MATHEMATICAL MODEL FOR SELECTING PRIORITY ENERGY-SAVING MEASURES UNDER UNCERTAINTY AND LIMITED RESOURCES

Abstract

This article develops a mathematical model for optimizing an investment portfolio of energy-saving measures under fuzzy input parameters and a strictly limited budget. Investment costs and annual energy savings for each candidate measure are modeled as triangular fuzzy numbers and converted into crisp point estimates by combining alpha-cut representations with the Hurwicz criterion asymmetrically: costs tend toward the upper bound of the alpha-cut (reflecting a cautious estimation), while savings tend toward the lower bound. The economic effect of each individual measure is evaluated through its net present value (NPV), computed over the asset’s useful service life at a constant discount rate. An integral priority coefficient combines two core components–the per-cost discounted return and the longevity factor–multiplied by a risk-adjustment factor that reflects the decision-maker’s specific level of risk aversion. The selection task is formulated as a 0–1 knapsack problem and solved via dynamic programming. The robustness of the generated optimal plan is systematically assessed using a vectorized Monte Carlo simulation of 8,000 realizations, with subsequent calculation of the 5%, 50%, and 95% quantiles. The model’s real-world applicability is demonstrated through a practical case study of a healthcare complex with ten candidate measures. Ultimately, the model provides a transparent ranking of measures, a feasible investment plan within the prescribed budget, and an interval-valued NPV estimate, thereby supporting efficient investment decisions under uncertainty.