Journal of the Faculty of Engineering and Architecture of Gazi University 37:1 (2022) 193-205 A goal programming model for balancing agent loads in the multi-resource generalized assignment problem Feriştah Özçelik* , Tuğba Saraç Department of Industrial Engineering, Eskisehir Osmangazi University, 26480, Eskisehir, Turkey Highlights: Graphical/Tabular Abstract  Balancing agent loads in the MRGAP problem is considered.  A goal programming model is proposed for balancing the loads.  A matheuristic algorithm is developed for solving the considered problem. Theory and Methods: In the MRGAP problem, it is essential to distribute the loads in balance to the agents. For this aim, bottleneck MRGAP (DB) and balanced MRGAP (DA) models have been proposed in the literature. In this study, the sum of load squares (YK) model is adapted to MRGAP and a goal programming (HP) model is developed. In addition, a matheuristic algorithm (MA) has been developed to solve large sized problems. Table A. Test results for HP and MA job# agent# z HP z MA t HP t MA 25 5 24.2 17.7 0.7 2.5 25 10 65.2 65.0 1035.7 63.5 50 5 23.3 18.1 256.9 78.0 50 10 24.1 18.7 1220.7 216.5 75 5 21.9 16.3 609.4 159.7 75 10 44.3 37.2 3155 643.4 100 50 22.6 15.9 3600 136 150 50 39.8 25.4 3600 196 200 50 30.7 23.5 3600 1511 250 50 24 20.1 3600 3475 Purpose: The aims of this study are to develop a new goal programming model and a matheuristic algorithm for the solution of this model for load balancing in multi-resource generalized assignment problem (MRGAP). Results: The proposed models are compared by using randomly generated test problems with 25, 50 and 75 jobs. The performance of the considered models is compared by using the percentage deviation criterion, which takes into account the maximum load, coefficient of variation and total load criteria. Table A summarizes the results for the objective function values (zHP, zMA) and CPU times (tHP, tMA) of HP and MA. The developed matheuristic algorithm has both solution quality and solution time advantage on HP model. Conclusion: The results obtained revealed the success of the proposed goal programming model and the matheuristic algorithm. Keywords:  Multi-Resource Generalized Assignment Problem  Load balancing  Goal programming  Matheuristic algorithm Article Info: Research Article Received: 03.03.2020 Accepted: 19.05.2021 DOI: 10.17341/gazimmfd.789915 Correspondence: Author: Feriştah Özçelik e-mail: fdurmaz@ogu.edu.tr phone: +90 222 239 3750