Bounded colouring motivated by the limited resource partially concurrent open shop problem

Hagai Ilani, Tal Grinshpoun, Elad Shufan

Research output: Contribution to journalArticlepeer-review


Partially Concurrent Open Shop Scheduling (PCOSS) is a relaxation of the well-known Open Shop Scheduling (OSS), where some of the operations that refer to the same job may be processed concurrently. Here we extend the study of the PCOSS model by considering an additional resource, which is limited to several units. We deal with the case of preemption PCOSS, where a few polynomial algorithms are known for its OSS counterpart. The scheduling problem is equivalent to the problem of conflict graph colouring. The restriction on the number of resource units bounds the size of colour classes. We thus study the problem of bounded vertex colouring. A new bound for the makespan is presented, and it is shown that for a 2-bounded colouring the bound is attainable. Some insight about a special case of PCOSS, composed of identical jobs, is given. The model correlates to a real-life timetabling project of assigning technicians to vehicles in a garage, with an additional resource, such as vehicle lift.

Original languageEnglish
Pages (from-to)461-476
Number of pages16
JournalAnnals of Operations Research
Issue number2
StatePublished - Jul 2021


  • Bounded colouring
  • Concurrent machines
  • Graph colouring
  • Limited resources
  • Open shop scheduling
  • Technician timetabling


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