Convexity and Supermodularity

Abstract

The concepts of convexity and supermodularity are important in the optimization and economics literature. These concepts have been widely applied in the analysis of a variety of supply chain models, from stochastic, multi-period inventory problems to pricing models. Hence, in this chapter, we provide a brief introduction to convexity and supermodularity, focusing on materials most relevant to our context. We also briefly introduce some concepts and results from discrete convex analysis, which interestingly is an elegant combination of both convexity and submodularity. For more details, readers are referred to the three excellent books Rockafellar (970) on convex analysis, Topkis (1998) on supermodularity, and Murota (2003) on discrete convex analysis.