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.