Multi-product and multi-period inventory lot-sizing with supplier selection under quantity discount

In this paper, we consider a multi-product and multi-period inventory lot-sizing problem with supplier selection under quantity discount. The suppliers are able to offer all-unit quantity discount in each product. The objectives are to minimise the total inventory cost, where the cost include purchase cost of the products, ordering cost for the suppliers, holding cost for remaining inventory and transportation cost for supplier. It is assumed that demand of multiple products is known over a planning horizon. The problem is formulated as a mixed integer programming (MIP) model and is solved with optimisation package like LINGO 12. Finally, numerical example is provided to illustrate the solution procedure. 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.