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2017, Volume 4, Issue 3

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Frontiers of Engineering Management >> 2017, Volume 4, Issue 3 doi: 10.15302/J-FEM-2017057

♮-convexity and its applications in operations

Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA; Changsha University of Science and Technology, Changsha 410114, China

Accepted: 2017-09-30 Available online: 2017-10-30
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Abstract

-convexity, one of the central concepts in discrete convex analysis, receives significant attentions in the operations literature in recent years as it provides a powerful tool to derive structures of optimal policies and allows for efficient computational procedures. In this paper, we present a survey of key properties of -convexity and some closely related results in lattice programming, several of which were developed recently and motivated by operations applications. As a new contribution to the literature, we establish the relationship between a notion called -differential monotonicity and -convexity. We then illustrate the techniques of applying -convexity through a detailed analysis of a perishable inventory model and a joint inventory and transshipment control model with random capacities.

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