Multi-Period Modeling of Two-Way Price Commitment Under Price-Dependent Demand

This paper examines the use of linear-pricing contracts as well as price-commitment policies in dynamic contracting of multiple-period, finite-time horizons. Two specific forms of price commitment are considered: one on the part of the retailer through retail-fixed-markup contracts and one on the part of the manufacturer through price-protection contracts. Optimal policies for each form of price commitment are analytically derived as are optimal policies for the traditional price-only and centralized supply chain scenarios. We prove that under non-increasing price-dependent demand, there are unique optimal solutions in each period for retail price and order size. We show that the existence of retailer inventories between periods causes the supply chain performance to differ from a static single-period model. Further, we show that a supplier offers a price-protection policy as a signal to the retailer to resolve the gaming that naturally occurs under price-only and effectively decouples the multi-period dynamic contracting setting into repeated single-period scenarios. However, this can actually inhibit supply chain performance. On the retail commitment side, we find that retail-fixed-markup policies are quite effective in improving supply chain efficiency. We show that such policies can lead to Pareto-improvement over price-only and can even coordinate the supply chain in some situations