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The Joint Replenishment Problem with Cycle Time Constraints under General-Integer Policy

The joint replenishment problem (JRP) is to determine the replenishment cycle times of a group of items over an infinite planning horizon. We investigated the JRP with cycle time constraints under general-integer policy that are popular in industries and can be extended to minimum order quantity, delivery frequency, and storage capacity constraints. Based on our theoretical analysis on the optimality solution structures, we categorized the items into four types and developed an efficient algorithm for solving this constrained JRP. Our numerical experiments demonstrated that the proposed algorithm is effective and performs better than the existing approaches in the literature.