Contracting for vendor-managed inventory with consignment stock and stockout-cost sharing

We examine the problem of designing a vendor-managed inventory (VMI) contract with consignment stock and stockout-cost sharing in a (Q, r) inventory system between a supplier and a retailer. In particular, the contract specifies fixed and proportional penalties charged to the supplier when stockouts occur at the retailer. The retailer chooses the penalties and offers the contract to the supplier, and the supplier can accept or reject the contract. If he accepts it, the supplier manages the inventory at the retailer and makes replenishment decisions. For the deterministic demand we characterize the optimal contract for the retailer and the corresponding optimal inventory policy for the supplier. Our computational study for the deterministic and stochastic demands provides several interesting results. In particular, it suggests that VMI may result in significant cost savings for both the retailer and the supplier, but that the retailer may not always benefit from VMI. Our study also sheds lights on the relationship between VMI and replenishment leadtime and the value of information sharing on the retailer's stockout quantity in VMI contracting.