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

Gerodimos, Alex E., Glass, Celia A. and Potts, Chris N. (2000) Scheduling the production of two-component jobs on a single machine. European Journal of Operational Research, 120, (2), 250-259. (doi:10.1016/S0377-2217(99)00154-X).


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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.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1016/S0377-2217(99)00154-X
ISSNs: 0377-2217 (print)
Related URLs:
Keywords: component scheduling, single machine, dynamic programming, NP-hard
Subjects: H Social Sciences > HD Industries. Land use. Labor > HD28 Management. Industrial Management
Q Science > QA Mathematics
Divisions : University Structure - Pre August 2011 > School of Mathematics > Operational Research
ePrint ID: 29611
Accepted Date and Publication Date:
Date Deposited: 19 Jul 2006
Last Modified: 31 Mar 2016 11:55

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