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
Scheduling two parallel machines with a single server: the general case
Computers and Operations Research
Parallel machine scheduling problems with a single server
Mathematical and Computer Modelling: An International Journal
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This paper explores a specific combinatorial problem relating to reentrant jobs on parallel primary machines, with a remote server machine. A middle operation is required by each job on the server before it returns to its primary processing machine. The problem, which is new to the literature, is inspired by the logistics of a semi-automated microbiology laboratory. We establish the NP-hard nature of the problem, and demonstrate various structural properties. A heuristic is developed and tested on randomly generated benchmark data. No alternative heuristics are available in the literature for comparison, but results indicate solutions reliably within 1.5% of optimum. Moreover, tests of our heuristic on real-life data from the microbiology laboratory provide a 20% improvement in throughput relative to current practice.