Scheduling the production of two-component jobs on a single machine

Scheduling the production of two-component jobs on a single machine

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Article ID: iaor2001203
Country: Netherlands
Volume: 120
Issue: 2
Start Page Number: 250
End Page Number: 259
Publication Date: Jan 2000
Journal: European Journal of Operational Research
Authors: , ,
Keywords: programming: dynamic
Abstract:

In this paper, we examine the scheduling of jobs, each of which comprises a standard and a specific component, on a single machine. A set-up time is required before each batch of standard components is processed. A job is completed when both its standard and specific components have been processed and are available. Standard components only become available when the batch to which they belong is completed, whereas specific components are available on completion of their processing. We present results for two well-known due-date related criteria. In particular, an O(n2) dynamic programming algorithm is derived for the problem of minimising the maximum lateness. For minimising the number of late jobs, we show that the problem is NP-hard and give a dynamic programming algorithm that requires pseudo-polynomial time. Finally, we show that a variant of the number of late jobs problem, in which there is a common processing time for the standard components, is solvable in O(n4 log n) time.

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