Abstract
In this work, a new method is presented for determining the binding constraints of a general linear maximization problem. The new method uses only objective function values at points which are determined by simple vector operations, so the computational cost is inferior to the corresponding cost of matrix manipulation and/or inversion. This method uses a recently proposed notion for addressing such problems: the average of each constraint. The identification of binding constraints decreases the complexity and the dimension of the problem resulting to a significant decrease of the computational cost comparing to Simplex-like methods. The new method is highly useful when dealing with very large linear programming (LP) problems, where only a relatively small percentage of constraints are binding at the optimal solution, as in many transportation, management and economic problems, since it reduces the size of the problem. The method has been implemented and tested in a large number of LP problems. In LP problems without superfluous constraints, the algorithm was 100% successful in identifying binding constraints, while in a set of large scale LP tested problems that included superfluous constraints, the power of the algorithm considered as statistical tool of binding constraints identification, was up to 90.4%.
Highlights
It is well-known, that in large linear programming (LP) problems there is a significant number of redundant constraints and variables
The new method is highly useful when dealing with very large linear programming (LP) problems, where only a relatively small percentage of constraints are binding at the optimal solution, as in many transportation, management and economic problems, since it reduces the size of the problem
The algorithm was considered as a statistical tool for correctly identifying binding constraints in random linear programming problems and the results of this statistical approach are presented in the third part of the section
Summary
It is well-known, that in large linear programming (LP) problems there is a significant number of redundant constraints and variables. This problem reduction, among others, results to less computational time and effort In this direction, many researchers including Andersen and Andersen [5], Balinsky [6], Boot [7], Brearly et al [8], Boneh et al [9], Caron et al [10], Ioslovich [11], Gal [12], Gutman and Isolovich [13], Mattheis [14], Nikolopoulou et al [15], Stojkovic and Staminirovic [16], Paulraj et al [17] [18] and Telgen [19] have proposed several algorithms to identify redundant constraints in order to reduce the dimension of the initial large scale LP problem.
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