Optimizing Budget Allocation Through First-Order Linear Differential Equations and Innovative Transform Techniques

Abstract

The resolution of a first-order mathematical system effectively tackles a wide range of physical problems. The technique illustrates that the quantity of authorised variables in the system may be depicted by the activities that need to be evaluated for cost, and that the system takes into consideration the connections between these costs. Mathematical systems adhere to primary conditions, resulting in derived solutions that are specific and reliant on a single independent variable representing the temporal aspect in cost computation. This enables the forecast of costs in future years. This study confronts the inadequacies found in traditional cost allocation methods used for organizational budgeting, often leading to a biased allocation of costs to departments, irrespective of their profitability. We introduce an innovative method that employs first-order linear differential equations to model the cost dynamics associated with various activities within an organization. Moreover, an innovative transformation technique is presented to solve these equation systems efficiently, thereby enabling a precise computation of activity-based costs over a three-year projection. The results illustrate that the proposed method provides a more precise and insightful budget allocation, suggesting potential applications for financial planning and management across diverse sectors.