Joint production and pricing decisions with setup costs and capacity constraints

We consider the problem of setting prices and choosing production quantities for a single product over a finite horizon for a capacity-constrained manufacturer facing price-sensitive demands. There is a fixed cost per production run and a variable cost per unit produced, both of which may vary by period. We characterize properties of the optimal solution, considering cases with constant and time-varying capacity, and with and without speculative motive for holding inventory. We show that, counter to intuition, optimal prices may increase as the capacity increases, even when capacity is constant over the horizon. We also show that increases in capacity do not always exhibit diminishing marginal returns. Our procedure produces solutions with much higher profits than can be obtained from a sophisticated sequential procedure in which a well-informed and optimum-seeking marketing department makes pricing decisions and the manufacturing department seeks to satisfy the resulting demands at minimum cost. Our results also suggest that firms with seasonal demand and tight capacity constraints should be more aggressive in setting prices to manage their demands than what is typically done in practice. Finally, we discuss how a decision maker can use our procedure as an aid in solving multiproduct versions of the problem.