Better to Bend than to Break: Sharing Supply Risk Using the Supply-Flexibility Contract

Abstract

Problem definition: We analyze a contract in which a supplier who is exposed to disruption risk offers a supply-flexibility contract comprising of a wholesale price and a minimum-delivery fraction (“flexibility” fraction) to a buyer facing random demand. The supplier is allowed to deviate below the order quantity by at most the flexibility fraction. The supplier’s regular production is subject to random disruption, but she has access to a reliable expedited supply source at a higher marginal cost. Academic/practical relevance: Despite the prevalence of supply-flexibility contracts in practice, to the best of our knowledge, there is no previous academic literature examining the optimal design of supply-flexibility contracts. As such, the level of flexibility in practice is usually set on an ad-hoc basis, with buyers typically reluctant to share risk with suppliers. Our analysis of supply-flexibility contracts informs practice in two ways: First, using analytically supported arguments, it educates managers on the effects of their decisions on the economic outcomes. Second, it shows that the supply-flexibility contract benefits both the supplier and the buyer, regardless of which player chooses how supply risk is allocated in the supply chain. Methodology: Non-cooperative game theory, non-convex optimization. Results: We derive the supplier-led optimal contract and show that supply chain efficiency improves relative to the price-only contract. More interestingly, even though the buyer lets the supplier decide how the two share supply risk, profits of both the players increase by the introduction of flexibility into the contract. Further, supply flexibility may be even more valuable for the buyer compared with the supplier. Interestingly, the flexibility fraction is not monotone in supplier reliability and a more reliable supplier may even prefer to transfer more risk to the buyer. The robustness of these findings is established on two extensions: one where we study a buyer-led contract (i.e., the buyer chooses the flexibility fraction) and the other where the expedited supply option is available to both the supplier and the buyer. Managerial implications: The supply-flexibility contract is mutually beneficial for both players and yet retains all the advantages of the price-only contract—it is easy to implement, it requires minimal operational and administrative burden, and there is evidence of the use of such contracts in practice. While our focus is not on supply chain coordination, we note that the combination of two mechanisms—the supply-flexibility contract derived in this paper to share supply risk and a buyback contract to share demand risk—yields a coordinating contract.