MODELING IN INVENTORY MANAGEMENT PROBLEMS UNDER UNCERTAINTY AND TAKING INTO ACCOUNT (INFLATION) RISKS

Abstract

A model that can be used in the problems of inventory management under uncertainty and taking into account various types of risks, in particular, inflation risks, is presented and substantiated. The strategy of stock management under uncertain (stochastic) demand usually requires the creation of a certain reserve of a predetermined volume, and then the next deliveries of stocks are made. If at a certain point in time the total stock is reduced to the size of the reserve, then an urgent order for delivery of a new batch is made. If the fulfillment of the request requires a certain time (this process is not instantaneous!), then the request for its replenishment is submitted when the stock decreases to a level exceeding the predetermined amount of the reserve. The study provides one of the simplest ways to solve the reserve problem, namely, applying the principle of guaranteed result, i.e. electing a large enough reserve that guarantees minimum risk, namely, compensation of any random deviations, which requires large costs for their storage and the like. This also leads to the so-called opportunity risk as large reserves are associated with the diversion of significant funds. In this connection, additional hypotheses are introduced in the paper, and the concept of acceptable risk - the probability that the need for reserves will not exceed the available reserve - is used as the basis for calculating the required reserve. The concept of risk coefficient is introduced, which expresses the probability that the need for reserves will be unsatisfactory due to the insufficiency of the reserve and will exceed its volume. The value of the risk coefficient can be equal to 5% or 1%. The paper uses a modified formula for calculating the nominal rate of interest with inflation interest rate risk, which includes the following components: 1) real safe rate of interest; 2) inflation premium; 3) inflation risk premium; 4) investment project risk premium (reserve creation is a kind of investment); 5) synergistic premium for investment project and inflation risk; 6) synergistic premium for investment project and inflation risk; 7) liquidity premium (in fact, it is an assessment of liquidity risk). In the study the volumes of raw materials (components) reserve are determined, which leads to the reduction of risk degree; within the framework of M. Miller and D. Orr's model the volumes of cash reserves are determined, where inflation risks are taken into account in the value of missed opportunities (which is related to the content of cash reserves balance); in the task of reserves management under uncertainty and the risk caused by it, the total costs of maintaining the reserve per unit of time are minimized and the value of the optimal reserve together with the reserve is determined (within the framework of the modified model of V. Miller and D. Orr). The paper provides a rather simple method of accounting for possible risks arising in the creation of stocks (raw materials, cash, etc.), solved the problem of selecting a specific rational value of the risk coefficient (based on expert procedures and utility theory), which allows to reflect and take into account the attitude of decision-making subjects to risk.