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

Kit-Nam Francis Leung

International Journal of Production Economics, 2008, vol. 113, issue 1, 275-281

Abstract: 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.

Date: 2008
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Citations: View citations in EconPapers (8)

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