Abstract
In this paper, we study two scheduling problems on a single machine with rejection and an operator non-availability interval. In the operator non-availability interval, no job can be started or be completed. However, a crossover job is allowed such that it can be started before this interval and completed after this interval. Furthermore, we also assume that job rejection is allowed. That is, each job is either accepted and processed in-house, or is rejected by paying a rejection cost. Our task is to minimize the sum of the makespan (or the total weighted completion time) of accepted jobs and the total rejection cost of rejected jobs. For two scheduling problems with different objective functions, by borrowing the previous algorithms in the literature, we propose a pseudo-polynomial-time algorithm and a fully polynomial-time approximation scheme (FPTAS), respectively.
Highlights
We introduce some models on scheduling with non-availability intervals, scheduling with rejection, and scheduling with rejection and non-availability intervals, respectively.1.1
Two models of the non-availability interval were studied mainly: one is the machine non-availability (MNA) intervals due to the machine maintenances and the other is the operator non-availability (ONA) intervals because the operator is resting from work
We are the first to consider scheduling with rejection and an operator non-availability interval
Summary
It is assumed that the machines are available at all times. For problem Pm|MNA(0, bi )|Cmax , i.e., each machine Mi has a machine release time b j , Lee [6] provided a modified LPT (MLPT) algorithm with a tight approximation ratio 43. Lee [6] studied the problem Pm|MNA( ai , bi )|Cmax with the assumption that one machine is always available. He showed that the approximation ratios of LS (List Scheduling) and LPT are m and m+. Aggoune [10] studied the flow-shop scheduling problem with several MNA intervals on each machine. A hybrid meta-heuristic and a lot of numerical testings were designed for the above problem
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
