Inventory decisions for a finite horizon problem with product substitution options and time varying demand

Abstract

• A finite horizon inventory model with product substitution is developed. • The demand for the two substitutable products is assumed to be time varying. • The conditions of existence and uniqueness of the optimal solution is found. • The order schedule for the two products that minimize the total cost is determined. • Numerical examples along with sensitivity analysis are also presented. The inventory control of substitutable products has been recognized as a problem worthy of study in the operations management literature. Product substitution provides flexibility in supply chain management and enhances response time in production control. This paper proposes a finite horizon inventory control problem for two substitutable products, which are ordered jointly in each replenishment epoch. Demand for the products are assumed to be time–varying. In case of a stock–out for one of the products, its demand is satisfied by using the stock of the other product. The optimal ordering schedule, for both products, that minimizes the total cost over a finite planning horizon is derived. Numerical examples along with sensitivity analyses are also presented.