TY - JOUR
T1 - Bounded colouring motivated by the limited resource partially concurrent open shop problem
AU - Ilani, Hagai
AU - Grinshpoun, Tal
AU - Shufan, Elad
N1 - Publisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2021/7
Y1 - 2021/7
N2 - 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.
AB - 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.
KW - Bounded colouring
KW - Concurrent machines
KW - Graph colouring
KW - Limited resources
KW - Open shop scheduling
KW - Technician timetabling
UR - http://www.scopus.com/inward/record.url?scp=85076846206&partnerID=8YFLogxK
U2 - 10.1007/s10479-019-03503-9
DO - 10.1007/s10479-019-03503-9
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AN - SCOPUS:85076846206
SN - 0254-5330
VL - 302
SP - 461
EP - 476
JO - Annals of Operations Research
JF - Annals of Operations Research
IS - 2
ER -