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This paper considers the periodic-review stochastic joint replenishmentproblem (JRP) under Bookbinder and Tan's static-dynamic uncertainty controlpolicy. According to a static-dynamic uncertainty control rule, the decisionmaker fixes timing of replenishments once and for all at the beginning of theplanning horizon, the inventory position is then raised to a predefinedorder-up-to-position at the beginning of each replenishment period. In thispolicy, freezing the replenishment times ameliorates the inherent difficultiespertinent to replenishment coordination of multiple products, whereas dynamicorder quantities facilitate dealing with uncertain demands. We adapt and extendan earlier mixed integer linear programming (MILP) model for computingstatic-dynamic uncertainty policy parameters, and demonstrate that the same canbe used to approximate the optimal control rule for the JRP, also known as$(\sigma, \vec{S})$ policy. An extensive computational study illustrates theeffectiveness of our approach when compared to alternative approaches in theliterature.

An (R, S) Based Heuristic Model for the Stochastic Joint Replenishment Problem