Single Resource Multi-Item Inventory Systems

We consider two economic order quantity models where multiple items use a common resource. In the tactical model, the objective is to establish and coordinate order quantities to minimize total inventory ordering and carrying costs without ever exceeding a capacity constraint on the resource. In the strategic model, the objective is to establish and coordinate order quantities to minimize the average cost which includes in addition to the ordering and inventory costs, a cost proportional to the peak usage of the resource. The common resource may be space in an automated warehouse or total capital invested in inventory. We show that a lower bound on the peak resource usage, known for certain subsets of policies, is valid for any feasible policy. We use this to derive lower bounds on the optimum average cost for both models and show that simple heuristics for either model have bounded worst-case performance ratios. More sophisticated heuristics require an effort to solve the embedded staggering problem of time-phasing the arrival of the orders to minimize the maximum use of the resource. We develop a heuristic for the staggering problem and use it to obtain efficient heuristics for the strategic and tactical models.