Two-agent scheduling with agent specific batches on an unbounded serial batching machine

Two-agent single-machine scheduling to minimize the batch delivery cost

“…They show that the makespan problem is polynomially solvable for the incompatible case and is NP-hard in the ordinary sense for the compatible case, and that the total completion time problem is NP-hard and is polynomially solvable for the incompatible case with a fixed number of job types. Kovalyov and Ameur Soukhal (2015) investigate the scheduling problems on the same serial unbounded batching machine with two agents. On this machine, jobs of the same batch complete simultaneously, and the batch processing time is equal to the total processing time of its jobs plus a setup time.…”

“…The model under consideration generalizes that studied in Hall and Potts (2003) by allowing two competing agents and by including setup times for the batches, and that studied in Kovalyov and Ameur Soukhal (2015) by allowing delivery cost, which renders the model more realistic. In addition, the solution method to solve the problems under consideration developed in this paper is different from that in Kovalyov and Ameur Soukhal (2015), by which one can show that the corresponding problems admit FPTASs, and, what is more, there are little results on FPTAS for the multiagent scheduling problems in the literature. The remaining part of the paper includes the following sections.…”

Two‐agent scheduling on a single sequential and compatible batching machine

“…Wang et al () addressed the two‐agent bounded parallel‐batching scheduling problem with unit processing time and non‐identical job sizes, where the objective is to minimize the makespan of one agent such that the makespan of the other agent does not exceed a fixed value. On the other hand, Mor and Mosheiov (), Kovalyov et al (), and Yin et al () considered problems in the sequential‐batching machine setting. Mor and Mosheiov () assumed agent‐dependent setup times and identical jobs, and both agents seek to minimize their own flowtimes.…”

“…Mor and Mosheiov () assumed agent‐dependent setup times and identical jobs, and both agents seek to minimize their own flowtimes. Kovalyov et al () presented polynomial and pseudo‐polynomial algorithms to solve problems involving combinations of various scheduling criteria. Yin et al () generalized the work of Kovalyov et al () by adding a delivery cost for each production batch.…”

CON/SLK due date assignment and scheduling on a single machine with two agents

“…Yin et al studied JIT scheduling on unrelated parallel machines, where each agent desires to maximize the weighted number of its just‐in‐time jobs that are completed exactly on their due dates. Li and Yuan studied two‐agent scheduling on a common unbounded parallel‐batching machine, where any number of jobs can be processed simultaneously in a batch, while Kovalyov et al and Yin et al focused on the unbounded serial‐batching machine case, where all the jobs in a batch are considered to have been completed together at the completion time of the last job in the batch.…”