Preservation of Supermodularity in Parametric Optimization: Necessary and Sufficient Conditions on Constraint Structures

Author:

Chen Xin1ORCID,Long Daniel Zhuoyu2ORCID,Qi Jin3ORCID

Affiliation:

1. Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801;

2. Department of Systems Engineering & Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong, China;

3. Department of Industrial Engineering and Decision Analytics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China

Abstract

The concept of supermodularity has received considerable attention in economics and operations research. It is closely related to the concept of complementarity in economics and has also proved to be an important tool for deriving monotonic comparative statics in parametric optimization problems and game theory models. However, only certain sufficient conditions (e.g., lattice structure) are identified in the literature to preserve the supermodularity. In this article, new concepts of mostly sublattice and additive mostly sublattice are introduced. With these new concepts, necessary and sufficient conditions for the constraint structures are established so that supermodularity can be preserved under various assumptions about the objective functions. Furthermore, some classes of polyhedral sets that satisfy these concepts are identified, and the results are applied to assemble-to-order systems.

Publisher

Institute for Operations Research and the Management Sciences (INFORMS)

Subject

Management Science and Operations Research,Computer Science Applications

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