Scheduling two parallel semiautomatic machines to minimize machine interference
Computers and Operations Research
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
Total completion time minimization in a computer system with a server and two parallel processors
Computers and Operations Research
On-line scheduling of two parallel machines with a single server
Computers and Operations Research
Scheduling reentrant jobs on parallel machines with a remote server
Computers and Operations Research
Robotics and Computer-Integrated Manufacturing
Parallel dedicated machine scheduling problem with sequence-dependent setups and a single server
Computers and Industrial Engineering
Scheduling with multiple servers
Automation and Remote Control
Computers and Operations Research
Preemptive scheduling on two parallel machines with a single server
Computers and Industrial Engineering
Online LPT algorithms for parallel machines scheduling with a single server
Journal of Combinatorial Optimization
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In this paper, we consider the problem of scheduling jobs on parallel machines with setup times. The setup has to be performed by a single server. The objective is to minimize the schedule length (makespan), as well as the forced idle time. The makespan problem is known to be NP-hard even for the case of two identical parallel machines. This paper presents a pseudopolynomial algorithm for the case of two machines when all setup times are equal to one. We also show that the more general problem with an arbitrary number of machines is unary NP-hard and analyze some list scheduling heuristics for this problem. The problem of minimizing the forced idle time is known to be unary NP-hard for the case of two machines and arbitrary setup and processing times. We prove unary NP-hardness of this problem even for the case of constant setup times. Moreover, some polynomially solvable cases are given.