Abstract
The utility to management of a new linear programming (LP) technique, Khachian's algorithm (KA), is assessed. This is accomplished by evaluating a set of cost-effectiveness utility measures which compare the managerial utility of KA to the main LP technique, the Simplex algorithm (SX). The utility measures are relative and only compare KA to the SX. Thus, it was necessary to first establish the utility of LP and the SX. It was not possible to do this by a costeffectiveness study. The best current measure of LP's managerial utility is its high and increasing usage rate. In addition, the SX works very well for LP and has no pressing problems. In particular, cost is not usually a factor in its use since most LP problems of practical interest are of “small” size (i.e. less than 500 constraints). The most pressing need is for a new algorithm useful for solving various non-LP problems. A set of technical evaluation criteria (also relative to the SX) was developed to facilitate use of the utility measures. To evaluate the criteria, two methods were used “expert opinion” (consisting of technical references, telephone interviews, and meetings) and a computer experiment. The computer experiment compared the two algorithms performance in solving SX exponential time problems. This represented a best possible case (for KA) and a worst possible case (for SX). The final evaluations of the utility measures are: • KA has no utility for LP problems. • KA may have potential for improvements with positive utility for non-LP problems. Recommended actions for management are: • Do not implement the present KA for LP problems. • Do not plan on implementing an improved version in the next few years for LP problems. • Large firms (able to absorb potential losses) with an interest in non-LP problems should fund KA research.
Published Version
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