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.
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References
Chen, X., Hu, P., & He, S. (2012b). Preservation of supermodularity in two dimensional parametric optimization problems and its applications. This paper has been accepted by Operations Research.
Hu, P. (2011). Coordinated pricing and inventory management (Ph.D. Dissertation, University of Illinois at Urbana-Champaign)
Murota, K. (2003). Discrete convex analysis. Philadelphia: Society for Industrial and Applied Mathematics.
Murota, K., & Shioura, A. (2004). Conjugacy relationship between M-convex and L-convex functions in continuous variables. Mathematical Programming, 101, 415–433.
Rockafellar, R. T. (1970). Convex analysis. Princeton, NJ: Princeton University Press.
Tarski, A. (1955). A lattice-theorectical fixpoint theorem and its applications. Pacific Journal of Mathematics, 5, 285–309.
Topkis, D. M. (1998). Supermodularity and complementarity. Princeton, NJ: Princeton University Press.
Zipkin, P. H. (2008). On the structure of lost-sales inventory models. Operation Research, 56, 937–944.
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Simchi-Levi, D., Chen, X., Bramel, J. (2014). Convexity and Supermodularity. In: The Logic of Logistics. Springer Series in Operations Research and Financial Engineering. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9149-1_2
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DOI: https://doi.org/10.1007/978-1-4614-9149-1_2
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