Minimizing the makespan with late start penalties added to processing times in a single facility scheduling problem

This paper considers the following scheduling problem: Minimize the makespan in a single facility problem where the processing time of a job consists of a fixed and a variable part. The variable part depends on the start time of the job. The objective is to minimize makespan. Two optimizing algorithms based on dynamic programming and branch-and-bound techniques and five heuristic rules have been proposed. The heuristic solutions have been compared with the optimal solution for up to 7 jobs to identify the best heuristic. The detailed computational results for the branch-and-bound and the best heuristic rules are then obtained for problems with up to 15 jobs.