In real-world municipal solid waste (MSW) management systems, identification of proper policies under uncertainty for accomplishing desired waste-disposal targets is critical. An inexact minimax regret integer programming (IMMRIP) method for the long-term planning of MSW management is developed. It incorporates the technique of minimax regret analysis (MMR) into an interval-parameter mixed-integer linear programming (IMILP) framework. The IMMRIP method can handle dual uncertainties presented as both random variables and interval values; it only needs a list of scenarios without any assumption on their probability distributions. It can facilitate dynamic analysis for decisions of system-capacity expansion and/or development within a multi-facility and multi-period context. Moreover, it can also be used for analyzing multiple scenarios associated with different system costs and risk levels. An interval-element cost matrix can be transformed into an interval-element regret matrix based on an interactive algorithm. Solutions based on an inexact minimax regret criterion can identify desired alternatives for MSW management and planning under a variety of uncertainties. In a companion paper, the developed method will be applied to a real case study in the City of Regina, Canada.

In this study, an inexact minimax regret mixed integer programming (IMMRIP) method is applied to long-term planning of municipal solid waste (MSW) management in the City of Regina. The method can help tackle the dynamic, interactive, and uncertain characteristics of the solid waste management system in the city, and can address issues concerning plans for cost-effective waste diversion and landfill prolongation. Thirty-six situations were examined based on multiple alternatives and scenarios under different waste-generation levels. Reasonable solutions have been generated for decisions of system-capacity expansion and waste-flow allocation, demonstrating complex tradeoffs among system cost, regret level, and constraint-violation risk. Solutions associated with further inexact minimax regret (IMMR) analyses can help tackle tradeoffs between minimized system cost and maximized system feasibility. Under the optimal alternative, the system would reach a maximum reliability with the lowest risks of penalty and wastage. Results provide valuable inputs for adjustment of the existing waste flow allocation patterns to satisfy the city's diversion goals, long-term capacity planning for the city's waste management system, and generation desired policies for managing the city's waste collection and treatment.

A hybrid fuzzy-stochastic water-management (FSWM) model is developed for agricultural sustainability under uncertainty, based on advancement of a multistage fuzzy-stochastic quadratic programming (MFSQP) approach. In MFSQP, uncertainties presented in terms of fuzziness and randomness can be incorporated within a multilayer scenario tree, such that revised decisions are permitted in each time period based on the realized values of the uncertain events. Moreover, fuzzy quadratic terms are used in the objective function to minimize the variation of satisfaction degrees among the constraints; it allows an increased flexibility in controlling the system risk in the optimization process. Results of the case study indicate that useful solutions for the planning of agricultural water management have been obtained. In the FSWM model, a number of policies for agricultural water supply are conducted. The results obtained can help decision makers to identify desired water-allocation schemes for agricultural sustainability under uncertainty, particularly when limited water resources are available for multiple competing users.

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, 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.