Determination of Economic Production Quantity with Regard to Machine Failure

Abstract

In this paper, we study an economic production quantity (EPQ) problem in which an item is produced by a single machine. We assume that the machine may fail in an exponential random time. The repair time is an exponential random variable. It is possible to satisfy the demand from an outside supplier when the machine is failed. The objective is to determine the production and order quantities in each cycle time to minimize the total inventory cost included set-up, ordering, holding, lost sales, production, and purchase costs. Since the cost function is a nonlinear mathematical function we propose an algorithm based on differentiation to obtain the optimum solution.