An n items joint replenishment inventory problem is considered here, where the demand of eachuditems are constant and deterministic. A joint replenishment is conducted periodically every T time intervals.udHowever, all items may not be included in each replenishment. Item i is only included every ZiT time intervals.udReplenishment of item are instantaneous and contain of imperfect quality items. After screening, items ofudpoor quality are sorted, kept in stock and sold at a salvage value as a single batch within the replenishmentudcycle. Shortages are allowed and completely backordered with maximum backordering quantity Bi.udMathematical model is formulated in order to determining the basic time cycle T, replenishment multiplier Zi,udand backordering quantity Bi in order to maximize the expected total profit per unit time. A solutionudmethodology is proposed for solve the model and a numerical example is provided for demonstrating theudeffectiveness of the proposed methodology.
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