Budget allocation problem for projects with considering risks, robustness, resiliency, and sustainability requirements

Budget Allocation Problem (BAP) for projects is considered one of the critical risks that necessitate the completion of projects in the shortest possible duration. This aspect is significant in extensive projects such as national endeavors directly impacting people's livelihoods. This research focuses on introducing Sustainable, Robust, Resilient, and Risk-averse Budget Allocation for Projects (S3RBAP). A hybrid robust stochastic optimization approach was employed, incorporating Weighted VaR (WVaR) and the minimum function as risk criteria to ensure the robustness of the objective function. This model is designed to minimize the weighted expected value, WVaR, and the minimum progress function, thereby promoting the 3R and sustainability framework to tackle budget fluctuations and enhance project viability. The case study revolves around the construction of national projects in Iran. Ultimately, the project's required budget was allocated within the budgetary constraints. Sensitivity analysis found that the integration of 3R and sustainability led to a 13.5 % reduction in the progress function compared to scenarios without these principles. Furthermore, increasing the conservatism coefficient to 20 % decreased the progress function to −0.58 %. Reducing the resiliency coefficient had an adverse effect by disrupting the budget allocation process. The computational time is increased gradually with the escalation of problem complexity, while the progress function decreases due to the increased number of projects. The findings demonstrate that using an exponential function promotes risk aversion, whereas a sine function encourages risk-seeking behaviour within this research context.