DEVELOPMENT OF AN ECONOMIC-MATHEMATICAL MODEL FOR THE APPLICATION OF KPI SYSTEMS IN INDUSTRIAL ENTERPRISES

This article develops an economic-mathematical model for assessing and forecasting the economic efficiency of Key Performance Indicator (KPI) systems in industrial enterprises, using "Almalyk MMC" JSC as a case study. The model comprises two interconnected blocks: (1) a production and efficiency block linking KPI sub-indices to operational indicators (labor productivity, localization volume, export volume, and energy efficiency); and (2) a financial results block translating operational outcomes into net profit and return on assets (ROA). Using data from "Almalyk MMC" JSC for 2017-2024, the model parameters were estimated using ordinary least squares (OLS) and time-series analysis procedures. All equations are statistically significant at the 95% confidence level (R² ranging from 0.875 to 0.983), with Durbin-Watson (DW) statistics within acceptable limits. Forecasts for 2025-2026 deviate from the enterprise's business plan by only 1.2-5%, confirming the model's practical reliability. The model enables the setting of target KPI values, optimal resource allocation, and risk scenario analysis. Recommendations are formulated for digitalizing KPI monitoring, strengthening localization and import substitution, increasing investment in workforce qualifications, integrating energy efficiency indicators into the KPI system, and conducting regular scenario forecasting. The study also examines the theoretical foundations of the KPI concept formulated by Kaplan and Norton (1992) within the Balanced Scorecard framework and presents regression, log-log, integral index, forecasting, and optimization models applicable to industrial enterprises.