A general approach for the derivation of optimal solutions without derivatives

Abstract

In recent years, there have been a number of approaches in the literature that determine closed form optimal solutions to some classical inventory problems and their various extensions without using derivatives. Earliest of such approaches are based on algebraic manipulations with some a priori assumptions about the optimal solutions or based on properties of the quadratic function, whereas more recent approaches are based on problem specific assumptions such as an infinite planning horizon and integer decision variables, and analysing limiting behaviour of the decision variables and the objective function. None of the approaches is extendable to other similar optimisation problems. In this paper, we propose a general approach without any a priori assumptions of the optimal solution and without any problem specific assumptions. We demonstrate the proposed approach by applying it to some classical problems such as the EOQ and EPQ, with and without planned backorders.

Keywords:

• Inventory
• EOQ
• economic order quantity
• algebraic methods
• cost comparisons

Data availability statement

There is no data used in this research.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Notes on contributors

Cenk Çalışkan

Dr. Cenk Çalışkan is an Associate Professor in the Department of Strategic Management & Operations, Woodbury School of Business, Utah Valley University. He received his B.S. degree in Industrial Engineering from Bilkent University and his M.S. and Ph.D. degrees in Industrial & Systems Engineering from the Daniel J. Epstein Department of Industrial & Systems Engineering, Viterbi School of Engineering, University of Southern California. He was earlier an Assistant Professor in the Alfred Lerner College of Business and Economics, University of Delaware. He has also worked as an inspector for the largest private bank of Turkey, Türkiye İş Bankası, for two years; and for various software companies in Silicon Valley for five years, specialising in production planning and supply chain visibility for distributed semiconductor manufacturing networks. His research interests are transportation, logistics, production planning, inventory, and network optimisation. His work has appeared in European Journal of Operational Research, Omega, IISE Transactions, Transportation Research, Networks, Computers & Industrial Engineering, Computers & Operations Research, Production Planning & Control, Applied Mathematical Modelling, American Journal of Mathematical and Management Sciences, Symmetry and Journal of Statistics & Management Systems.