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A ZERO-ONE GOAL PROGRAMMING ALGORITHM USING PARTITIONING AND CONSTRAINT AGGREGATION (MULTI-OBJECTIVE METHODS, BIVALENT, BINARY)
Abstract
During the past decade, goal programming has proved to be a useful and flexible multiple objective quantitative technique that has been widely used to support management decision making. The most commonly used zero-one goal programming algorithm was developed by Lee and Morris (1977) and Morris (1976). This research was conducted to develop an improved zero-one goal programming algorithm that would be computationally more efficient than the Lee and Morris algorithm. A subordinate goal was to develop a micro computer version of the algorithm. The algorithm developed in this research is based upon an aggregation scheme presented by Babu and Balasurbramanian (1982). This scheme combines all constraints in one operation and also generates relatively small coefficients. The multipliers used are of the form ln p, where p denotes a distinct prime number. The algorithm determines the upper and lower bounds for the number of nonzero variables required to satisfy each constraint and each priority level. These bounds are used to partition the constraints according to the priority structure, forming a subprogram. The subprogram consists of the first k priority levels in which all goals may be completely achieved. Invariant decision variables and redundant constraints are also identified for the subprogram based upon the range for the number of nonzero variables. A set of necessary and sufficient conditions are derived which are used to provide an efficient procedure to generate the optimal solution. The algorithm was coded in Pascal and tested on the IBM 3081D mainframe computer. Criteria established to compare the algorithm's performance with the Lee and Morris algorithm were: robustness, accuracy and reliability, sensitivity to parameters and data, and, computational effort. The results of the test data indicated the algorithm was superior to the Lee and Morris Algorithm based upon the established criteria. The virtual CPU time for all of the test problems was less than ten percent of that required by the Lee and Morris Algorithm.
Subject Area
Management
Recommended Citation
LUEBBE, RICHARD L, "A ZERO-ONE GOAL PROGRAMMING ALGORITHM USING PARTITIONING AND CONSTRAINT AGGREGATION (MULTI-OBJECTIVE METHODS, BIVALENT, BINARY)" (1985). ETD collection for University of Nebraska-Lincoln. AAI8602114.
https://digitalcommons.unl.edu/dissertations/AAI8602114