A branch‐and‐price approach to the multitasking scheduling with batch control on parallel machines

Abstract

AbstractThis paper addresses multitasking scheduling with batch control on parallel machines. The specific scenario can be found in the maintenance activities of skilled workers. The objective is to minimize the total weighted completion time. In the problem, each machine needs to be allocated at least to one batch of jobs. On each machine, the processing of a primary job may be interrupted by the waiting jobs of the same machine, which can be described as the multitasking scheduling. The existing algorithms and mathematical formulations of such a scheduling problem are not suitable for the problem. An exact branch‐and‐price algorithm with heuristic pricing strategy is devised. To fast find the minimized reduced cost of the pricing problem, an artificial bee colony algorithm is developed. Specifically, it is aimed at obtaining a partitioning schedule with a minimized reduced cost, which involves the allocation of batches and the multitasking scheduling of jobs. A weak enumeration operator is proposed to cope with the batch allocation. The computational results demonstrate that the branch‐and‐price algorithm with heuristic pricing strategy outperforms general‐purpose pure CPLEX solver by orders of magnitude.