Optimization of inventory management models with variable input parameters by perturbation methods

Authors

DOI:

https://doi.org/10.15587/1729-4061.2020.204231

Keywords:

inventory management model, small parameter, perturbation method, asymptotic expansion, order quantity.

Abstract

Lines of optimization of the model of the economic order quantity (EOQ) under a condition of insignificant changes of input parameters by perturbation methods were offered.

To achieve the objective, analytical formulas of the EOQ model based on the asymptotic approach under conditions of minor changes in the input parameters were obtained. The discrete increase in the order fulfillment costs and the inventory storage costs which depend on the "small parameter" as well as periodic fluctuations in demand for products were taken as variable parameters of the system.

Based on the asymptotic method of perturbations, a convenient-to-use formula for determining EOQ under the condition of an insignificant increase in the order fulfillment costs was derived. The percentage deviation of the "perturbed" order quantity from that of Wilson's formula was also determined. Evaluation of the sensitivity of the EOQ model has revealed that the relative deviation of the "perturbed" order quantity from the optimal one at insignificantly changing costs of the order fulfillment varied from 1 % to 15 % depending on the period. Comparative analysis of the total costs calculated using the asymptotic formula and Wilson's formula has found that taking into account changes in order quantities leads to a reduction in the company’s expenditures.

A two-parameter model of optimal order quantity was constructed. It takes into account both minor changes in the order fulfillment costs and inventory storage costs. Two-parameter asymptotic formulas were derived to determine optimal order quantity and total costs which correspond to the "perturbed" order quantity.

The proposed asymptotic model which takes into account a discrete insignificant increase in the order fulfillment costs and periodic nature of fluctuations in demand for products has practical significance. This model can be used to optimize the logistics management system of the enterprise due to its proximity to realities and the ease of use.

Author Biographies

Damir Bikulov, Zaporizhzhya National University Zhukovskoho str., 66, Zaporizhzhya, Ukraine, 69600

Doctor of Sciences in Public Administration, Professor

Department of Business Administration and International Management

Olha Holovan, College of Economics and Law of Zaporizhzhya National University Zhukovskoho str., 66-В, Zaporizhzhya, Ukraine, 69600

PhD, Associate Professor

Cyclic Commission of Economic Disciplines and Management

Oleksandr Oliynyk, Zaporizhzhya National University Zhukovskoho str., 66, Zaporizhzhya, Ukraine, 69600

PhD, Associate Professor

Department of Business Administration and International Management

Karyna Shupchynska, Zaporizhzhya National University Zhukovskoho str., 66, Zaporizhzhya, Ukraine, 69600

Department of Business Administration and International Management

Svitlana Markova, College of Economics and Law of Zaporizhzhya National University Zhukovskoho str., 66-В, Zaporizhzhya, Ukraine, 69600

PhD, Associate Professor

Cyclic Commission of Economic Disciplines and Management

Anna Chkan, College of Economics and Law of Zaporizhzhya National University Zhukovskoho str., 66-В, Zaporizhzhya, Ukraine, 69600

PhD, Associate Professor

Cyclic Commission of Economic Disciplines and Management

Evgenia Makazan, College of Economics and Law of Zaporizhzhya National University Zhukovskoho str., 66-В, Zaporizhzhya, Ukraine, 69600

PhD, Associate Professor

Cyclic Commission of Economic Disciplines and Management

Kateryna Sukhareva, Municipal Institution «Zaporizhzhya Regional Center of Scientific and Technical Creativity of Student Youth «Grani» of Zaporizhzhya Regional Council Maiakovskoho ave., 14, Zaporizhzhya, Ukraine, 69035

PhD, Associate Professor

Olena Kryvenko, Zaporizhzhya National University Zhukovskoho str., 66, Zaporizhzhya, Ukraine, 69600

Рostgraduate Student

Department of Business Administration and International Management

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Published

2020-06-30

How to Cite

Bikulov, D., Holovan, O., Oliynyk, O., Shupchynska, K., Markova, S., Chkan, A., Makazan, E., Sukhareva, K., & Kryvenko, O. (2020). Optimization of inventory management models with variable input parameters by perturbation methods. Eastern-European Journal of Enterprise Technologies, 3(3 (105), 6–15. https://doi.org/10.15587/1729-4061.2020.204231

Issue

Vol. 3 No. 3 (105) (2020): Control processes

Section

Control processes

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Copyright (c) 2020 Damir Bikulov, Olha Holovan, Oleksandr Oliynyk, Karyna Shupchynska, Svitlana Markova, Anna Chkan, Evgenia Makazan, Kateryna Sukhareva, Olena Kryvenko

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