Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-09T08:45:55.022Z Has data issue: false hasContentIssue false

2 - Mixed-Integer Programming

from Part I - Background

Published online by Cambridge University Press:  01 May 2021

Christos T. Maravelias
Affiliation:
Princeton University, New Jersey
Get access

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.

Type
Chapter
Information
Chemical Production Scheduling
Mixed-Integer Programming Models and Methods
, pp. 32 - 64
Publisher: Cambridge University Press
Print publication year: 2021

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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):393410.CrossRefGoogle Scholar
Gomory, RE. Outline of an Algorithm for Integer Solutions to Linear Programs. Bull Amer Math Soc. 1958;64:275278.CrossRefGoogle Scholar
Land, AH, Doig, AG. An Automatic Method of Solving Discrete Programming Problems. Econometrica. 1960;28(3):497520.CrossRefGoogle Scholar
Dakin, RJ. A Tree-Search Algorithm for Mixed Integer Programming Problems. Computer Journal. 1965;8(3):250253.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):3741.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):523528.CrossRefGoogle Scholar
Balas, E. Disjunctive Programming and a Hierarchy of Relaxations for Discrete Optimization Problems. Siam J Algebra Discr. 1985;6(3):466486.CrossRefGoogle Scholar
Raman, R, Grossmann, IE. Modeling and Computational Techniques for Logic-Based Integer Programming. Comput Chem Eng. 1994;18(7):563578.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):26112623.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):238252.CrossRefGoogle Scholar
Fisher, ML. The Lagrangian Relaxation Method for Solving Integer Programming Problems. Manage Sci. 1981;27(1):118.Google Scholar
Atamturk, A, Savelsbergh, MWP. Integer-Programming Software Systems. Annals of Operations Research. 2005;140(1):67124.Google Scholar
Belotti, P, Kirches, C, Leyffer, S, Linderoth, J, Luedtke, J, Mahajan, A. Mixed-Integer Nonlinear Optimization. Acta Numerica. 2013;22:1131.CrossRefGoogle Scholar
Kronqvist, J, Bernal, DE, Lundell, A, Grossmann, IE. A Review and Comparison of Solvers for Convex MINLP. Optim. Eng. 2019;20(2):397455.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×