Development of a Joint Economic Lot Size Model for Vendor-Buyer with Normal Demand and Empirical Delivery Time with Service level and Incremental Discount

This study addresses the single-product joint vendor-buyer lot-sizing problem with normal and empirical distributions for demand and delivery time respectively. A service level constraint is assumed for the buyer in which unsatisfied demand might be lost or backordered. The vendor produces products at a certain rate and as a fraction of the received order and, subsequently, ships the produced product to the buyer. The shipments are assumed to be equal in size. Also, to encourage the buyer to place further orders, the vendor adopts the incremental discount policy. The purpose is to determine the number of shipments delivered by the vendor to the buyer, as well as buyer’s reorder point, buyer’s order quantity, and buyer’s safety stock, so as to minimize the average costs incurred by both the buyer and the vendor. Once the problem has been formulated, the particle swarm optimization (PSO) algorithm was implemented to solve it.