Scheduling two parallel semiautomatic machines to minimize machine interference
Computers and Operations Research
Parallel machine scheduling with a common server
Discrete Applied Mathematics
Scheduling parallel machines with a single server: some solvable cases and heuristics
Computers and Operations Research
Equal processing and equal setup time cases of scheduling parallel machines with a single server
Computers and Operations Research
Sequencing and Scheduling in Robotic Cells: Recent Developments
Journal of Scheduling
On-line scheduling of two parallel machines with a single server
Computers and Operations Research
Scheduling two parallel machines with a single server: the general case
Computers and Operations Research
Scheduling with multiple servers
Automation and Remote Control
Parallel machine scheduling problems with a single server
Mathematical and Computer Modelling: An International Journal
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This paper addresses a preemptive scheduling problem on two parallel machines with a single server. Each job has to be loaded (setup) by the server before being processed on the machines. The preemption is allowed in this paper. The goal is to minimize the makespan. We first show that it is no of use to preempt the job during its setup time. Namely, every optimal preemptive schedule can be converted to another optimal schedule where all the setup times are non-preemptively performed on one machine. We then present an algorithm with a tight bound of 4/3 for the general case. Furthermore, we show 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.