A note on modeling multiple choice requirements for simple mixed integer programming solvers
This note introduces the Special Ordered Inequalities (SOI) as a new technique for integer programming modeling of multiple choice requirements and piecewise linear functions. The standard modeling technique based on the use of Special Ordered Set (SOS) structure requires a branch and bound solver t...
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| Published in: | Computers & operations research Vol. 23; no. 2; pp. 199 - 205 |
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| Main Author: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
Oxford
Elsevier Ltd
01.02.1996
Elsevier Science Pergamon Press Inc |
| Subjects: | |
| ISSN: | 0305-0548, 1873-765X, 0305-0548 |
| Online Access: | Get full text |
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| Abstract | This note introduces the Special Ordered Inequalities (SOI) as a new technique for integer programming modeling of multiple choice requirements and piecewise linear functions. The standard modeling technique based on the use of Special Ordered Set (SOS) structure requires a branch and bound solver to be armed with the special tools for SOS processing. Otherwise, the standard branching rule applied on individual SOS variables may lead to enormously long computation process thus making impossible to solve quite small problems in a reasonable time. The proposed SOI modeling technique allows us to eliminate the necessity of the special branching rule for handling SOS structure. The standard branching on individual variables of SOI is equivalent to the special SOS branching. Thus the proposed modeling technique seems to be very attractive for users of simple mixed integer programming solvers as well as for those who want to build solver independent mathematical programming models. |
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| AbstractList | The Special Ordered Inequalities (SOI) is introduced as a new technique for integer programming modeling of multiple choice requirements and piecewise linear functions. The standard modeling technique based on the use of Special Ordered Set (SOS) structure requires a branch and bound solver to be armed with the special tools for SOS processing. Otherwise, the standard branching rule applied on individual SOS variables may lead to an enormously long computation process thus making it impossible to solve quite small problems in a reasonable time. The proposed SOI modeling technique allows us to eliminate the necessity of the special branching rule for handling SOS structure. The standard branching on individual variables of SOI is equivalent to the special SOS branching. Thus, the proposed modeling technique seems to be very attractive for users of simple mixed integer programming solvers as well as for those who want to build solver independent mathematical programming models. This note introduces the Special Ordered Inequalities (SOI) as a new technique for integer programming modeling of multiple choice requirements and piecewise linear functions. The standard modeling technique based on the use of Special Ordered Set (SOS) structure requires a branch and bound solver to be armed with the special tools for SOS processing. Otherwise, the standard branching rule applied on individual SOS variables may lead to enormously long computation process thus making impossible to solve quite small problems in a reasonable time. The proposed SOI modeling technique allows us to eliminate the necessity of the special branching rule for handling SOS structure. The standard branching on individual variables of SOI is equivalent to the special SOS branching. Thus the proposed modeling technique seems to be very attractive for users of simple mixed integer programming solvers as well as for those who want to build solver independent mathematical programming models. |
| Author | Ogryczak, Włodzimierz |
| Author_xml | – sequence: 1 givenname: Włodzimierz surname: Ogryczak fullname: Ogryczak, Włodzimierz organization: Université Libre de Bruxelles, Service de Mathématiques de la Gestion, B-1050 Brussels, Belgium |
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| Cites_doi | 10.1007/BF01581273 10.1287/mnsc.26.3.242 10.1007/BF02591892 10.1287/mnsc.20.5.736 10.1145/364005.364087 10.1287/opre.29.5.853 10.1287/mnsc.25.2.117 10.1016/S0167-5060(08)70351-0 10.1287/opre.12.1.122 10.1287/opre.33.4.803 10.1287/opre.19.4.946 10.1016/0377-2217(84)90002-X 10.1016/S0167-5060(08)70352-2 10.1287/mnsc.16.1.93 |
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| Keywords | Integer programming Mixed integer programming Choice Multiple Modeling Mathematical programming |
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J. Opl Res. doi: 10.1016/0377-2217(84)90002-X – start-page: 447 year: 1970 ident: 10.1016/0305-0548(95)00005-7_BIB11 article-title: Special facilities in a general Mathematical programming system for non-convex problems using ordered sets of variables – start-page: 221 year: 1979 ident: 10.1016/0305-0548(95)00005-7_BIB15 article-title: Computer codes for problems of integer programming doi: 10.1016/S0167-5060(08)70352-2 – start-page: 190 year: 1985 ident: 10.1016/0305-0548(95)00005-7_BIB16 article-title: Software – volume: 16 start-page: 93 year: 1969 ident: 10.1016/0305-0548(95)00005-7_BIB5 article-title: Multiproject scheduling with limited resources: A zero-one programming approach publication-title: Mgmt Sci. doi: 10.1287/mnsc.16.1.93 |
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| Title | A note on modeling multiple choice requirements for simple mixed integer programming solvers |
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