Technical note : A use of the complete squares method to solve and analyze a quadratic objective function with two decision variables exemplified via a deterministic inventory model with a mixture of backorders and lost sales

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

36 Scopus Citations
View graph of relations

Related Research Unit(s)


Original languageEnglish
Pages (from-to)275-281
Journal / PublicationInternational Journal of Production Economics
Issue number1
Publication statusPublished - May 2008


Several researchers have recently derived formulae for economic-order quantities (EOQs) 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 average annual cost. The purpose of this paper is twofold. Exemplifying a use of the complete squares method through solving and analyzing Montgomery et al.'s [Montgomery, D.C., Bazaraa, M.S., Keswani, A.C., 1973. Inventory models with a mixture of backorders and lost sales. Naval Research Logistics Quarterly 20, 255-263] model, i.e. the EOQ model taking into account the case of partial backordering first we can readily derive global optimal expressions from a non-convex quadratic cost function with two decision variables in an algebraic manner, second we can straightforwardly identify some analytic cases in a way that is not as easy to do this using calculus. A numerical example has been solved to illustrate the solution procedure. Finally, some special cases can be deduced from the EOQ model under study, and concluding remarks are drawn. © 2007 Elsevier B.V. All rights reserved.

Research Area(s)

  • Analytic cases, Backorders, Lost sales, Non-convex, The complete squares method

Citation Format(s)