Modeling Daily Sales Revenue Fluctuation in Small Retail Shops Using Runge-Kutta Method for Better Cash Management Planning

Abstract

Among the shifting trends of small retail business operations, accurate estimation and management of day-to-day cash flows are necessary for feasibility and competitiveness. In this research, the significant problem of estimating revenue fluctuations in small retail shops is addressed through a deterministic mathematical modeling approach by the fourth-order Runge-Kutta method. Our main objective is to develop a numerically stable model that would assist in short-term cash flow prediction, liquidity optimization, inventory control, and expenditure planning. We apply the method to actual daily revenue data from an open-access retail economic dataset, confirming the predictive power of the model through both qualitative trends and numerical precision. Results illustrate how the Runge-Kutta approach is applied to nonlinear revenue dynamics, reducing forecast errors by orders of magnitude compared to standard linear models. Such integration of numerical techniques with business analytics provides an empirical, new approach to cash management in real time for small-scale retail environments.