A Comparison of Mixed-Integer Programming Models for Nonconvex Piecewise Linear Cost Minimization Problems

We study a generic minimization problem with separable nonconvex piecewise linear costs, showing that the linear programming (LP) relaxation of three textbook mixed-integer programming formulations each approximates the cost function by its lower convex envelope. We also show a relationship between...

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Bibliographic Details
Published in:Management science Vol. 49; no. 9; pp. 1268 - 1273
Main Authors: Croxton, Keely L, Gendron, Bernard, Magnanti, Thomas L
Format: Journal Article
Language:English
Published: Linthicum INFORMS 01.09.2003
Institute for Operations Research and the Management Sciences
Series:Management Science
Subjects:
Algorithms
Business studies
Cost analysis
Cost functions
Costs
Discourse functions
Economics
Integer Programming
Lagrangian function
Lagrangian Relaxation
Linear programming
Linear Relaxation
Management
Management science
Minimization
Minimization of cost
Objective functions
Operations research
Optimal solutions
Piecewise Linear
Polyhedrons
Production planning
Relaxation
Studies
Technology
Telecommunications
Textbooks
Transport
Variable costs
Variables
ISSN:0025-1909, 1526-5501
Online Access:Get full text
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Summary:We study a generic minimization problem with separable nonconvex piecewise linear costs, showing that the linear programming (LP) relaxation of three textbook mixed-integer programming formulations each approximates the cost function by its lower convex envelope. We also show a relationship between this result and classical Lagrangian duality theory.
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ISSN:0025-1909
1526-5501
DOI:10.1287/mnsc.49.9.1268.16570