Multitasking scheduling with job switching allowed between alternate periods

This paper explores the multitasking scheduling problem via alternate periods, which is common in manufacturing and service industries. The shift pattern comprises regular shifts interspersed with breaks, allowing job switching. We focus on two alternate periods consisting of odd periods and even periods. Each job is not only processed completely within odd periods or completely within even periods, but job switching is also allowed between alternate periods with additional overhead. For this problem, we propose two job switching models. The first model is alternate periods multitasking scheduling with switching time, where a fixed switching time is incurred whenever a job is switched from one period to its adjacent period. The second model is alternate periods multitasking scheduling with diverse speeds, where an urgent switching cost is produced if a job is processed through the alternate periods with different speeds. For the two models, we study three scheduling objectives including minimising the total completion time, minimising the maximum lateness, and minimising the number of tardy jobs, respectively. For each of the problems under consideration, we investigate the structural properties of the optimal schedule and develop the corresponding pseudo-polynomial time dynamic programming algorithm. Furthermore, we give examples to effectively illustrate the proposed algorithms.