Optimal Order and Production Quantity with Defective Items and Learning in Production for Finite Planning Horizon

In this paper, we propose an integrated supplier-retailer inventory model in which the production process is imperfect and the quantity of defective items is affected by learning effect, i.e., the percentage of defective items is changing over time. Our aim is to determine the retailer's optimal order cycle, the order quantity, and the supplier's optimal product quantity so that the supply system has maximum profit in finite planning horizon. A simple algorithm is designed to find the optimal solution for the supply chain. Several numerical examples are provided to illustrate the theoretical results and sensitivity analysis of the major parameters is presented.