Production cost functions and demand uncertainty effects in price-only contracts

The price-only contract is the simplest and most common contract between a supplier and buyer in a supply chain. In such a contract, the supplier proposes a fixed wholesale price, and the buyer chooses a corresponding order quantity. The buyer's optimal behavior is modeled using the Newsvendor model and the supplier's optimal behavior is modeled as the solution to an optimization problem. This article explores, for the first time, the impact of general production costs on the supplier's and buyer's behavior. It is revealed that increased supplier's production efficiency, reflected in lower marginal production costs, increases the buyer's optimal profit. Therefore, a buyer would always prefer the more efficient supplier. A higher supplier efficiency, however, may or may not increase the supplier's optimal profit, depending on the production function's fixed costs. The effect of demand uncertainty, as measured by the coefficient of variation, is shown to increase the optimal order quantity. The uncertainty effect on the firms' optimal profits is analyzed. Also, the relationship between production efficiency and the response to demand uncertainty is explored and it is shown that a higher efficiency level increases the responsiveness and volatility of the supplier's production quantities. Thus, higher-efficiency suppliers are better positioned to respond to changes in the demand uncertainty in the supply chain.