Asymptotic model of import purchase optimization at food industry enterprises under the conditions of changes in logistics costs

Abstract

The paper is devoted to the development of a model for optimizing food industry enterprises import purchases in the context of changes in the external environment based on the asymptotic approach. Fluctuations in raw material prices, increasing logistics costs and unpredictable events on international markets complicate procurement planning, as a result of which traditional optimization methods become less effective. The aim of the work is to develop an analytical model for optimizing purchases at food industry importing enterprises in the context of rising prices and logistics costs. The proposed approach is based on the use of asymptotic perturbation methods, which allows taking into account gradual changes in purchase prices and delivery costs and adapting the economic order size model to these changes.

In the work, based on the classical economic order quantity model (EOQ), “perturbed” formulas for determining the order size and total logistics costs have been obtained. To take into account changes in delivery costs and purchase prices, the model has used asymptotic expansions for small perturbation parameters, which made it possible to obtain a solution in analytical form. The practical application of the model has been carried out on the example of enterprises in the coffee market in Ukraine, which is characterized by significant dependence on imports and significant price fluctuations. The calculation results have been compared with the traditional model, which made it possible to evaluate the effectiveness of the proposed approach in conditions of dynamic changes.

The study has found that an increase in the purchase price causes a decrease in the optimal order size due to an increase in inventory holding costs, while an increase in delivery costs, on the contrary, stimulates enterprises to increase the volume of imported purchases to minimize the frequency of deliveries. The comparison of total logistics costs confirmed that the proposed asymptotic model allows enterprises to more effectively adapt their purchasing strategy and reduce costs compared to traditional methods.

The results of the study confirm the practical significance of the asymptotic model for managing import purchases under turbulent conditions. Using the model will allow food industry enterprises to make more reasoned decisions regarding import volumes and reduce total logistics costs.