Linear penalty contract for coordinating capacity procurement and sales promotion

A typical supply chain setting is analyzed, where the supplier's capacity building and the retailer's sales promotion needs to be launched simultaneously before demand is realized. Firstly it is demonstrated that the contract of a wholesale price with a lump sum transfer can coordinate the supply chain only when it is enforced under forced compliance. However forced compliance is not a realistic assumption. For coordinating the supply chain, a linear penalty contract is proposed, in which the supplier's penalty is linear with the capacity deficiency. And with the linear penalty contract the supply chain's optimal solution is the unique Nash equilibrium.