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1991 Discrete Applied Mathematics  
Chapter 5: Dual Fractional Mixed Integer Programming. The basic approach. The form of the cut. An illustration. The derivation of the cut. Apply- ing the mixed cut to the integer program.  ...  Group theoretic algorithms (Chapter 11)). Chapter 4: Dual Fructional Integer Programming. The basic approach. Nota- tion: The Beale tableau. The form of the (Gomory) cut. Illustrations.  ... 
doi:10.1016/0166-218x(91)90034-t fatcat:alt7e3uayfdxncpp7upicindka

Examining Optimal Criterion Weights in Mixed Integer Programming Approaches to the Multiple-Group Classification Problem

Robert Pavur, Constantine Loucopoulos
1995 Journal of the Operational Research Society  
We investigate conditions under which a degenerate solution can occur in mixed integer programming approaches to the multiple-group classification problem.  ...  Alll rights reserved. 0160-5682/95 $172.00 Re Examining Optimal Criterion Weights in Mixed Integer Programming Approaches to the Multiple-group Classification Problem ROBERT PAVUR' and CONSTANTINE LOUCOPOULOS  ... 
doi:10.2307/2584535 fatcat:uneu7ahowbdunptr3frwkxadsy

Page 626 of The Journal of the Operational Research Society Vol. 46, Issue 5 [page]

1995 The Journal of the Operational Research Society  
We investigate conditions under which a degenerate solution can occur in mixed integer programming approaches to the multiple-group classification problem.  ...  Alll rights reserved. 0160-5682/95 $172.00 Re Examining Optimal Criterion Weights in Mixed Integer Programming Approaches to the Multiple-group Classification Problem ROBERT PAVUR' and CONSTANTINE LOUCOPOULOS  ... 

Page 12 of The Journal of the Operational Research Society Vol. 52, Issue 8 [page]

2001 The Journal of the Operational Research Society  
A theoretical assessment and a Monte Carlo simulation are used to determine the impact of different gap sizes on a mixed integer programming model using a single function classification model for the three-group  ...  A major drawback of mixed integer programming approaches to the classification problem has been the computational intensity of such formulations.  ... 

Page 1796 of Mathematical Reviews Vol. 48, Issue 5 [page]

1974 Mathematical Reviews  
Chen, Der San; Zionts, Stanley 10495 An exposition of the group theoretic approach to integer linear programming. Opsearch 9 (1972), 75-102.  ...  The author deals with an approach to solving the mixed and pure integer programming problems.  ... 

Page 8 of The Journal of the Operational Research Society Vol. 49, Issue 6 [page]

1998 The Journal of the Operational Research Society  
They developed a [0,1] integer program formulation with a quadratic objective function (which they show to be NP- hard), and two equivalent linear, mixed integer models.  ...  Hill et al'' use a linear [0,1] integer programming approach with the goal of maximising student preferences in assigning students to project teams, and students to job interviews.  ... 

Mixed integer programming

Jon Lee, Adam N. Letchford
2007 Discrete Optimization  
Editorial Mixed integer programming The IMA Special Workshop on Mixed-Integer Programming was held in Minneapolis on July [25][26][27][28][29] 2005, at the Institute for Mathematics and its Applications  ...  We believe that these papers give an excellent 'snapshot' of the state-of-the-art in integer and mixed-integer programming, reflecting well the current trends in the field.  ...  Margot, in his paper, generalizes his group-theoretic techniques for combating symmetry in 0/1 linear programs to general integer linear programs. • Another recent development is the discovery of powerful  ... 
doi:10.1016/j.disopt.2006.10.005 fatcat:yofa7pyiivaqfborh55fcqmy3m

Page 2773 of Mathematical Reviews Vol. , Issue 87e [page]

1987 Mathematical Reviews  
(I-IASI) 87e:90069 Lagrangian and group-theoretic relaxation in integer programming.  ...  The properties of the Lagrangian relaxation and of the group- theoretic relaxation for integer linear programming are studied and surveyed in detail.  ... 

Some thoughts on the development of integer programming during my research career – lecture delivered upon receiving the EURO Gold Medal, July 9, 2001, Rotterdam

Egon Balas
2002 European Journal of Operational Research  
The prevailing research direction in cutting plane theory was at the time the group theoretic approach.  ...  Thus one of the first insights yielded by the disjunctive programming approach was to identify the main characteristic that distinguishes 0-1 programming (pure or mixed) from general integer programming  ... 
doi:10.1016/s0377-2217(02)00172-8 fatcat:6qb73ktj6jhd3ewa6texfeadwe

The Synchronization of Traffic Signals by Mixed-Integer Linear Programming

John D. C. Little
1966 Operations Research  
The research in mathematical programming has centered on integer and mixed integer problems. The adaptive control work has dealt with special classes of stochastic decision problems.  ...  In queuing theory, which has long been descriptive in its approach, the emphasis has been on normative models, especially Markovian decision processes.  ...  The usefulness of group theoretic methods in solving integer pro-A gramning (IP) problems is extended by procedures for controlling the A size of the groups.  ... 
doi:10.1287/opre.14.4.568 fatcat:7hhuqjnnujgdnms2bgovc2xqau

The atoms of integer programming

Ralph E. Gomory
2007 Annals of Operations Research  
The connection with Integer Programming comes from the fact that we can map, in a natural way, solutions to the IP problem into paths in the group G.  ...  With computers, this sort of experimental work is now possible in some areas of mathematics. But in our area the two approaches, the experimental and the theoretical usually seem quite far apart.  ... 
doi:10.1007/s10479-006-0110-z fatcat:zndxqpig4fdr7dr6stm3nee74y

Evaluating the effect of gap size in a single function mathematical programming model for the three-group classification problem

R Pavur, C Loucopoulos
2001 Journal of the Operational Research Society  
This approach was recognized by Ragsdaie and Stam.'* Koehler and Erenguc'* also considered a mixed integer programming model in which they consid- ered a gap.  ...  Few papers in the literature have investigated the effects of the estimates of parameters used in mixed integer programming models for solving the classification problem.  ... 
doi:10.1057/palgrave.jors.2601116 fatcat:ffjctye6ifcgbcilx3h45ovdg4

True

2001 Journal of the Operational Research Society  
This approach was recognized by Ragsdaie and Stam.'* Koehler and Erenguc'* also considered a mixed integer programming model in which they consid- ered a gap.  ...  Few papers in the literature have investigated the effects of the estimates of parameters used in mixed integer programming models for solving the classification problem.  ... 
doi:10.1057/palgrave/jors/2601116 fatcat:vgzses43fzcmhhgrmigvp4jjym

Preface [chapter]

2022 Multi-level Mixed-Integer Optimization  
Theoretic and algorithmic developments on the solution of mixed-integer multilevel optimization problems, along with many applications in the areas of economics and process systems engineering, have been  ...  More specifically, this book focuses on the solution of (i) bilevel mixed-integer linear programming problems, (ii) bilevel mixed-integer quadratic programming problems, (iii) trilevel mixed-integer linear  ...  Finally, the last chapter consider es the implementation of the algorithms discussed in Chapters 2 and 3 in a MATLAB® based toolbox, B-POP®, along with computational studies to highlight the capabilities  ... 
doi:10.1515/9783110760316-201 fatcat:svx7tnkv6reepczfs534ybz65e

Page 220 of Mathematical Reviews Vol. 46, Issue 1 [page]

1973 Mathematical Reviews  
Finkel’stein (RZMat 1969 #10 V316) ECONOMICS, OPERATIONS RESEARCH, PROGRAMMING, GAMES Wolsey, Laurence A. 1330 Group-theoretic results in mixed integer programming.  ...  The general mixed integer programming problem (MIPP) | can be discretized. After this it is equivalent to a shortest- route problem over a finite abelian group. An asymptotic MIPP is defined.  ... 
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