Coordinated replenishments in inventory systems with correlated demands

Demand correlation among different inventory items is common in real‐life multi‐item inventory systems. However, this phenomenon has not received sufficient attention in the existing inventory literature. In this paper, we construct a Markovian model for a two‐item inventory system with correlated demands and coordinated replenishments. We obtain an expression for the long‐run total cost per unit of time under the can‐order replenishment policy. For the scenario with independent replenishments, the explicit formula for the long‐run total cost per time unit can be derived, which leads to analytical solutions for the optimal policies. We then present numerical examples of the optimal can‐order policies and discuss some managerial insights regarding demand correlation and replenishment coordination. Our numerical results also suggest a possible heuristic method for obtaining can‐order replenishment policies for multi‐item systems.