A goal programming model for balancing agent loads in the multi-resource generalized assignment problem

The multi-resource generalized assignment problem (MRGAP) is the assignment of jobs to agents under capacity constraints to minimize the total assignment. In this problem, each agent has multiple resources, each job is assigned to only one agent, and multiple jobs can be assigned to one agent. In the MRGAP problem, it is essential to distribute the loads in balance to the agents. In the literature, for balancing agent loads, bottleneck MRGAP with the aim of minimizing the maximum agent load, and balanced assignment MRGAP models with the aim of minimizing the difference between the maximum agent load and the minimum agent load have been proposed. In this study, the sum of load squares model has been adapted for MRGAP, as well as a new goal programming MRGAP model and a matheuristic algorithm for the solution of this model are developed. The performances of the proposed model and the algorithm were compared with the models taken from the literature by using randomly derived test problems. The quality of the obtained solutions is determined by considering the maximum load, coefficient of variation and total load criteria. The test results are evaluated in terms of these three criteria. The results obtained revealed the success of the proposed goal programming model and the matheuristic algorithm.