Minimizing makespan of personal scheduling problem in available time-windows with split-min and setup-time constraints

Abstract

This paper deals with personal scheduling problem in available time-windows with split-min and setup-time constraints. The jobs are splittable into sub-jobs and a common lower bound on the size of each sub-job is imposed. The objective function aims to find a feasible schedule that minimizes the total completion time of all jobs. The proposed scheduling problem was proved to be strongly NP-hard by a reduction to previous problem in the preliminary results. We propose in this paper an exact method based on MILP model to find optimal solution, some heuristics to find feasible solution and a meta-heuristic based on tabu search algorithm to find good solution. The computational results show the performance of proposed exact method, some heuristics and tabu search algorithm.