On the Interaction between Demand Substitution and Production Changeovers

This paper analyzes the trade-off between (demand) substitution costs and (production) changeover costs in a discrete-time production-inventory setting using a two-product dynamic lot-sizing model with changeover, inventory carrying, and substitution costs. We first show that the problem is polynomially solvable and then develop several insights into the behavior of such systems and identify strategies for effectively managing them. A key driver for the extent of substitution is the ratio of changeover cost to the substitution cost associated with mean demand. The interaction between changeovers and substitution is most prominent when this ratio is neither too high nor too low. Furthermore, the value of this ratio also influences the length of an appropriate rolling horizon; an increase in the value of the ratio signals an increase in the length of a near-optimal rolling horizon. We identify a complementary relationship between substitution and changeover costs: When the changeover cost is large, it is better to invest in reducing the substitution cost and vice versa. As the holding cost of the substitutable product increases, substitution is (respectively, changeovers are) utilized more when the changeover (respectively, substitution) cost is large.