Decision support for multi-objective linear programming using an interactive graphic presentation.

Abstract

Many decisions in real world applications are based on conflicting criteria or objectives. In order to improve one objective, it is necessary to sacrifice another. Linear programming has long been used to optimize a single objective. When a linear programming problem involves multiple objectives (MOLP), it is usually not possible to locate a single solution that simultaneously optimizes all objectives. Hence, a methodology is needed to help the decision maker (DM) explore the space of feasible solutions in order to locate an acceptable compromise solution. An interactive approach that supports the DM in the exploration process is presented. The methodology is implemented on a microcomputer running a graphical user interface. The computations are based on an expansion of the Dror-Gass (1987) methodology in which candidate solutions are located using weak order preferences for variables and objectives. It differs from previous methodologies in that it does not require burdensome trade-off ratios or strength of preference comparisons. During exploration, the DM is presented a multi-faceted graphical representation of solutions for consideration. Previous studies of the effectiveness of graphics to support the decision making process have used static presentations of the data. The graphic presentation as implemented is dynamic. It makes use of animation, interactive zoom (or inspect), and interactive highlighting of the results to improve its effectiveness. In the design of the interface, special attention was paid to the requirements for supporting interaction with large LP problems. The software implementation and methodology were tested by subjects drawn from faculty and students at the University of Arizona. It was also reviewed in industry. The results are presented.