Pricing and Operational Recourse in Coproduction Systems

Abstract

Coproduction systems, in which multiple products are produced simultaneously in a single production run, are prevalent in many industries. Such systems typically produce a random quantity of vertically differentiated products. This product hierarchy enables the firm to fill demand for a lower-quality product by converting a higher-quality product. In addition to the challenges presented by random yields and multiple products, coproduction systems often serve multiple customer classes that differ in their product valuations. Furthermore, the sizes of these classes are uncertain. Employing a utility-maximizing customer model, we investigate the production, pricing, downconversion, and allocation decisions in a two-class, stochastic-demand, stochastic-yield coproduction system. For the single-class case, we establish that downconversion will not occur if prices are set optimally. In contrast, we show that downconversion can be optimal in the two-class case, even if prices are set optimally. We consider the benefit of postponing certain operational decisions, e.g., the pricing or allocation-rule decisions, until after uncertainties are resolved. We use the term recourse to denote actions taken after uncertainties have been resolved. We find that recourse pricing benefits the firm much more than either downconversion or recourse allocation do, implying that recourse demand management is more valuable than recourse supply management. Special cases of our model include the single-class and two-class random-yield newsvendor models.