Introduction of a new class of variables to discrete and integer programmingproblems

M.T. Hajian, R. Rodosek and B. Richards

Annals of Operations Research, 1999, vol. 86, issue 0, 39-51

Abstract: In formulating a combinatorial optimisation problem (COP) using Discrete or IntegerProgramming (IP) modelling techniques, the modeller is restricted to use only certain predefineddiscrete variables and sets which are linked by sets of linear equality and inequalityconstraints. Definition of many COPs includes restrictions in which the use of disequality(DI) constraints in their mathematical representation is inevitable. To represent this type ofconstraint a number of binary variables and extra constraints are usually introduced, whichlead to an increase in the size of the model in terms of variables and constraints. In thispaper, we introduce a new class of discrete variables which enables the modeller to representDI constraints more efficiently in the mathematical formulation of a combinatorial optimisationproblem. We have also introduced a new branching scheme to the conventional simplexbased Branch and Bound (B & B) algorithm in order to deal with this type of variables. Tostudy the effect of these variables, we modelled and solved a set of five classic problems,first using conventional MP variables and second, exploiting the new proposed variables,and compared the results. The empirical results show a promising improvement on theperformance of the B & B algorithm. The contribution of this paper is (1) the introduction ofa new class of discrete variables which can help to build smaller models, and (2) newbranching schemes on these variables that can improve the B & B performance. Copyright Kluwer Academic Publishers 1999

Date: 1999
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DOI: 10.1023/A:1018923306255

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