An inexact inventory-theory-based chance-constrained programming model for solid waste management

In this study, an inexact inventory-theory-based chance-constrained programming (IICP) model is proposed for planning waste management systems. The IICP model is derived through introducing inventory theory model into a general inexact chance-constrained programming framework. It can not only tackle uncertainties presented as both probability distributions and discrete intervals, but also reflect the influence of inventory problem in decision-making problems. The developed method is applied to a case study of long-term municipal solid waste (MSW) management planning. Solutions of total waste allocation, waste allocation batch and waste transferring period associated different risk levels of constraint violation are obtained. The results can be used to identify inventory-based MSW management planning with minimum system cost under various constraint-violation risks. Compared with the ICP model, the developed IICP model can more actually reflect the complexity of MSW management systems and provide more useful information for decision makers.     

An inexact stochastic optimization model for agricultural irrigation management with a case study in China

In this study, an inexact stochastic optimization model (ITSOM) is developed for agricultural irrigation management with a case study in China. Functional intervals are introduced into the modeling framework to much accurately address the spatial and temporal variation of system components. According to the results of case study, the developed model shows effectiveness in dealing with functional information of system parameters, and brings no difficulty in obtaining optimal water allocation patterns. It is indicated that the surface water resource (i.e. Heshui River) has better be used as the major source, and proper exploration of groundwater can curtail the related expense and further increase the system net benefit. Among eight farms, hybrid rice farm is going to obtain the greatest amount of water than the others, while watermelon farm has the priority to get water due to its highest benefit and penalty rate. In comparison, water allocations to rapeseed and tea farms are to be minimal within the respective fluctuation ranges. Scenario analysis is also conducted to clarify the differences between ITSOM and a conventional interval two-stage stochastic programming (ITSP) model. A total of 60 scenarios are initiated respectively linking to 60 monthly ITSP models for the entire planning horizon. The results show that the optimal objective function values of all ITSP models always fall into the range of that obtained from ITSOM. As each ITSP solution can only correspond to the system condition under a certain time point, it is highly vulnerable to system variation.     

Development of an inexact two-stage stochastic model with downside risk control for water quality management and decision analysis under uncertainty

Water quality management along rivers involves making water-allocation plans, establishing water quality goals, and controlling pollutant discharges, which is complicated itself but further challenged by existence of uncertainties. In this study, an inexact two-stage stochastic downside risk-aversion programming (ITSDP) model is developed for supporting regional water resources allocation and water quality management problems under uncertainties. The ITSDP method is a hybrid of interval-parameter programming, two-stage stochastic programming, and downside risk measure to tackle uncertainties described in terms of interval values and probability distributions. A water quality simulation model was provided for reflecting the relationship between the water resources allocation, wastewater discharge, and environmental responses. The proposed approach was applied to a hypothetical case for a shared stream water quality management with one municipal, three industrial and two agricultural sectors. A number of scenarios corresponding to different river inflows and risk levels were examined. The results demonstrated that the model could effectively communicate the interval-format and random uncertainties, and risk-aversion into optimization process, and generate a trade-off between the system economy and stability. They could be helpful for seeking cost-effective management strategies under uncertainties, and gaining an in-depth insight into the water quality management system characteristics, and make cost-effective decisions.     

Agricultural effluent control under uncertainty: An inexact double-sided fuzzy chance-constrained model

An inexact double-sided fuzzy chance-constrained programming (IDFCCP) method was developed in this study and applied to an agricultural effluent control management problem. IDFCCP was formulated through incorporating interval linear programming (ILP) into a double-sided fuzzy chance-constrained programming (DFCCP) framework, and could be used to deal with uncertainties expressed as not only possibility distributions associated with both left- and right-hand-side components of constraints but also discrete intervals in the objective function. The study results indicated that IDFCCP allowed violation of system constraints at specified confidence levels, where each confidence level consisted of two reliability scenarios. This could lead to model solutions with high system benefits under acceptable risk magnitudes. Furthermore, the introduction of ILP allowed uncertain information presented as discrete intervals to be communicated into the optimization process, such that a variety of decision alternatives can be generated by adjusting the decision-variable values within their intervals. The proposed model could help decision makers establish various production patterns with cost-effective water quality management schemes under complex uncertainties, and gain in-depth insights into the trade-offs between system economy and reliability.     

Water quality management in a wetland system using an inexact left-hand-side chance-constrained fuzzy multi-objective approach

Water quality management is a significant item in the sustainable development of wetland system, since the environmental influences from the economic development are becoming more and more obvious. In this study, an inexact left-hand-side chance-constrained fuzzy multi-objective programming (ILCFMOP) approach was proposed and applied to water quality management in a wetland system to analyze the tradeoffs among multiple objectives of total net benefit, water quality, water resource utilization and water treatment cost. The ILCFMOP integrates interval programming, left-hand-side chance-constrained programming, and fuzzy multi-objective programming within an optimization framework. It can both handle multiple objectives and quantify multiple uncertainties, including fuzziness (aspiration level of objectives), randomness (pollutant release limitation), and interval parameters (e.g. water resources, and wastewater treatment costs). A representative water pollution control case study in a wetland system is employed for demonstration. The optimal schemes were analyzed under scenarios at different probabilities (p _i , denotes the admissible probability of violating the constraint i). The optimal solutions indicated that, most of the objectives would decrease with increasing probability levels from scenarios 1 to 3, since a higher constraint satisfaction probability would lead to stricter decision scopes. This study is the first application of the ILCFMOP model to water quality management in a wetland system, which indicates that it is applicable to other environmental problems under uncertainties.     

An emission source inversion model based on satellite data and its application in air quality forecasts

This paper aims at constructing an emission source inversion model using a variational processing method and adaptive nudging scheme for the Community Multiscale Air Quality Model (CMAQ) based on satellite data to investigate the applicability of high resolution OMI (Ozone Monitoring Instrument) column concentration data for air quality forecasts over the North China. The results show a reasonable consistency and good correlation between the spatial distributions of NO2 from surface and OMI satellite measur...     

Dual inexact fuzzy chance-constrained programming for planning waste management systems

This study develops a dual inexact fuzzy chance-constrained programming (DIFCCP) method for planning municipal solid waste (MSW) management systems. The concept of random boundary interval (RBI) is introduced to address the high uncertain parameters in the studied system. Fuzzy flexible programming and chance-constrained programming are also introduced to take into account the uncertainties of RBIs and various uncertainties in MSW management system. Compared with the existing methods, the developed method could deal with the uncertainty without simplification and thus is more robust. Moreover, the potential system-failure risks in MSW management system due to the existing uncertainties could be quantified by means of violation levels and satisfaction levels in DIFCCP. The developed method then is applied to a MSW management system. The obtained solutions could be used for generating efficient management schemes. The values of violation and satisfaction levels could help decision makers understand the tradeoffs between system cost and system-failure risk, and identify desired strategy according to the practical economic and environmental situation.     

Study of statistically correcting model CMAQ-MOS for forecasting regional air quality

Based on analysis of the air pollution observational data at 8 observation sites in Beijing including outer suburbs during the period from September 2004 to March 2005, this paper reveals synchronal and in-phase characteristics in the spatial and temporal variation of air pollutants on a city-proper scale at deferent sites; describes seasonal differences of the pollutant emission influence between the heating and non-heating periods, also significantly local differences of the pollutant emission influence between the urban district and outer suburbs, i.e. the spatial and temporal distribution of air pollutant is closely related with that of the pollutant emission intensity. This study shows that due to complexity of the spatial and temporal distribution of pollution emission sources, the new generation Community Multi-scale Air Quality (CMAQ) model developed by the EPA of USA produced forecasts, as other models did, with a systematic error of significantly lower than observations, albeit the model has better capability than previous models had in predicting the spatial distribution and variation tendency of multi-sort pollutants. The reason might be that the CMAQ adopts average amount of pollutant emission inventory, so that the model is difficult to objectively and finely describe the distribution and variation of pollution emission sources intensity on different spatial and temporal scales in the areas, in which the pollution is to be forecast. In order to correct the systematic prediction error resulting from the average pollutant emission inventory in CMAQ, this study proposes a new way of combining dynamics and statistics and establishes a statistically correcting model CMAQ-MOS for forecasts of regional air quality by utilizing the relationship of CMAQ outputs with corresponding observations, and tests the forecast capability. The investigation of experiments presents that CMAQ-MOS reduces the systematic errors of CMAQ because of the uncertainty of pollution emission inventory and improves the forecast level of air quality. Also this work employed a way of combining point and area forecasting, i.e. taking the products of CMAQ for a center site to forecast air pollution for other sites in vicinity with the scheme of model products "reanalysis" and average over the "area".     

An inexact programming method for agricultural irrigation systems under parameter uncertainty

Rapid population growth and economy development have led to increasing reliance on water resources. It is even aggravated for agricultural irrigation systems where more water is necessary to support the increasing population. In this study, an inexact programming method based on two-stage stochastic programming and interval-parameter programming is developed to obtain optimal water-allocation strategies for agricultural irrigation systems. It is capable of handling such problems where two-stage decisions need to be suggested under random- and interval-parameter inputs. An interactive solving procedure derived from conventional interval-parameter programming makes it possible for the impact of lower and upper bounds of interval inputs to be well reflected in the resulting solutions. An agricultural irrigation management problem is then provided to demonstrate the applicability, and reasonable solutions are obtained. Compared to the solutions from a representative interval-parameter programming model where only one decision-stage exists, the interval of optimized objective-function value is narrow, indicating more alternatives could be provided when water-allocation targets are rather high. However, chances of obtaining more benefits exist in association with a risk of paying more penalties; such a relationship becomes apparent when the variation of water availability is much intensive.     

A recourse-based nonlinear programming model for stream water quality management

A recourse-based nonlinear programming (RBNP) method is developed for stream water quality management under uncertainty. It can not only reflect uncertainties expressed as interval values and probability distributions but also address nonlinearity in the objective function. A 0-1 piecewise linearization approach and an interactive algorithm are advanced for solving the RBNP model. The RBNP is applied to a case of planning stream water quality management. The RBNP modeling system can provide an effective linkage between environmental regulations and economic implications expressed as penalties or opportunity losses caused by improper policies. The solutions can be used for generating a variety of alternatives under different combinations of pre-regulated targets, which are also associated with different water-quality-violation risk levels and varied potential economic penalty or loss values.     

An empirical model of water quality for use in rapid management strategy evaluation in Southeast Queensland, Australia

Simulation models have been widely adopted in fisheries for management strategy evaluation (MSE). However, in catchment management of water quality, MSE is hampered by the complexity of both decision space and the hydrological process models. Empirical models based on monitoring data provide a feasible alternative to process models; they run much faster and, by conditioning on data, they can simulate realistic responses to management actions. Using 10 years of water quality indicators from Queensland, Australia, we built an empirical model suitable for rapid MSE that reproduces the water quality variables' mean and covariance structure, adjusts the expected indicators through local management effects, and propagates effects downstream by capturing inter-site regression relationships. Empirical models enable managers to search the space of possible strategies using rapid assessment. They provide not only realistic responses in water quality indicators but also variability in those indicators, allowing managers to assess strategies in an uncertain world.     

Grey fuzzy optimization model for water quality management of a river system

A grey fuzzy optimization model is developed for water quality management of river system to address uncertainty involved in fixing the membership functions for different goals of Pollution Control Agency (PCA) and dischargers. The present model, Grey Fuzzy Waste Load Allocation Model (GFWLAM), has the capability to incorporate the conflicting goals of PCA and dischargers in a deterministic framework. The imprecision associated with specifying the water quality criteria and fractional removal levels are modeled in a fuzzy mathematical framework. To address the imprecision in fixing the lower and upper bounds of membership functions, the membership functions themselves are treated as fuzzy in the model and the membership parameters are expressed as interval grey numbers, a closed and bounded interval with known lower and upper bounds but unknown distribution information. The model provides flexibility for PCA and dischargers to specify their aspirations independently, as the membership parameters for different membership functions, specified for different imprecise goals are interval grey numbers in place of a deterministic real number. In the final solution optimal fractional removal levels of the pollutants are obtained in the form of interval grey numbers. This enhances the flexibility and applicability in decision-making, as the decision-maker gets a range of optimal solutions for fixing the final decision scheme considering technical and economic feasibility of the pollutant treatment levels. Application of the GFWLAM is illustrated with case study of the Tunga–Bhadra river system in India.     

Statistical assessment of air quality interventions

This paper presents a general spatio-temporal model for assessing the air quality impact of environmental policies which are introduced as abrupt changes. The estimation method is based on the EM algorithm and the model allows to estimate the impact on air quality over a region and the reduction of human exposure following the considered environmental policy. Moreover, impact testing is proposed as a likelihood ratio test and the number of observations after intervention is computed in order to achieve a certain power for a minimal reduction. An extensive case study is related to the introduction of the congestion charge in Milan city. The consequent estimated reduction of airborne particulate matters and total nitrogen oxides motivates the methods introduced while its derivation illustrates both implementation and inferential issues.     

Using geostatistical simulation to disaggregate air quality model results for individual exposure estimation on GPS tracks

In this work, we address the mismatch in spatio-temporal resolution between individual, point-location based exposure and grid cell based air quality model predictions by disaggregating the grid model results. Variability of PM₁₀ point measurements was modelled within each grid cell by the exponential variogram, using point support concentration measurements. Variogram parameters were estimated over the study area globally using constant estimates, and locally by multiple regression models using traffic, weather and land use data. Model predictions of spatio-temporal variability were used for geostatistical unconditional simulation, estimating the deviation of point values from grid cell averages on GPS tracks. The distribution of deviations can be used as an estimate of uncertainty for individual exposure. Results showed a relevant impact of the disaggregation uncertainties compared to other uncertainty sources, dependent of the model used for spatio-temporal variability. Depending on individual behaviour and variability of the pollutant, these uncertainties average out again over time.     

An inexact fuzzy-chance-constrained two-stage mixed-integer linear programming approach for flood diversion planning under multiple uncertainties

In this study, an inexact fuzzy-chance-constrained two-stage mixed-integer linear programming (IFCTIP) approach is developed for flood diversion planning under multiple uncertainties. A concept of the distribution with fuzzy boundary interval probability is defined to address multiple uncertainties expressed as integration of intervals, fuzzy sets and probability distributions. IFCTIP integrates the inexact programming, two-stage stochastic programming, integer programming and fuzzy-stochastic programming within a general optimization framework. IFCTIP incorporates the pre-regulated water-diversion policies directly into its optimization process to analyze various policy scenarios; each scenario has different economic penalty when the promised targets are violated. More importantly, it can facilitate dynamic programming for decisions of capacity-expansion planning under fuzzy-stochastic conditions. IFCTIP is applied to a flood management system. Solutions from IFCTIP provide desired flood diversion plans with a minimized system cost and a maximized safety level. The results indicate that reasonable solutions are generated for objective function values and decision variables, thus a number of decision alternatives can be generated under different levels of flood flows.     

A stochastic conflict resolution model for water quality management in reservoir–river systems

In this paper, optimal operating rules for water quality management in reservoir–river systems are developed using a methodology combining a water quality simulation model and a stochastic GA-based conflict resolution technique. As different decision-makers and stakeholders are involved in the water quality management in reservoir–river systems, a new stochastic form of the Nash bargaining theory is used to resolve the existing conflict of interests related to water supply to different demands, allocated water quality and waste load allocation in downstream river. The expected value of the Nash product is considered as the objective function of the model which can incorporate the inherent uncertainty of reservoir inflow. A water quality simulation model is also developed to simulate the thermal stratification cycle in the reservoir, the quality of releases from different outlets as well as the temporal and spatial variation of the pollutants in the downstream river. In this study, a Varying Chromosome Length Genetic Algorithm (VLGA), which has computational advantages comparing to other alternative models, is used. VLGA provides a good initial solution for Simple Genetic Algorithms and comparing to Stochastic Dynamic Programming (SDP) reduces the number of state transitions checked in each stage. The proposed model, which is called Stochastic Varying Chromosome Length Genetic Algorithm with water Quality constraints (SVLGAQ), is applied to the Ghomrud Reservoir–River system in the central part of Iran. The results show, the proposed model for reservoir operation and waste load allocation can reduce the salinity of the allocated water demands as well as the salinity build-up in the reservoir.     

An interval-parameter multi-stage stochastic programming model for water resources management under uncertainty

In this study, an interval-parameter multi-stage stochastic linear programming (IMSLP) method has been developed for water resources decision making under uncertainty. The IMSLP is a hybrid methodology of inexact optimization and multi-stage stochastic programming. It has three major advantages in comparison to the other optimization techniques. Firstly, it extends upon the existing multi-stage stochastic programming method by allowing uncertainties expressed as probability density functions and discrete intervals to be effectively incorporated within the optimization framework. Secondly, 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. Thirdly, it cannot only handle uncertainties through constructing a set of scenarios that is representative for the universe of possible outcomes, but also reflect dynamic features of the system conditions through transactions at discrete points in time over the planning horizon. The developed IMSLP method is applied to a hypothetical case study of water resources management. The results are helpful for water resources managers in not only making decisions of water allocation but also gaining insight into the tradeoffs between environmental and economic objectives.     

Analytical trajectory model of air pollution

Summary The basic principles of the method of calculating air pollution in a complex terrain are presented. The method is based on a trajectory air pollution model. The formula for the distribution of pollutant concentration in a puff is obtained by solving a simple turbulent diffusion equation analytically. An example of the model's application is given.