Consider an N-item, periodic review, infinite-horizon, undiscounted, inventory model with stochastic demands, proportional holding and shortage costs, and full backlogging. For 1 ≤ j ≤ N, orders for item j can arrive in every period, and the cost of receiving them is negligible (as in a JIT setting). Every Tj periods, one reviews the current stock level of item j and decides on deliveries for each of the next Tj periods, thus incurring an item-by-item fixed cost kj. There is also a joint fixed cost whenever any item is reviewed. The problem is to find review periods T1,T2,...,TN and an ordering policy satisfying the average cost criterion. The current article builds on earlier results for the single-item case. We prove an optimal policy exists, give conditions where it has a simple form, and develop a branch and bound algorithm for its computation. We also provide two heuristic policies with O(N) computational requirements. Computational experiments indicate that the branch and bound algorithm can handle normal demand problems with N ⩽ 10 and that both heuristics do well for a wide variety of problems with N ranging from 2 to 200; moreover, the performance of our heuristics seems insensitive to N.
