Lower Bounds for the Head-Body-Tail Problem on Parallel Machines: A Computational Study of the Multiprocessor Flow Shop
Ann Vandevelde, Han Hoogeveen, Cor Hurkens, Jan Karel Lenstra
INFORMS Journal on Computing · 2005 · Volume 17 · Issue 3
Abstract
The multiprocessor flow-shop is the generalization of the flow-shop in which each machine is replaced by a set of identical machines. As finding a minimum-length schedule is NP-hard, we set out to find good lower and upper bounds. The lower bounds are based on relaxation of the capacities of all machine sets except one. This results in a parallel-machine scheduling problem with release dates and delivery times, for which we derive a number of lower bounds. We pay special attention to the time complexity of algorithms for computing these bounds. To obtain the upper bounds a constructive algorithm in subsequent stages is used. We present an experimental comparison of the various lower and upper bounds for the multiprocessor flow-shop problem.
Keywords
multiprocessor flow-shop, parallel machine scheduling, head-body-tail problems, preemptive schedule, lower bound, computational study
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