Journal Article10.4028/WWW.SCIENTIFIC.NET/AMR.945-949.3344
Mixed Integer Programming Models for Two Identical Parallel Machines with a Single Server
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TL;DR: The results show that the sequence indexed model outperforms on the number of variables and computational time, which can be used to solve the instance of 20 jobs.
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Abstract: This paper addresses the problem of scheduling jobs on two identical parallel machines with a single server such that the makespan is minimized. Each job can be processed by either one of the two parallel machines, but before processing, a setup operation must be done by a single server. Two mixed integer programming models for the considered scheduling problem are developed using time indexed variable and sequence indexed variable respectively. To evaluate the performance of the two models, CPLEX is used to test instances generated randomly. The results show that the sequence indexed model outperforms on the number of variables and computational time, which can be used to solve the instance of 20 jobs.
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Citations
Approximation algorithm for parallel machine scheduling with a common server
Guoqing Wang,T.C.E. Cheng +1 more
- 01 Jan 2001
TL;DR: In this paper, the scheduling of a given set of jobs on several identical parallel machines tended by a common server is studied, where each job must be processed on one of the machines and the objective is to schedule the jobs so as to minimize the total weighted job completion times.
25
References
Scheduling parallel machines with a single server: some solvable cases and heuristics
Amir Abdekhodaee,Andrew Wirth +1 more
TL;DR: This paper considers the problem of scheduling two identical parallel machines with a single server which is required to carry out the job setups, and an integer program formulation is presented that is NP-complete in the strong sense.
75
Approximation algorithm for parallel machine scheduling with a common server
Guoqing Wang,T.C.E. Cheng +1 more
- 01 Jan 2001
TL;DR: In this paper, the scheduling of a given set of jobs on several identical parallel machines tended by a common server is studied, where each job must be processed on one of the machines and the objective is to schedule the jobs so as to minimize the total weighted job completion times.
25
On-line scheduling of two parallel machines with a single server
Lele Zhang,Andrew Wirth +1 more
TL;DR: A lower bound for the equal length job case is given, and two heuristics with tight asymptotic competitive ratios for the other two cases are proposed.
24
Preemptive scheduling on two parallel machines with a single server
Yiwei Jiang,Jianming Dong,Min Ji +2 more
TL;DR: This paper addresses a preemptive scheduling problem on two parallel machines with a single server with a tight bound of 4/3 and shows that the algorithm can produce optimal schedules for two special cases: equal processing times and equal setup times, which are NP-hard in the non-preemptive version.
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Preemptive scheduling on two parallel machines with a single server q
Yiwei Jiang,Jianming Dong,Min Ji +2 more
- 01 Jan 2013
TL;DR: In this paper, a preemptive scheduling problem on two parallel machines with a single server is addressed, where each job has to be loaded (setup) by the server before being processed on the machines.
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