Analytical approach to solution of multi-product static inventory management model with limited warehouse capacity - Holovan, Olha; Oliinyk, Oleksandr; Oliіnyk Maksym; Kutornytska, Olena (Management and Entrepreneurship: Trends of Development, 2024)
The problem of inventory and logistics costs optimization at enterprises during the war becomes relevant due to the growing complexity of logistics processes, the destruction of logistics infrastructure, resource constraints, as well as political and economic instability in the country. The paper proposes an analytical approach to solving a multi-product inventory management model under conditions of limited warehouse capacity. The main goal of the study is to develop a mathematical model for optimizing order quantity and variable costs, taking into account the spatial limitations of the warehouse and the interdependence between goods. The proposed model is based on the adaptation of the classical Wilson formula and the use of the Lagrange method to optimize order quantities in real business conditions. The obtained closed analytical formulas for determining the optimal quantities of delivery batches and variable costs can be effectively used by managers when ordering a different range of goods under conditions of limited warehouse capacity. The convenience of the proposed analytical approach is that the Lagrange multiplier is presented in the form of a formula, while in many conditional optimization problems it is determined using numerical methods. The paper analyzes the dependence of both total order and storage costs on the warehouse area and storage tariffs, which allows to adapt the model to the specific needs of the enterprise. Calculations for different groups of goods have showed that the practical use of the proposed model allows to optimize total costs and effectively use limited warehouse space. Future research directions include the development of models for multi-warehouse logistics, taking into account seasonality of demand, limitations on capital that is expected to be invested in inventories, and the model adaptation to changes in market conditions, which will contribute to increasing the efficiency of logistics processes. JEL Classification: D12, L81, M10, С51