TY - JOUR
T1 - Optimal production lot sizing with backlogging, random defective rate, and rework derived without derivatives
AU - Leung, K. N F
PY - 2009/8/1
Y1 - 2009/8/1
N2 - 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. © IMechE 2009.
AB - 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. © IMechE 2009.
KW - Complete backlogging
KW - Complete/perfect-squares method
KW - Defective items
KW - Finite production
KW - Perfect repair
UR - http://www.scopus.com/inward/record.url?scp=68849121899&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-68849121899&origin=recordpage
U2 - 10.1243/09544054JEM1530
DO - 10.1243/09544054JEM1530
M3 - RGC 21 - Publication in refereed journal
SN - 0954-4054
VL - 223
SP - 1081
EP - 1084
JO - Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture
JF - Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture
IS - 8
ER -