Joint Economic Lot Sizing Optimization in a Supplier-Buyer Inventory System When the Supplier Offers Decremental Temporary Discounts

Abstract

This research discusses mathematical models of joint economic lot size optimization in a supplier-buyer inventory system in a situation when the supplier offers decremental temporary discounts during a sale period. Here, the sale period consists of n phases and the phases of discounts offered descend as much as the number of phases. The highest discount will be given when orders are placed in the first phase while the lowest one will be given when they are placed in the last phase. In this situation, the supplier attempts to attract the buyer to place orders as early as possible during the sale period. The buyers will respon these offers by ordering a special quantity in one of the phase. In this paper, we propose such a forward buying model with discount-proportionally-distributed time phases. To examine the behaviour of the proposed model, we conducted numerical experiments. We assumed that there are three phases of discounts during the sale period. We then compared the total joint costs of special order placed in each phase for two scenarios. The first scenario is the case of independent situation – there is no coordination between the buyer and the supplie-, while the second scenario is the opposite one, the coordinated model. Our results showed the coordinated model outperform the independent model in terms of producing total joint costs. We finally conducted a sensitivity analyzis to examine the other behaviour of the proposed model.

Keywords: supplier-buyer inventory system, forward buying model, decremental temporary discounts, joint economic lot sizing, optimization.