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Approximation algorithms for flexible job shop problems

The Flexible Job Shop Problem is a generalization of the classical job shop scheduling problem in which for every operation there is a group of machines that can process it. The problem is to assign operations to machines and to order the operations on the machines, so that the operations can be processed in the smallest amount of time. We present a linear time approximation scheme for the non-preemptive version of the problem when the number m of machines and the maximum number μ of operations per job are fixed. We also study the preemptive version of the problem when m and μ are fixed, and present a linear time (2 + e)-approximation algorithm for the problem with migration.