Abstract
We study a single‐period inventory planning problem for a category of substitutable products. This is an important practical problem facing category managers who have to maintain high service levels for constantly expanding product catalogs. We formulate the problem as a stochastic optimization model that minimizes the total stocking cost subject to service level requirements, which consist of product‐specific and category‐wide targets for inventory availability (ready rates) through the selling season. Our model accounts for stochastic customer arrivals, captures stockout‐based substitutions, and determines initial stocking quantities jointly for all products. Recognizing the challenges that these aspects pose in solving the problem, we propose an optimization‐based method that estimates the ready rates using a deterministic approximation and discretizes the selling season into a finite number of time intervals. This novel modeling approach permits us to recast the stochastic optimization model as a deterministic mixed integer linear program that can accommodate several common stockout‐based substitution schemes. We characterize the worst‐case behavior of this approach to develop performance guarantees. We also implemented and applied this model to randomly generated numerical instances featuring different types of product differentiation and varying in parameter values. We observe that the approach is robust to changes in problem parameter values and yields solutions very quickly, outperforming an enumeration‐based alternative, a practical heuristic, and an approach based on extant literature. Finally, we applied our approach to data from a re‐seller of Information Technology products. Results illustrate that our approach scales well and has the potential to generate savings in inventory costs.