Simulated Annealing for Two-Agent Scheduling Problem with Exponential Job-Dependent Position-Based Learning Effects

In this paper, we consider a two-agent single-machine scheduling problem with exponential job-dependent position-based learning effects. The objective is to minimize the total weighted completion time of one agent with the restriction that the makespan of the other agent cannot exceed an upper bound. First, we propose a branch-andbound algorithm by developing some dominance /feasibility properties and a lower bound to find an optimal solution. Second, we design an efficient simulated annealing (SA) algorithm to search a near optimal solution by considering six different SAs to generate initial solutions. We show the performance superiority of the suggested SA using a numerical experiment. Specifically, we verify that there is no significant difference in the performance of % errors between different considered SAs using the paired t-test. Furthermore, we testify that random generation method is better than the others for agent A, whereas the initial solution method for agent B did not affect the performance of% error.