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

Shisheng Li, T. C.E. Cheng, C. T. Ng, Jinjiang Yuan

Research output: Journal article publicationJournal articleAcademic researchpeer-review

10 Citations (Scopus)


We study two-agent scheduling on a single sequential and compatible batching machine in which jobs in each batch are processed sequentially and compatibility means that jobs of distinct agents can be processed in a common batch. A fixed setup time is required before each batch is started. Each agent seeks to optimize some scheduling criterion that depends on the completion times of its own jobs only. We consider several scheduling problems arising from different combinations of some regular scheduling criteria, including the maximum cost (embracing lateness and makespan as its special cases), the total completion time, and the (weighted) number of tardy jobs. Our goal is to find an optimal schedule that minimizes the objective value of one agent, subject to an upper bound on the objective value of the other agent. For each problem under consideration, we provide either a polynomial-time or a pseudo-polynomial-time algorithm to solve it. We also devise a fully polynomial-time approximation scheme when both agents’ scheduling criteria are the weighted number of tardy jobs.

Original languageEnglish
Pages (from-to)628-641
Number of pages14
JournalNaval Research Logistics
Issue number8
Publication statusPublished - Dec 2017


  • dynamic programming
  • sequential and compatible batch
  • single-machine scheduling
  • two agents

ASJC Scopus subject areas

  • Modelling and Simulation
  • Ocean Engineering
  • Management Science and Operations Research


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