Single machine and flowshop scheduling problems with sum-of-processing time based learning phenomenon

Abstract

<p style='text-indent:20px;'>This paper addresses single machine and flowshop machines with the learning phenomenon. The learning phenomenon means that the actual jobs processing time of a job is a non-increasing function of the sum of processing times of jobs already processed. Under single machine, some properties firstly are presented to solve the objectives of minimizing the makespan problem, the total (weighted) completion time problem, the maximum lateness problem and the total tardiness problem. We show that minimizing the makespan problem and the total completion time problem can be solved in polynomial time. For the weighted completion time problem, the maximum lateness problem and the total tardiness problem, we give heuristic algorithm based on the corresponding optimal schedule and analyze the worst case error bound. Furthermore, we also show that the three problems are polynomially solvable under certain conditions. Under flowshop machines, we finally show that the makespan problem and the total completion time problem under more specialized proportional job processing times can be solved in polynomial time.