A JOINT POLICY FOR PRICING, STATISTICAL INSPECTION AND LOTSIZING PLANNING PROBLEM

Due to the necessity of communication between production and marketing functions, joint lot size and pricing decisions play an important role in supply chain planning. Moreover in many real world problems there is a fraction of defective items in a received lot that their quality should be evaluated before storage. In this paper, we focus on the problem of simultaneously determining of optimal lot-sizing, pricing and inspection policy with and without replacement of nonconforming items for an inventory system in which demand is price sensitive. The proposed model is based on a maximization of total profit for buyer. It is assumed that the fraction of nonconforming items in a received lot follows a beta distribution and buyer conducts some kind of inspection policies, that include no inspection, inspection and sampling inspection. In addition, in sampling inspection manufacture's risk and the buyer's acceptable quality level are considered to obtain a fair sampling plan. We assume two standard demand functions which are linear and exponential function of price. We first study our NLP model mathematically and then we develop an analytical algorithm to solve the problem and obtain the optimal inventory -inspection-marketing policies. Finally numerical examples are presented to conduct a sensitivity analysis for important model parameters and to illustrate important issues about the developed models.