A Survey on Minimizing Makespan for the Preemptive Job Shop with Two Machines

We survey results for the job shop scheduling problem J2 |pmtn |Cmax for the case of two machines with preemption. With respect to polynomial time approximation algorithms, the problem is essentially equivalent to the case in which there are two machines and each operation has unit length. This assumption can be achieved in polynomial time with only loss by scaling and rounding the inputs to give polynomial-valued operation lengths. Then since preemption is allowed we may take an operation to be composed of multiple unit-length operations (on the same machine). (The assumption can be removed with no loss for all but the last algorithm presented but will be used throughout to simplify descriptions.)

By: Tracy Kimbrel

Published in: RC23639 in 2005


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