A multi-stochastic fractional programming for sustainable forestry ecological restoration: Managing uncertainties in Kashgar Region, Xinjiang

Forest ecological restoration is becoming increasingly crucial in global sustainable development plans aimed at mitigating climate change and achieving carbon neutrality. Optimal management is now a key component in this process. To address the challenges and evolving demands of stakeholders in forest ecological restoration, this study integrates interval linear programming (ILP), chance-constrained programming (CCP), mixed-integer programming (MIP), and fractional planning (FP) within an optimization framework, developing an interval linear chance-constrained mixed integer fractional programming (ICCMFP) model. The model offers several key advantages in optimizing ecological, economic, and social challenges in forestry: (1) managing compound risks from uncertainties in land resources, price fluctuations, and water availability; (2) balancing conflicting objectives while enabling broader stakeholder participation in the management process; (3) supporting multi-scenario analyses to quantitatively evaluate optimal strategies and offer valuable insights for decision-makers. Taking the Xinjiang Kashgar region as a case study, the applicability of the proposed model has been evaluated under multiple objectives and scenarios. The results indicate that the ICCMFP model provides robust strategies across various water allocation scenarios, price fluctuations, and default risks. In the CB-C model, increased carbon benefits correspond to a greater willingness to expand, resulting in the total area of expansion growing from [18,524.0, 24,953.7] ha at the Chinese carbon price to [23,503.6, 30,626.0] ha at the European Union carbon price in the S1 ($p_i$ = 0.01) scenario. Compared to the interval chance-constrained mixed integer programming (ICCMP) model, the ICCMFP model offers more flexible optimization solutions through fractional programming, demonstrating its adaptability and reliability. This model is expected to offer substantial support for decision-making in sustainable ecological restoration projects globally.