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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Vydáno v:Management science Ročník 49; číslo 9; s. 1268 - 1273
Hlavní autoři: Croxton, Keely L, Gendron, Bernard, Magnanti, Thomas L
Médium: Journal Article
Jazyk:angličtina
Vydáno: Linthicum INFORMS 01.09.2003
Institute for Operations Research and the Management Sciences
Edice:Management Science
Témata:
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
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Shrnutí: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