Supply chain contracts with capacity investment decision: Two-way penalties for coordination

Supply chain contracting has been discussed usually under the two compliance regimes, forced and voluntary. Various contracts show different coordination characteristics in these two regimes. However, in practice, the enforcement of contracted quantities in case of forced compliance is always an issue of concern. We propose a price compliance regime for contract where the penalties, in the form of price for non-compliance on quantity, are enforceable on both parties. In this paper, we model a contract where a supplier needs to build capacity before demand is realized under the proposed price compliance regime. A need for investment in capacity can be of the form of new capacity installation or capacity enhancement or updation, and is prevalent in practice, especially in industries that witness short product life cycles, have a high rate of new product launches or deploy high technology. When a supplier makes an investment decision under uncertainty of demand, she might under-invest in capacity. This is a major concern for a manufacturer, since it directly leads to loss of sales. We include the capacity and cost to build the capacity as variables in the contract modeled and analyze how the manufacturer can influence the capacity decision of the supplier with the given contract. We analyze the impact of various penalty parameters on the supplier's capacity decision, supply chain efficiency and relative allocation of supply chain profit across partners. Further, we consider a special case of uniformly distributed demand and find analytical closed-form conditions for a sub-set of coordinating contracts. We also consider a special case where the buyer and supplier arrive at a consensus on capacity-related decision and capacity is verifiable by the buyer.