Multitasking scheduling and due date assignment with deterioration effect and efficiency promotion

Abstract

We investigate a multitasking scheduling and due date assignment problem with position-dependent deterioration effect and efficiency promotion. Multitasking scheduling allows the processing of a primary job being interrupted by the waiting jobs that are available but unfinished. The duration of processing a primary job is comprised of three parts: the processing time of the remaining part of the primary job, the interruption time denoting the time of the partial processing of the waiting jobs, and the switching time denoting the time during which no jobs are processed when the primary job being scheduled. We consider two behavioral factors which may affect the production efficiency. One is the position-dependent deterioration effect on primary jobs, and the other is the linear efficiency promotion on waiting jobs. The position-dependent deterioration effect means that the productivity deteriorates over time due to personnel fatigue, thereby increasing the actual processing times of primary jobs depending on their scheduled positions. The efficiency promotion indicates that switching between different jobs can keep them from being bored, thereby leading to an increase in productivity when operators tackle the interruption parts of waiting jobs. The due dates of jobs are decision variables in two well-known due date assignment models, i.e., the common and unrestricted due date assignment models. We study several scheduling criteria including the makespan, the total completion time, and two due date-related criteria. For each considered problem, we design an efficient polynomial time algorithm, and present the structural properties of the optimal schedules under different conditions considering the relationships between deterioration effect and efficiency promotion.