The Scheduled Joint Replenishment Problem

In many complex, integrated transportation and production settings, determining when customers are replenished is a highly debated tactical-level decision, given the interests of various upstream and downstream supply chain processes. In operational reality, such a replenishment schedule is often determined exogenously. Based on these observations, we introduce the stochastic Scheduled Joint Replenishment Problem (S-JRP), an extension of the classical stochastic Joint Replenishment Problem (JRP) that accounts for realistic operational constraints by incorporating exogenously set schedules that determine whether a replenishment order can be placed at any given period. A key distinguishing feature is that these schedules are different for each retailer. We define such schedules as infinitely repeating cycles that correspond, for example, to a week or month, making the S-JRP an extension of the periodic JRP. We model the S-JRP as a Markov decision process and determine optimal policies using value iteration. To solve larger problem sizes, we propose a time period-dependent can-order policy. The policy prescribes, for each replenishment opportunity of each retailer, a reorder point, an order-up-to-level, and a can-order level, at which an order is placed only if another retailer orders. We find the best parameters for this policy via a tailored genetic algorithm. We benchmark our period-dependent can-order policy against the optimal policy and various established heuristics from the JRP literature. Results demonstrate that the period-dependent heuristic achieves only 0.61% higher costs per period than the optimal policy without sacrificing service levels, and it significantly outperforms established heuristics that are not tailored to the retailers’ individual replenishment opportunities. We also highlight the period-dependent can-order policy structure, which closely resembles the optimal policy structure. In an extensive numerical study with up to 30 retailers, we observe that the Genetic Algorithm consistently provides well-performing policy parameters, with running times proportional to the number of retailers.