Algorithms for the joint multitasking scheduling and common due date assignment problem
研究了单机上联合多任务调度与公共交货期指派问题，提出多项式时间算法，并通过数值实验验证其效率，发现多任务场景下最优解有时优于无多任务场景。
In this paper, we investigate a joint multitasking scheduling and common due date assignment problem on a single machine, for which examples can be found in product delivery process in logistics. Multitasking allows the machine to perform multiple tasks. The multitasking phenomenon has been observed in various practical domains, including manufacturing and administration. In multitasking settings, each waiting job interrupts a currently in-processing job, causing an interruption time and a switching time. In common due date assignment problems, the objective is to determine the optimal value of this due date with the purpose of minimising a total penalty function, which is associated with service quality. For the problem with general interruption functions, analytical properties are obtained to reduce the search space of the optimal solutions. For the cases with linear interruption functions, we develop a polynomial-time algorithm. Numerical experiments have been conducted to validate the efficiency of our proposed algorithm. Computational results also demonstrate an interesting phenomenon that in some cases, the optimal solutions under multitasking are superior to the counterparts without multitasking. Besides, we also devise a mixed integer programme for the cases with linear interruption function.