needs to determine what products to order in what quantities with which suppliers in which periods, in order to satisfy overall demand.