Optimal inventory policies when stockouts result from defective products

Abstract

An implicit assumption underlying most inventory systems is that the lot ordered will not contain any defective, i.e., unsaleable items when delivered and so there will be no ‘shortages’ in the delivery in the sense that every unit of the product in the accepted lot is of perfect quality and therefore fully acceptable to the customers. Such an assumption is not always tenable in view of the extensive use of acceptance sampling by business and industry in the quality control process. The presence of defective items in the traditional inventory models which foresee no such possibility would certainly disrupt the systems in use, and consequently entail higher operating cost on the inventory management. With an aim to broaden the base of applications, and to demonstrate the impacts of the possible presence of defective products upon the structure and the cost of certain inventory systems, this paper extends two inventory models to the case where the proportion of defective units in the accepted lot is a random variable with known probability distributions. Optimal solutions to the modified systems are developed and comparisons with the traditional models are also presented via numerical examples.