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