Matching formulation of the Staff Transfer Problem: meta-heuristic approaches

In this paper, the Staff Transfer Problem (STP) in Human Resource Management is addressed as a stable matching problem. Earlier, formulation of this problem was of scheduling/allocation type. Here, the stable matching formulation is completely a new and more practical approach to the problem. This new formulation involves two preference lists: the first list contains the offices/locations preferred by the employees undergoing transfer and the second list contains the employees preferred by the employer of an office/location where those employees want to be transferred. The capacity of an office/location would act as a hard constraint. While matching these two lists, the objective is to maximize the number of transfers and at the same time to stabilize the matching, i.e., to minimize the number of blocking pairs. The resulting STP instance belongs to an instance of Maximum Size Minimum Blocking Pair Stable Matching with incomplete preference list (MAX SIZE MIN BP SMI) and has been proved in this paper to be NP-hard. As the problem is new in formulation, no previous work, method or result is available. There was no preference in selecting meta-heuristics. Among a large number of existing meta-heuristics, some most widely used meta-heuristics, namely, Simulated Annealing, Genetic Algorithms, Tabu Search and some variants of them have been chosen. Based on them four meta-heuristic approaches have been proposed, namely, btSA_match, gtSA_match, GA_match and TS_match. The variants btSA_match and gtSA_match are obtained from modifications made upon Simulated Annealing. EGA_match and TS_match are based on modified Genetic Algorithms and Tabu Search respectively. As there is no previous result in the existing literature, the performance has been compared among these four methods. It is observed that, variants of Simulated Annealing (SA) outperform others w.r.t. the performance metrics. The SA-variant with greedy nature, incorporated with a tabu list (gtSA_match) has shown that the best result on the basis of statistical analysis.