Comparison between minimum purchase, quantity flexibility contracts and spot procurement in a supply chain

When, in a supply chain, a supplier and a buyer have the choice of transaction form to do business, the equilibrium transaction form which emerges is much more constrained than previously envisaged in literature. In this paper, two forms of long-term supply contracts and procurement in the spot market are compared. A capacity constrained service provider and a buyer of such service choose among three different transaction forms: spot procurement, minimum purchase commitment and quantity flexibility contracts. The ultimate demand the buyer has to satisfy and the spot market price of the input she has to purchase from the supplier are exogenous stochastic processes. Complete analytical results and a numerical example are presented. This paper builds upon recent supply chain contract literature by trying to join in one setting problems which up till now were considered in isolation.