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

Abstract

This 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.

Parallel optimization over the integer efficient set

“…Thus, techniques integrating new architectures such as multicore CPUs have been used in order to reduce the solving time in an economical way. Parallelism brings computing power to many applications that are scientific (see Chen and Senar, 2019;Kantour et al, 2019;Gao et al, 2022), technical (see Khurpia et al, 1990), medical (see Sutter et al, 1998), military (see Langerz et al (2012)), who have huge needs (in terms of computing and storage power), and that cannot be satisfied by classic sequential machines, as efficient as they are. In this section, we introduce some parallel building blocks used in the implementation of the second method.…”