Optimization of Inventory Management Models With Variable Input Parameters by Perturbation Methods

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