An operational consignment stock policy under normally distributed demand with controllable lead time and buyer’s space limitation

Abstract

This paper studies a vendor–buyer integrated inventory system with buyers’ variable demand and warehouse space limitation where the consignment stock (CS) replenishment operates under a controllable lead time. Within any cycle, the production rate, the number of shipments and the shipping size are all fixed. Based upon the CS policy, the vendor agrees to maintain the buyer’s inventory to be above a safety level and less than the buyer’s space limitation. Due to the uncertainty in the demand, shortages/over stocks are sometimes inevitable. In such cases, penalties are incurred to discourage such occurrence. The holding cost consists of a storage component and a financial component, and the lead time is controlled with an extra investment which is a function of both the shipment size and the reduced time. Two-constraint, five-variable mix-integer optimisation models are established to describe the CS system. Two doubly-hybrid meta-heuristic algorithms are employed to solve the models that are complex and difficult to solve with available techniques. Two numerical examples are used to illustrate the solution procedure and the analysis of the computational results reveals the effects of some important parameters used for the annual joint total expected cost of the integrated system. The computational efficiency and quality of the solutions are evaluated by comparing them with other existing and popular methods. The results founds in all comparative evaluation are very encouraging and competitive.