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Manufacturing sequences for the Economic Lot Scheduling problem

Published online by Cambridge University Press:  17 April 2009

James M. Fitz-Gerald  and
Elizabeth J. Billington
James M. Fitz-Gerald
Affiliation:
Department of Mathematics, University of Queensland, St Lucia, Queensland 4067, Australia.
Elizabeth J. Billington
Affiliation:
Department of Mathematics, University of Queensland, St Lucia, Queensland 4067, Australia.
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Abstract

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In the basic Economic Lot Scheduling problem, a production schedule is required to manufacture sequentially a number of products on a single machine, with the schedule chosen to minimize set-up and inventory costs. The products suffer continuous demand, and no shortfall is allowed. A recent approach involves repetitions of a production cycle (such as ABCBC for three products A, B and C, with manufacturing times chosen to prevent shortage occurring); an exhaustive search is performed over a large set of possible cycles to discover the optimal schedule.

This paper discusses the question “How many such sycles need to be examined?”, Since the answer is very relevant to practical application of the method. The case of three products is considered. Complete information is obtained for cycles up to length 12 (that is, 12 production switch overs), and partial results for longer ones. An estimate, apparently reasonable, is obtained for cycles of any length. The major trend to emerge is that surprisingly few cycles are involved.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 24 , Issue 3 , December 1981 , pp. 405 - 431
Copyright
Copyright © Australian Mathematical Society 1981

References

[1]Bomberger, Earl E., “A dynamic programming approach to a lot size scheduling problem”, Management Sci. Ser. A 12 (1966), 778–784.Google Scholar
[2]Elmaghraby, Salah E., “The economic lot scheduling problem (ELSP): review and extensions”, Management Sci. 24 (1977/1978), 587–598.CrossRefGoogle Scholar
[3]Fitz-Gerald, James M., “Repetitive multiple period cycles in the Economic Lot Scheduling problem” (Operations Research Report, University of Queensland, St Lucia, to appear).Google Scholar