Supply chain contracting in environments with volatile input prices and frictions

Problem description: Purchase costs of raw materials required in production tend to fluctuate over time. Mild cost fluctuations merely a ect firms’ profitability. Significant variations can lead to supply chain disruption. What are the best contracts to be used in supply chains exposed to fluctuating raw material costs? We ask this question in two contexts—in the presence and the absence of working capital constraint. Academic/practical relevance: We add a framework on how to optimally contract in the presence of stochastic costs and working capital constraints and help managers understand how they can increase profitability. Methodology: We present a game-theoretic study of a bilateral monopoly supply chain with stochastic demand, stochastic input costs, production lead times, and working capital constraints. The upstream firm announces a supply contract to which the downstream firm responds with an order quantity. The contract is a single-price, multi-instrument contract with optional default penalties. Many previously studied coordinating contracts, as well as some noncoordinating ones, are special cases of our general contract. Results: We derive necessary and su cient conditions that the instruments of the general contract must satisfy for the contract to induce a coordinated outcome—both with and without working capital constraints. Then we translate these requirements into implementable contracts. Indexing (I) on raw material prices and using default penalties (Ps) is necessary, and an I&P revenue-sharing contract turns out to be the most versatile contract for these environments. Managerial implications: We provide clear guidelines on how to contract in situations where production costs of every supply chain member fluctuate significantly, possibly in the presence of working capital constraints.