Given a set of jobs, with associated processing times, and a set of identical machines, each of which can process at most one job at a time, the Parallel Machine Scheduling Problem is to assign each job to exactly one machine so as to minimize the maximum completion time of a job. The problem is strongly NP-hard, and has been intensively studied since the Sixties.We present a metaheuristic and an exact algorithm, and analyze their average behavior on a large set of test instances from the literature.The metaheuristic algorithm, which is based on a scatter search paradigm, computationally proves to be highly effective, and capable of solving to optimality a very high percentage of the publicly available test instances. The exact algorithm, which is based on a specialized binary search and a branch-and-price scheme, was able to quickly solve to optimality all remaining instances.

Heuristic and Exact Algorithms for the Identical Parallel Machine Scheduling Problem / Dell'Amico, Mauro; Iori, Manuel; S., Martello; M., Monaci. - In: INFORMS JOURNAL ON COMPUTING. - ISSN 1091-9856. - STAMPA. - 20(2008), pp. 333-344. [10.1287/ijoc.1070.0246]

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