Minimax Distribution-Free Procedure for Mixture Inventory Model with Variable Lead Time and a Service Level Constraint by Reducing Order Cost

Abstract

SYNOPTIC ABSTRACTAs supply chains have become more extended in recent years, coordination and information sharing among supply chain members to improve system efficiency have attracted much interest. In order to achieve a higher degree of coordination and automation among the supply chain parties, the supply chain sometimes invests in reducing the ordering cost to streamline and speed up transactions via the application of information technology. If the ordering cost per order could be reduced effectively, then the total relevant cost per unit time could be automatically improved. In this study, we investigate a continuous review inventory model involving controllable lead time for the mixtures of distributions of the lead time demand, subject to a service level constraint in order to accommodate more practical features of the real inventory systems. Further, ordering cost can be reduced by an investment in which the optimal inventory control approach is shaped to account for the service level restriction.We assume that any mixture of distribution functions of the lead time demand gives only known finite, first two moments, but its probability distribution is unknown, and we apply a minimax distribution-free procedure to find the optimal solution. Moreover, a computational algorithm with the help of a computer code using the software MATLAB 7.0 is developed to solve the problem. A numerical example is presented to illustrate the theoretical results, and a sensitivity analysis is performed with respect to the various system parameters. Through sensitivity analysis, some observations and managerial implications are presented.