Abstract:

Matching and multi-criteria multi-alternative problems are two well-known problems in decision science. Over the years, many solutions, tools, and techniques have been developed to solve each problem. When a situation arises where both problems intersect, then one may use approaches developed for each to tackle it. Given the competitive and dynamic business environment, problems with such attributes are bound to take place. Hence, this research paper extends the Gale-Shapley algorithm, which is a well-known algorithm that solves matching problems with the analytic hierarchy process (AHP), weighted-product model (WPM), and weighted-sum model (WSM). The extended Gale-Shapley algorithm is dubbed the Extended-GS (E-GS) algorithm and is referred to as E-GS. The basic idea of the E-GS algorithm is feeding the preference lists to the Gale-Shapley algorithm to produce an optimum match using the WSM, WPM, and AHP models. E-GS combines the powers of all four algorithms to provide an optimum solution.