Scheduling problems with effects of deterioration and truncated job-dependent learning

Abstract

We study the scheduling problems with effects of deterioration and truncated job-dependent learning effect on a single machine, where the actual processing time of a job is a function of the job-dependent learning effect, its starting time, and a control parameter. The objective functions are to minimize the makespan, the total completion time, the total waiting time, the total absolute deviation of completion time, the total absolute deviation of waiting time, the earliness, tardiness and common (CON) (slack (SLK), unrestricted (DIF)) due date penalty, respectively. For the general case, by reducing them to a linear assignment problem, we solve them in polynomial time \(O(n^3)\). For the special case where all the jobs have a common learning rate, we present an \(O(n \log n)\) algorithm to obtain the optimal solution.