Dynamic Lot Sizing With Multiple Age‐Differentiated Demands of a Perishable Product

In this paper, we study a dynamic lot sizing problem in which a manufacturer produces a perishable product and supplies it to several customers, each having a different requirement on the product freshness and only accepting inventory stock whose age is not older than a customer‐dependent threshold. Both production and inventory holding cost functions are assumed to be concave. The manufacturer makes joint production and inventory allocation decisions to minimize the total cost. We explore structural properties and develop an optimal algorithm for solving the problem in polynomial time. More efficient optimal algorithms are also developed for two important special cases. We conduct computational experiments to demonstrate that the proposed algorithm significantly outperforms the commercial solver CPLEX. Through computational experiments, we also obtain managerial insights into the bottleneck customer, who has the highest freshness requirement.