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A REVISED SIMPLEX ALGORITHM FOR LARGE-SCALE GOAL PROGRAMMING MODELS
Abstract
It has been well established that virtually every decision making problem involves several key criteria since the decision maker works in a multi-criteria environment. Mathematical programming techniques based on a single objective criterion are restricted in application to real-world problems. Among the various techniques which have been developed to handle multicriteria decision making problems, goal programming is perhaps the most promising approach as it is an appropriate, powerful, flexible, and pragmatic tool. The two principal areas of this research are: (1) development of efficient algorithms for large-scale linear goal programming problems: RSMGP and RSMPGP, and (2) a comparison of their computational efficiency with existing algorithms. RSMGP is based on a combination of the revised simplex method with product form and the modified simplex method while RSMPGP is a combination of the product representation of the inverse and some features of the goal partitioning algorithm. The explicit form of the inverse over the regular simplex method and the product representation over the explicit form have various advantages in terms of speed, storage savings, and accuracy. The product form of the inverse matrix method has been widely used for commercial computer codes for solving large-scale linear programming problems. The new algorithms have been tested, using ten different models of various sizes, structures, and complexities, against existing algorithms. Computational experience indicates that the degree of sparsity of the model has a negative correlation with computer time. The new algorithms have shown consistently greater relative efficiency over the existing goal programming algorithms when the size of the model becomes larger.
Subject Area
Business community
Recommended Citation
KANG, KUM-SIK, "A REVISED SIMPLEX ALGORITHM FOR LARGE-SCALE GOAL PROGRAMMING MODELS" (1980). ETD collection for University of Nebraska-Lincoln. AAI8100770.
https://digitalcommons.unl.edu/dissertations/AAI8100770