Inventory Model With Stochastic Price Discount And Special Replenishment

In the modern business environment, enterprises take a variety of methods to achieve competitiveness, and the price discount may be the most popular one. From the perspective of suppliers, the price discount can not only motivate retailers to make larger orders, but also help the supplier to reduce storage and clear stock to relieve their capital pressure. However, suppliers do not always have the incentive to provide the price discount since the price discount may be lead to the losses of his selling profit. Usually, the price discount occurs under some situations such as there being a large number of backlog of inventory by the end of a selling period or the enterprise facing a tight budget. This means that the occurrence of the price discount is an uncertain event.For the two-echelon supply chain consisting of a supplier and a retailer, we establish a stochastic short-term discount model. In this mechanism, the supplier may provide a price discount to the retailer with uncertainty at a definite future time, and if the discount takes place at that time, it will be lasted for a short time and the retailer has one-time ordering opportunity during the discount period. The retailer has to decide the order size before the special order, the special order size and time when the price discount takes place. In this paper, the expected increased profit relative to the EOQ model is the objective function, and the retailer’s optimal ordering policy should maximize the above function. Through the analysis of the model, we obtain the properties of retailer’s optimal ordering policy, and we give three heuristic inventory policies. Moreover, we derive an optimal replenishment policy for the retailer and present a solution method for the model. Numerical experiments on sensitivity analysis are given to illustrate the validity of the model. Concidering the supplier may make a constraint on the special order size, we further investigate the model when there is a constraint on the the special ordering quantity. We get the optimal replenishment policy through the model analysis and present an algorithm to make the model more in line with reality.