Effective planning of resources management is important for facilitating socio-economic development and eco-environmental sustainability. Such a planning effort is complicated with a variety of uncertain, dynamic and nonlinear factors as well as their interactions. In this study, an inexact-stochastic quadratic programming with recourse (ISQP-R) method is developed for reflecting dynamics of system uncertainties based on a complete set of scenarios as well as tackling nonlinearities in the objective function to reflect the effects of marginal utility on system benefits and costs. Moreover, since penalties are exercised with recourse against any infeasibility, the ISQP-R can support the analysis of various policy scenarios that are associated with different levels of economic consequences when the promised targets are violated. The developed method is applied to a case study of planning resources management and developing regional ecological sustainability. The results have been generated and are helpful for decision makers in not only identifying desired resources-allocation strategies but also gaining insight into the tradeoff between economic objective and eco-environment violation risk.

In this study, an inexact fuzzy-stochastic constraint-softened programming method is developed for municipal solid waste (MSW) management under uncertainty. The developed method can deal with multiple uncertainties presented in terms of fuzzy sets, interval values and random variables. Moreover, a number of violation levels for the system constraints are allowed. This is realized through introduction of violation variables to soften system constraints, such that the model's decision space can be expanded under demanding conditions. This can help generate a range of ecision alternatives under various conditions, allowing in-depth analyses of tradeoffs among economic objective, satisfaction degree, and constraint-violation risk. The developed method is applied to a case study of planning a MSW management system. The uncertain and dynamic information can be incorporated within a multi-layer scenario tree; revised decisions are permitted in each time period based on the realized values of uncertain events. Solutions associated with different satisfaction degree levels have been generated, corresponding to different constraint-violation risks. They are useful for supporting decisions of waste flow allocation and system-capacity expansion within a multistage context.

In this study, a multistage fuzzy-stochastic programming (MFSP) model is developed for tackling uncertainties presented as fuzzy sets and probability distributions. A vertex analysis approach is proposed for solving multiple fuzzy sets in the MFSP model. Solutions under a set of a-cut levels can be generated by solving a series of deterministic submodels. The developed method is applied to the planning of a case study for water-resources management. Dynamics and uncertainties of water availability (and thus water allocation and shortage) could be taken into account through generation of a set of representative scenarios within a multistage context. Moreover, penalties are exercised with recourse against any infeasibility, which permits in-depth analyses of various policy scenarios that are associated with different levels of economic consequences when the promised water-allocation targets are violated. The modeling results can help to generate a range of alternatives under various system conditions, and thus help decision makers to identify desired water-resources management policies under uncertainty.

In this study, an integrated two-stage optimization model (ITOM) is developed for the planning of municipal solid waste (MSW) management in the City of Regina, Canada. The ITOM improves upon the existing optimization approaches with advantages in uncertainty reflection, dynamic analysis, policy investigation, and risk assessment. It can help analyze various policy scenarios that are associated with different levels of economic penalties when the promised policy targets are violated, and address issues concerning planning for a cost-effective diversion program that targets on the prolongation of the existing landfill. Moreover, violations for capacity and diversion constraints are allowed under a range of significance levels, which reflect the tradeoffs between system-cost and constraint-violation risk. The modeling results are useful for generating a range of decision alternatives under various environmental, socio-economic, and system-reliability conditions. They are valuable for supporting the adjustment (or justification) of the existing waste-management practices, the long-term capacity planning for the city's waste-management system, and the identification of desired policies regarding waste generation and management.