A note on the can-order policy for the two-item stochastic joint-replenishment problem

In this paper, a two-item continuous-review inventory system is studied. Demands for item 1 and item 2 occur at epochs generated by independent Poisson processes. In addition to the standard cost structure, there is economy of scale in joint replenishment. For the continuous joint replenishment problem, the literature proposes the can-order policy. Under this policy, an order is triggered by item 1 at its demand epoch, when its inventory position falls to its reorder level. In this situation, if the inventory position of item 2 is at or below its ‘can-order’ level, item 2 is also included in this order and a discounted fixed ordering cost is charged for it. As a result, the inventory positions of both items are raised to their respective order-up-to levels. Reciprocally, the same procedure is valid at the demand epoch of item 2. In this study, this two-item inventory system is modeled as a semi-Markov decision process and a simple enumeration algorithm is proposed for its solution. We show that previous formulations of the problem do not necessarily converge to the best can-order policy by providing numerical examples.