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2 - Mixed-Integer Programming

from Part I - Background

Published online by Cambridge University Press:  01 May 2021

Christos T. Maravelias
Christos T. Maravelias
Affiliation:
Princeton University, New Jersey
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Summary

This chapter provides an overview of mixed-integer programming (MIP) modeling and solution methods.In Section 2.1, we present some preliminary concepts on optimization and mixed-integer programming. In Section 2.2, we discuss how binary variables can be used to model features commonly found in optimization problems. In Section 2.3, we present some basic MIP problems and models. Finally, in Section 2.4, we overview the basic approaches to solving MIP models and present some concepts regarding formulation tightness and decomposition methods.Finally, we discuss software tools for modeling and solving MIP models in Section 2.5.

Keywords

Optimizationmixed-integer programminggraphnetworkbranch-and-bound algorithmcutting planedecompositionoptimization software
Type
Chapter
Information
Chemical Production Scheduling
Mixed-Integer Programming Models and Methods
 , pp. 32 - 64
Publisher: Cambridge University Press
Print publication year: 2021

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References

Dantzig, G, Fulkerson, R, Johnson, S. Solution of a Large-Scale Traveling-Salesman Problem. Journal of the Operations Research Society of America. 1954;2(4):393–410.CrossRefGoogle Scholar
Gomory, RE. Outline of an Algorithm for Integer Solutions to Linear Programs. Bull Amer Math Soc. 1958;64:275–278.CrossRefGoogle Scholar
Land, AH, Doig, AG. An Automatic Method of Solving Discrete Programming Problems. Econometrica. 1960;28(3):497–520.CrossRefGoogle Scholar
Dakin, RJ. A Tree-Search Algorithm for Mixed Integer Programming Problems. Computer Journal. 1965;8(3):250–253.CrossRefGoogle Scholar
Bixby, R, Rothberg, E. Progress in Computational Mixed Integer Programming – a Look Back from the Other Side of the Tipping Point. Annals of Operations Research. 2007;149(1):37–41.CrossRefGoogle Scholar
Williams, HP. Model Building in Mathematical Programming. 5th ed. Hoboken: Wiley; 2013.Google Scholar
Balas, E. Note on Duality in Disjunctive Programming. Journal of Optimization Theory and Applications. 1977;21(4):523–528.CrossRefGoogle Scholar
Balas, E. Disjunctive Programming and a Hierarchy of Relaxations for Discrete Optimization Problems. Siam J Algebra Discr. 1985;6(3):466–486.CrossRefGoogle Scholar
Raman, R, Grossmann, IE. Modeling and Computational Techniques for Logic-Based Integer Programming. Comput Chem Eng. 1994;18(7):563–578.Google Scholar
Turkay, M, Grossmann, IE. Disjunctive Programming Techniques for the Optimization of Process Systems with Discontinuous Investment Costs Multiple Size Regions. Ind Eng Chem Res. 1996;35(8):2611–2623.CrossRefGoogle Scholar
Nemhauser, GL, Wolsey, LA. Integer and Combinatorial Optimization. New York: Wiley; 1988.CrossRefGoogle Scholar
Wolsey, LA. Integer Programming. New York: Wiley; 1998.Google Scholar
West, DB. Introduction to Graph Theory. 2nd ed. Upper Saddle River: Prentice Hall; 2001.Google Scholar
Ahuja, RK, Magnanti, TL, Orlin, JB. Network Flows : Theory, Algorithms, and Applications. Englewood Cliffs: Prentice Hall; 1993.Google Scholar
Benders, JF. Partitioning Procedures for Solving Mixed-Variables Programming Problems. Numerische Mathematik. 1962;4(1):238–252.CrossRefGoogle Scholar
Fisher, ML. The Lagrangian Relaxation Method for Solving Integer Programming Problems. Manage Sci. 1981;27(1):1–18.Google Scholar
Atamturk, A, Savelsbergh, MWP. Integer-Programming Software Systems. Annals of Operations Research. 2005;140(1):67–124.Google Scholar
Belotti, P, Kirches, C, Leyffer, S, Linderoth, J, Luedtke, J, Mahajan, A. Mixed-Integer Nonlinear Optimization. Acta Numerica. 2013;22:1–131.CrossRefGoogle Scholar
Kronqvist, J, Bernal, DE, Lundell, A, Grossmann, IE. A Review and Comparison of Solvers for Convex MINLP. Optim. Eng. 2019;20(2):397–455.Google Scholar

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