Conducting almost any business requires maintaining a certain level of various types of inventory. The necessity for inventory arises from, among other things, the seasonality of raw materials, the length of the production cycle, delivery delays, the efficiency and precision of production planning, its control and coordination, prevailing trends, etc. Maintaining inventory at an optimal level in an enterprise ensures the continuity of fulfilling customer orders with proper production rhythm. Therefore, it is crucial to correctly determine the postulated size and structure of inventory. Inventory is an internally diverse category, including raw materials, supplies, work-in-progress, semi-finished products, finished goods, and merchandise. These items are characterized by the lowest degree of financial liquidity among all elements of a company’s current assets. The formation of inventory in an enterprise significantly affects its financial position. Excessive inventory ties up large financial resources, leading to the freezing of part of the working capital and reducing the company’s financial liquidity. Excessive inventory entails high storage costs, including opportunity costs. On the other hand, it eliminates the problem of shortages of raw materials, supplies, or semi-finished products. Conversely, a shortage of inventory increases the risk of disrupting production continuity (this applies to raw materials and supplies) or sales (this applies to finished goods and merchandise). It is therefore necessary to find an optimum in this regard. Correctly building a mathematical model is of key importance for making optimization decisions in inventory management. Thanks to such a model, it becomes possible to determine the most favorable size of a single purchase (a single delivery batch). The problem of optimizing the size of a single purchase should be considered as minimizing the total annual cost associated with inventory accumulation. For example, let an enterprise purchase a certain type of good in quantity Q over a year. Consumption occurs evenly throughout the accepted period. The company buys this good in batches. When purchasing individual batches, the enterprise pays a fixed unit purchase price pz. Each purchase transaction involves additional fixed costs Ks, incurred during order preparation and transaction execution. Furthermore, the enterprise incurs storage costs for this good, amounting to km per unit annually. Thus, a decision problem arises: how much to buy so that the total costs associated with inventory accumulation are minimal. Below, a method for determining the delivery size of a good, optimal from the point of view of minimizing total purchase, preparation, transaction, and storage costs, will be presented. In order to build a useful mathematical model in this regard, the main cost items that determine the total costs of inventory accumulation Kc will be defined and classified. They consist of two types of costs that differ in essence:
• costs associated with transactions performed
• costs associated with holding inventory in the warehouse.
Costs associated with transactions performed are the sum of two components:
• fixed transaction costs incurred during order preparation and execution (including transport costs, if they are borne by the recipient)
• purchase costs.
Costs associated with transactions performed can also be called acquisition costs.
In turn, the costs associated with holding inventory in the warehouse are mainly:
• storage costs
• insurance costs (against accidental damage, theft, etc.)
• opportunity costs (for example, potential interest on capital frozen in the form of inventory).