Guohe Huang

A GREY LINEAR PROGRAMMING APPROACH FOR MUNICIPAL SOLID WASTE MANAGEMENT PLANNING UNDER UNCERTAINTY

Abstract In optimization analysis by linear programming, uncertainties may exist in model coefficients and stipulations (right-hand side constraints). These uncertainties can propagate through the analysis and generate uncertainties in the results. However, among the previous methods dealing with uncertainty, some were too complicated to be applied to actual problems, and some were unable to reflect completely the uncertainties of the input and output information. In this paper, a grey linear programming (GLP) model is introduced to the civil engineering area. This method allows uncertainties in the model inputs to be communicated into the optimization process, and thereby solutions reflecting the inherent uncertainties can be derived. A grey linear programming problem can be solved easily by running a simplex program several times. The modelling approach is applied to a hypothetical problem of waste flow allocation planning within a municipal solid waste management system. The results indicate that reaso...

AN INEXACT TWO-STAGE STOCHASTIC PROGRAMMING MODEL FOR WATER RESOURCES MANAGEMENT UNDER UNCERTAINTY

Abstract An inexact two-stage stochastic programming (ITSP) model is proposed for water resources management under uncertainty. The model is a hybrid of inexact optimization and two-stage stochastic programming. It can reflect not only uncertainties expressed as probability distributions but also those being available as intervals. The solution meth od for ITSP is computationally effective, which makes it applicable to practical problems. The ITSP is applied to a hypothetical case study of water resources system operation. The results indicate that reasonable solutions have been obtained. They are further analyzed and interpreted for generating decision alternatives and identifying significant factors that affect the systems performance. The information obtained through these post-optimality analyses can provide useful decision support for water managers.

Grey integer programming: An application to waste management planning under uncertainty

Abstract This paper introduces a grey integer programming (GIP) method for facility expansion planning under uncertainty, by incorporating the concepts of grey number and grey mathematical programming into a mixed integer linear programming optimization framework. The approach is an improvement upon previous integer programming methods in terms of its technical characteristics and applicability. It allows uncertain information to be effectively communicated into the optimization process and the resulting solutions. It also has low computational requirements and is thus applicable to practical problems. The modelling approach is applied to a hypothetical planning problem of waste flow allocation and treatment/disposal facility expansion within a regional solid waste management system. The binary variable solutions provide the ranges of different development alternatives within a multi-period, multi-facility and multi-scale context, and the continuous variable solutions provide optimal schemes for waste flow allocation corresponding to the upper and lower bounds of the objective function value. The results indicate that reasonable and useful solutions can be achieved through the developed approach.

A hybrid inexact-stochastic water management model

Abstract An inexact-stochastic water management (ISWM) model is proposed and applied to a case study of water quality management within an agricultural system. The model is based on an inexact chance-constrained programming (ICCP) method, which improves upon the existing inexact and stochastic programming approaches by allowing both distribution information in B and uncertainties in A and C to be effectively incorporated within its optimization process. In its solution process, the ICCP model (under a given pi level) is first transformed into two deterministic submodels, which correspond to the upper and lower bounds for the desired objective function value. This transformation process is based on an interactive algorithm, which is different from normal interval analysis or best/worst case analysis. Interval solutions, which are feasible and stable in the given decision space, can then be obtained by solving the two submodels sequentially. Thus, decision alternatives can be generated by adjusting decision variable values within their solution intervals. The obtained ICCP solutions are also useful for decision makers to obtain insight regarding tradeoffs between environmental and economic objectives and between increased certainties and decreased safeties (or increased risks). Results of the case study indicate that useful solutions for the planning of agricultural activities in the water quality management system have been obtained. A number of decision alternatives have been generated and analyzed based on projected applicable conditions. Generally, some alternatives can be considered when water quality objective is given priority, while the others may provide compromises between environmental and economic considerations. The above alternatives represent various options between environmental and economic tradeoffs. Willingness to accept low agricultural income will guarantee meeting the water quality objectives. A strong desire to acquire high agricultural income will run into the risk of violating water quality constraints.

IPWM: AN INTERVAL PARAMETER WATER QUALITY MANAGEMENT MODEL

This paper provides an interval parameter water quality management (IPWM) model and its application to a case study of water pollution control planning within an agricultural system. The model allows uncertain information, presented as interval numbers, to be effectively communicated into the optimization process and resulting solutions, such that decision alternatives can be generated through interpretation of the solutions (presented as stable intervals), which are flexible in reflecting possible system condition variations caused by the existence of input uncertainties. This IPWM solution feature may be favored by decision makers because of the increased flexibility and applicability for determining the final decision schemes. The method also does not lead to complicated intermediate models, and thus has reasonable computational requirements. Results of the case study indicate that reasonable solutions for agricultural activities in the study system have been generated. Sensitivity analyses of the effe...

An interval-parameter fuzzy two-stage stochastic program for water resources management under uncertainty

This study presents an interval-parameter fuzzy two-stage stochastic programming (IFTSP) method for the planning of water-resources-management systems under uncertainty. The model is derived by incorporating the concepts of interval-parameter and fuzzy programming techniques within a two-stage stochastic optimization framework. The approach has two major advantages in comparison to other optimization techniques. Firstly, the IFTSP method can incorporate pre-defined water policies directly into its optimization process and, secondly, it can readily integrate inherent system uncertainties expressed not only as possibility and probability distributions but also as discrete intervals directly into its solution procedure. The IFTSP process is applied to an earlier case study of regional water resources management and it is demonstrated how the method efficiently produces stable solutions together with different risk levels of violating pre-established allocation criteria. In addition, a variety of decision alternatives are generated under different combinations of water shortage.

An Interval-Parameter Fuzzy-Stochastic Programming Approach for Municipal Solid Waste Management and Planning

In this study, an integrated fuzzy-stochastic linear programming model is developed and applied to municipal solid waste management. Methods of chance-constrained programming and fuzzy linear programming are incorporated within a general interval-parameter mixed-integer linear programming framework. It improves upon the existing optimization methods with advantages in uncertainty reflection, data availability, and computational requirement. The model can be used for answering questions related to types, times and sites of solid waste management practices, with the objective of minimizing system costs over the planning horizon. The model can effectively reflect dynamic, interactive, and uncertain characteristics of municipal waste management systems. In its solution process, the model is transformed into two deterministic submodels, corresponding to upper and lower bounds of the desired objective function values under a given significance level, based on an interactive algorithm. Results of the methods application to a hypothetical case indicate that reasonable outputs have been obtained. It demonstrates the practical applicability of the proposed methodology.

An integrated multi-criteria decision analysis and inexact mixed integer linear programming approach for solid waste management

Abstract This paper reports on an integration of multi-criteria decision analysis (MCDA) and inexact mixed integer linear programming (IMILP) methods to support selection of an optimal landfill site and a waste-flow-allocation pattern such that the total system cost can be minimized. Selection of a landfill site involves both qualitative and quantitative criteria and heuristics. In order to select the best landfill location, it is often necessary to compromise among possibly conflicting tangible and intangible factors. Different multi-objective programming models have been proposed to solve the problem. A weakness with the different multi-objective programming models used to solve the problem is that they are basically mathematical and ignore qualitative and often subjective considerations such as the risk of groundwater pollution as well as other environmental and socio-economic factors which are important in landfill selection. The selection problem also involves a change in allocation pattern of waste-flows required by construction of a new landfill. A waste flow refers to the routine of transferring waste from one location in a city to another. In selection of landfill locations, decision makers need to consider both the potential sites that should be used as well as the allocation pattern of the waste-flow at different periods of time. This paper reports on our findings in applying an integrated IMILP/MCDA approach for solving the solid waste management problem in a prairie city. The five MCDA methods of simple weighted addition, weighted product, co-operative game theory, TOPSIS, and complementary ELECTRE are adopted to evaluate the landfill site alternatives considered in the solid waste management problem, and results from the evaluation process are presented.

Grey linear programming, its solving approach, and its application

Abstract In systems analysis, uncertainties may exist in model parameters and input data. Those uncertainties can propagate through the analysis and generate uncertainty in the results. Grey systems theory offers a method for incorporating uncertainties into systems analysis. In this paper, a new method of solution for a grey linear programming (GLP) model is advanced. The GLP model allows grey messages concerning the model parameters and input data to be communicated into optimization processes and solutions. A new application field—grey systems analysis of water resource planning and decision making under uncertainty—is introduced, and a case study is reported of water quantity allocation and quality planning in a drainage basin area connected to a water delivery canal in Xiamen, China. The results indicate that the solutions derived are feasible for the study area. Sensitivity tests of the effects of grey inputs on grey outputs are reported. It is indicated that the grey degrees of the solutions increa...

A TWO-STAGE INTERVAL-STOCHASTIC PROGRAMMING MODEL FOR WASTE MANAGEMENT UNDER UNCERTAINTY

Abstract This study introduces a two-stage interval-stochastic programming (TISP) model for the planning of solid-waste management systems under uncertainty. The model is derived by incorporating the concept of two-stage stochastic programming within an interval-parameter optimization framework. The approach has the advantage that policy determined by the authorities, and uncertain information expressed as intervals and probability distributions, can be effectively communicated into the optimization processes and resulting solutions. In the modeling formulation, penalties are imposed when policies expressed as allowable waste-loading levels are violated. In its solution algorithm, the TISP model is converted into two deterministic submodels, which correspond to the lower and upper bounds for the desired objective-function value. Interval solutions, which are stable in the given decision space with associated levels of system-failure risk, can then be obtained by solving the two submodels sequentially. Two special characteristics of the proposed approach make it unique compared with other optimization techniques that deal with uncertainties. First, the TISP model provides a linkage to predefined policies determined by authorities that have to be respected when a modeling effort is undertaken; second, it furnishes the reflection of uncertainties presented as both probabilities and intervals. The developed model is applied to a hypothetical case study of regional solid-waste management. The results indicate that reasonable solutions have been generated. They provide desired waste-flow patterns with minimized system costs and maximized system feasibility. The solutions present as stable interval solutions with different risk levels in violating the waste-loading criterion and can be used for generating decision alternatives.