Optimal production lot sizing with backlogging, random defective rate, and rework derived without derivatives

Abstract Several researchers have recently derived formulae for economic production quantities (EPQs) with some variants without reference to the use of derivatives, neither for first-order necessary conditions nor for second-order sufficient conditions. In addition, this algebraic derivation immedi...

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Bibliographic Details
Published in:Proceedings of the Institution of Mechanical Engineers. Part B, Journal of engineering manufacture Journal of engineering manufacture, 2009-08, Vol.223 (8), p.1081-1084
Main Author: Leung, K N F
Format: Article
Language:English
Subjects:
Algebra
Applied sciences
Decomposition
Defective products
Derivation
Derivatives
Economics
Exact sciences and technology
Inventory control, production control. Distribution
Logistics
Lot sizing
Mathematical programming
Operational research and scientific management
Operational research. Management science
Optimization
Unity
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Summary:Abstract Several researchers have recently derived formulae for economic production quantities (EPQs) with some variants without reference to the use of derivatives, neither for first-order necessary conditions nor for second-order sufficient conditions. In addition, this algebraic derivation immediately produces an individual formula for evaluating the minimum expected annual cost. The purpose of this note is twofold. First, this study extends earlier results to the EPQ formula, taking the imperfect rework process into account. Second, the algebraic complete-squares and perfect-squares methods can readily derive optimal expressions from an objective function in a more simple, direct, and natural manner than the algebraic method of unity decomposition adopted earlier. A numerical example has been solved to illustrate the solution procedure, and some remarks are made to conclude the note.
ISSN:0954-4054
2041-2975
DOI:10.1243/09544054JEM1530