The coordination of pricing and scheduling decisions

This paper considers the coordination of pricing and scheduling decisions in a make-to-order environment. Following common industry practice, we assume knowledge of a deterministic demand function that is nonincreasing in price. We consider three alternative measures of scheduling cost: total work-in-process inventory cost of orders, total penalty for orders delivered late to customers, and total capacity usage. The objective is to maximize the total net profit, i.e., revenue less scheduling cost, resulting from the pricing and scheduling decisions. We develop computationally efficient optimal algorithms for solving the three pricing and scheduling problems. Because these problems are formally intractable, much faster algorithms are not possible. We develop a fully polynomial time approximation scheme for each problem. We also estimate the value of coordinating pricing and production scheduling decisions by comparing solutions delivered by (a) an uncoordinated approach where pricing and scheduling decisions are made independently, (b) a partially coordinated approach that uses only general information about scheduling that a marketing department typically knows, (c) a simple heuristic approach for solving the coordinated problem, and (d) our optimal algorithm for solving the coordinated problem. Our main managerial insight is that there is a significant benefit even if pricing and scheduling are only heuristically or partially coordinated. Moreover, heuristic and partial coordination are simple to achieve.