Promised Lead-Time Contracts Under Asymmetric Information

We study the important problem of how a supplier should optimally share the consequences of demand uncertainty (i.e., the cost of inventory excesses and shortages) with a retailer in a two–level supply chain facing a finite planning horizon. In particular, we characterize a multiperiod contract form, the promised lead–time contract, that reduces the supplier's risk from demand uncertainty and the retailer's risk from uncertain inventory availability. Under the contract terms, the supplier guarantees on–time delivery of complete orders of any size after the promised lead time. We characterize the optimal promised lead time and the corresponding payments that the supplier should offer to minimize her expected inventory cost, while ensuring the retailer's participation. In such a supply chain, the retailer often holds private information about his shortage cost (or his service level to end customers). Hence, to understand the impact of the promised lead–time contract on the supplier's and the retailer's performance, we study the system under local control with full information and local control with asymmetric information. By comparing the results under these information scenarios to those under a centrally controlled system, we provide insights into stock positioning and inventory risk sharing. We quantify, for example, how much and when the supplier and the retailer overinvest in inventory as compared to the centrally controlled supply chain. We show that the supplier faces more inventory risk when the retailer has private service–level information. We also show that a supplier located closer to the retailer is affected less by information asymmetry. Next, we characterize when the supplier should optimally choose not to sign a promised lead–time contract and consider doing business under other settings. In particular, we establish the optimality of a cutoff level policy. Finally, under both full and asymmetric service–level information, we characterize conditions when optimal promised lead times take extreme values of the feasible set, yielding the supplier to assume all or none of the inventory risk—hence the name all–or–nothing solution. We conclude with numerical examples demonstrating our results.