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.

In this study, an inexact multistage stochastic integer programming (IMSIP) method is developed for water resources management under uncertainty. This method incorporates techniques of inexact optimization and multistage stochastic programming within an integer programming framework. It can deal with uncertainties expressed as both probabilities and discrete intervals, and reflect the dynamics in terms of decisions for water allocation through transactions at discrete points of a complete scenario set over a multistage context. Moreover, the IMSIP can facilitate analyses of the multiple policy scenarios that are associated with economic penalties when the promised targets are violated as well as the economies-of-scale in the costs for surplus water diversion. A case study is provided for demonstrating the applicability of the developed methodology. The results indicate that reasonable solutions have been generated for both binary and continuous variables. For all scenarios under consideration, corrective actions can be undertaken dynamically under various pre-regulated policies and can thus help minimize the penalties and costs. The IMSIP can help water resources managers to identify desired system designs against water shortage and for flood control with maximized economic benefit and minimized systemfailure risk.

In this study, a two-stage fuzzy robust integer programming (TFRIP) method has been developed for planning environmental management systems under uncertainty. This approach integrates techniques of robust programming and two-stage stochastic programming within a mixed integer linear programming framework. It can facilitate dynamic analysis of capacity-expansion planning for waste management facilities within a multi-stage context. In the modeling formulation, uncertainties can be presented in terms of both possibilistic and probabilistic distributions, such that robustness of the optimization process could be enhanced. In its solution process, the fuzzy decision space is delimited into a more robust one by specifying the uncertainties through dimensional enlargement of the original fuzzy constraints. The TFRIP method is applied to a case study of long-term waste-management planning under uncertainty. The generated solutions for continuous and binary variables can provide desired waste-flow-allocation and capacity-expansion plans with a minimized system cost and a maximized system feasibility.

An interval-fuzzy multistage programming (IFMP) method is developed for water resources management under uncertainty. This method improves upon the existing multistage stochastic programming methods by allowing uncertainties presented as discrete intervals, fuzzy sets, and probability distributions to be effectively incorporated within its optimization framework. The IFMP method can adequately reflect dynamic variations of system conditions, particularly for large-scale multistage problems with sequential structures. The uncertain information can be incorporated within a multi-layer scenario tree; revised decisions are permitted in each time period based on the realized values of the uncertain events. Moreover, this method can be used for analyzing various policy scenarios that are associated with different levels of economic consequences when the promisedwater-allocation targets are violated.Acase study ofwater resources management is then provided for demonstrating applicability of the developed method. For all scenarios under consideration, corrective actions are allowed to be taken dynamically in reference to the preregulated policies and the realized uncertainties. The results can help quantify the relationships among system benefit, satisfaction degree, and constraint-violation risk. Thus, desired decision alternatives can be generated under different conditions of supply-demand dynamics.