A simulation-based approach to designing a staff KPI-based reward matrix using CDF-based productivity normalization

This article focuses on developing a simulation-based approach to designing personnel reward KPI grids, utilizing Monte Carlo modeling of productivity distribution and CDF normalization. Particular attention is paid to comparing alternative bonus models based on budget parameters, the alignment of rewards with productivity levels, the scope of employee bonus eligibility, and the smoothness of reward rate adjustments. The study aims to develop a simulation approach for creating and evaluating personnel reward KPI grids by modeling productivity distribution via the Monte Carlo method and normalizing bonus rates using the Cumulative Distribution Function (CDF). To compare alternative grids, the study employs metrics such as the P95 budget, the correlation between productivity and rewards, employee bonus coverage, the average reward rate, and curve shape indicators. The results indicate that the CDF-based pooled grid entails the highest average P95 budget (242.02 thousand UAH), whereas the linear grid stands at 218.95 thousand UAH, and the one-threshold grid at 150.46 thousand UAH. The linear grid results in a P95 budget that is, on average, 23.06 thousand UAH (or 9.53%) lower than that of the CDF-based pooled grid. While both the linear and CDF-based pooled grids demonstrate an identical average correlation between performance and reward (0.897), they differ in terms of the proportion of employees receiving bonuses and the average bonus rate. The results reveal a trade-off between budget risk, the scope of bonus eligibility, and the smoothness of reward progression relative to performance. The study's scientific novelty lies in integrating labor productivity simulation, scenario analysis, and CDF-based normalization of KPI thresholds into a unified approach to reward system design. A methodology is proposed for comparing KPI grids based not only on budgetary parameters but also on the statistical alignment of rewards with performance and the shape of the bonus curve. The practical significance lies in the ability to pre-test various bonus schemes under simulated operational conditions and assess their potential budget risk prior to actual implementation. This methodology can be used to calibrate KPI thresholds, determine bonus rates, and select a reward structure that aligns with an organization's financial and motivational priorities.