Vol.:(0123456789) OPSEARCH https://doi.org/10.1007/s12597-019-00432-w 1 3 APPLICATION ARTICLE Matching formulation of the Staf Transfer Problem: meta‑heuristic approaches S. Acharyya 1  · A. K. Datta 2 Accepted: 30 November 2019 © Operational Research Society of India 2019 Abstract In this paper, the Staf 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 frst list contains the ofces/locations preferred by the employ- ees undergoing transfer and the second list contains the employees preferred by the employer of an ofce/location where those employees want to be transferred. The capacity of an ofce/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 result- ing 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 select- ing 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 modifcations made upon Simulated Annealing. EGA_match and TS_match are based on modifed 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) out- perform 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. Keywords Human resource planning · Staf transfer · Stable matching · Optimization · Meta-heuristics Extended author information available on the last page of the article