Untruthful probabilistic demand forecasts in vendor-managed revenue-sharing contracts: Coordinating the chain

Vendor-managed revenue-sharing arrangements are common in the newspaper and other industries. Under such arrangements, the supplier decides on the level of inventory while the retailer effectively operates under consignment, sharing the sales revenue with his supplier. We consider the case where the supplier is unable to predict demand, and must base her decisions on the retailer-supplied probabilistic forecast for demand. We show that the retailer's best choice of a distribution to report to his supplier will not be the true demand distribution, but instead will be a degenerate distribution that surprisingly induces the supplier to provide the system-optimal inventory quantity. (To maintain credibility, the retailer's reports of daily sales must then be consistent with his supplied forecast.) This result is robust under nonlinear production costs and nonlinear revenue-sharing. However, if the retailer does not know the supplier's production cost, the forecast "improves" and could even be truthful. That, however, causes the supplier's order quantity to be suboptimal for the overall system.