Dynamic balancing of inventory in supply chains

We consider the dynamic version of the classic problem of allocation of inventories to a set of retailers to rectify the imbalance of inventories amongst them. While most research is focused on analyzing different allocation strategies with a predetermined time of shipment (static policy), we investigate the benefit of using real time demand (inventory) information to schedule rebalancing shipments in a retail network. We model the dynamic rebalancing problem that has two decisions, the timing of the balancing shipments and determination of the new stocking levels at the retailers, as a dynamic program (DP). We obtain structural properties for the optimal allocation, rebalancing and timing strategies. We also present conditions under which a greedy heuristic to decide how much to ship from one retailer to another is optimal. The DP for determining the optimal timing and quantity of shipments has a very large state space. We present an algorithm to solve this DP efficiently. We also provide a heuristic solution procedure to the dynamic problem that performs very close to optimal. Numerical results show that dynamic allocation policies can lead to substantial benefits over the static policy especially in systems in which the starting inventories at the retailers are balanced or when high service levels are required.