Revisit of the Scheduling Problems with Integrated Production and Delivery on Parallel Batching Machines

摘要

In the paper, we revisit the scheduling problems with integrated production and delivery on parallel batching machines. There are n jobs and m identical and parallel batching machines. The machines have identical capacities and the jobs have identical processing time. When a job is processed and delivered to customers in time, the company earns profit; otherwise, it earns nothing. A third party logistic (3PL) provider will be used to deliver the jobs. It provides certain vehicles with identical capacities at some certain time points. In the paper [Kai Li, Zhao-hong Jia, Joseph Y.-T. Leung (2015) Integrated production and delivery on parallel batching machines, European Journal of Operational Research, 247(3), 755-763.], the authors considered the scheduling problems and designed the algorithms to deal with them. But unfortunately, there are some wrong conclusions. Specifically, we construct counterexamples to show that both of Theorem 4 and Theorem 5 are invalid. Furthermore, we provide two faster algorithms than Algorithm Sch-Id-Size.