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We study the joint replenishment problem (JRP) for M items under deterministic demand, with a minimum order quantity constraint for each item in the replenishment order. We first study an iterative procedure that proves to be not efficient in this case. Further, we derive bounds on the basic cycle time and propose an efficient global optimisation procedure to solve the JRP with constraints. Moreover, we also consider the case where a correction is made for empty replenishment occasions. The algorithms are tested in a real case.

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