Stochastic Model of the Operating Cycle

Abstract

In this paper, we analyze the impact of revenue uncertainty on the current assets of a company. The process of revenue generation is assumed to follow the geometric Brownian motion. The trend and random components of the revenue are singled out. These characteristics are considered from the point of view of the concept of sustainable growth. The solution of the cost equation is given, which includes the assessment of the actual and alternative costs of the company arising from the excess and shortage of current assets. We propose a model of the operating cycle that allows establishing analytical dependence of the duration of the operational cycle on the standard deviation of the logarithm of the growth rate of the company’s revenue. The equation obtained includes the duration of the operational cycle in the absence of uncertainty and the coefficient whose value is proportional to the mathematical expectation of the deviation of revenue from the maximum value. We considered the impact of the dominant factors, the change of which leads to a change in the duration of the operational cycle in the absence of uncertainty. The results obtained are checked against the data reflecting the current assets of 41 enterprises in the coal industry.