An inexact two-stage mixed integer linear programming method for solid waste management in the City of Regina

In this study, an interval-parameter two-stage mixed integer linear programming (ITMILP) model is developed for supporting long-term planning of waste management activities in the City of Regina. In the ITMILP, both two-stage stochastic programming and interval linear programming are introduced into a general mixed integer linear programming framework. Uncertainties expressed as not only probability density functions but also discrete intervals can be reflected. The model 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. Three scenarios are considered based on different waste management policies. The results indicate that reasonable solutions have been generated. They are valuable for supporting the adjustment or justification of the existing waste flow allocation patterns, the long-term capacity planning of the City's waste management system, and the formulation of local policies and regulations regarding waste generation and management.     

A two-stage support-vector-regression optimization model for municipal solid waste management - a case study of Beijing, China

In this study, a two-stage support-vector-regression optimization model (TSOM) is developed for the planning of municipal solid waste (MSW) management in the urban districts of Beijing, China. It represents a new effort to enhance the analysis accuracy in optimizing the MSW management system through coupling the support-vector-regression (SVR) model with an interval-parameter mixed integer linear programming (IMILP). The developed TSOM can not only predict the city's future waste generation amount, but also reflect dynamic, interactive, and uncertain characteristics of the MSW management system. Four kernel functions such as linear kernel, polynomial kernel, radial basis function, and multi-layer perception kernel are chosen based on three quantitative simulation performance criteria [i.e. prediction accuracy (PA), fitting accuracy (FA) and over all accuracy (OA)]. The SVR with polynomial kernel has accurate prediction performance for MSW generation rate, with all of the three quantitative simulation performance criteria being over 96%. Two cases are considered based on different waste management policies. The results are valuable for supporting the adjustment of the existing waste-allocation patterns to raise the city's waste diversion rate, as well as the capacity planning of waste management system to satisfy the city's increasing waste treatment/disposal demands.     

Waste management with recourse: An inexact dynamic programming model containing fuzzy boundary intervals in objectives and constraints

The existing inexact optimization methods based on interval-parameter linear programming can hardly address problems where coefficients in objective functions are subject to dual uncertainties. In this study, a superiority–inferiority-based inexact fuzzy two-stage mixed-integer linear programming (SI-IFTMILP) model was developed for supporting municipal solid waste management under uncertainty. The developed SI-IFTMILP approach is capable of tackling dual uncertainties presented as fuzzy boundary intervals (FuBIs) in not only constraints, but also objective functions. Uncertainties expressed as a combination of intervals and random variables could also be explicitly reflected. An algorithm with high computational efficiency was provided to solve SI-IFTMILP. SI-IFTMILP was then applied to a long-term waste management case to demonstrate its applicability. Useful interval solutions were obtained. SI-IFTMILP could help generate dynamic facility-expansion and waste-allocation plans, as well as provide corrective actions when anticipated waste management plans are violated. It could also greatly reduce system-violation risk and enhance system robustness through examining two sets of penalties resulting from variations in fuzziness and randomness. Moreover, four possible alternative models were formulated to solve the same problem; solutions from them were then compared with those from SI-IFTMILP. The results indicate that SI-IFTMILP could provide more reliable solutions than the alternatives.     

IFRP: a hybrid interval-parameter fuzzy robust programming approach for waste management planning under uncertainty

In this study, an interval-parameter fuzzy-robust programming (IFRP) model is developed and applied to the planning of solid waste management systems under uncertainty. As an extension of the existing fuzzy-robust programming and interval-parameter linear programming methods, the IFRP can explicitly address system uncertainties with complex presentations. Parameters in the IFRP model can be represented as interval numbers and/or fuzzy membership functions, such that the uncertainties can be directly communicated into the optimization process and resulting solution. Furthermore, highly uncertain information for the lower and upper bounds of interval parameters that exist due to the complexity of the real world can be effectively handled through introducing the concept of fuzzy boundary interval. Consequently, robustness of the optimization process and solution can be enhanced. Results of the case study indicate that useful solutions for planning municipal solid waste management practices can be generated. They reflect a compromise between optimality and stability of the study system. Willingness to pay higher costs will guarantee the system stability; however, a desire to reduce the costs will run the risk of potential instability of the system. The results also suggest that the proposed hybrid methodology is applicable to practical problems that are associated with highly complex and uncertain information.     

Inexact fuzzy-stochastic mixed-integer programming approach for long-term planning of waste management – Part A: Methodology

In this study, an inexact fuzzy chance-constrained two-stage mixed-integer linear programming (IFCTIP) approach is proposed for supporting long-term planning of waste-management systems under multiple uncertainties in the City of Regina, Canada. The method improves upon the existing inexact two-stage programming and mixed-integer linear programming techniques by incorporating uncertainties expressed as multiple uncertainties of intervals and dual probability distributions within a general optimization framework. The developed method can provide an effective linkage between the predefined environmental policies and the associated economic implications. Four special characteristics of the proposed method make it unique compared with other optimization techniques that deal with uncertainties. Firstly, it provides a linkage to predefined policies that have to be respected when a modeling effort is undertaken; secondly, it is useful for tackling uncertainties presented as intervals, probabilities, fuzzy sets and their incorporation; thirdly, it facilitates dynamic analysis for decisions of facility-expansion planning and waste-flow allocation within a multi-facility, multi-period, multi-level, and multi-option context; fourthly, the 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 solid waste-generation rates are violated. In a companion paper, the developed method is applied to a real case for the long-term planning of waste management in the City of Regina, Canada.     

An interval-based regret-analysis method for identifying long-term municipal solid waste management policy under uncertainty

In this study, an interval-based regret-analysis (IBRA) model is developed for supporting long-term planning of municipal solid waste (MSW) management activities in the City of Changchun, the capital of Jilin Province, China. The developed IBRA model incorporates approaches of interval–parameter programming (IPP) and minimax–regret (MMR) analysis within an integer programming framework, such that uncertainties expressed as both interval values and random variables can be reflected. The IBRA can account for economic consequences under all possible scenarios associated with different system costs and risk levels without making assumptions on probabilistic distributions for random variables. A regret matrix with interval elements is generated based on a matrix of interval system costs, such that desired decision alternatives can be identified according to the interval minimax regret (IMMR) criterion. The results indicate that reasonable solutions have been generated. They can help decision makers identify the desired alternatives regarding long-term MSW management with a compromise between minimized system cost and minimized system-failure risk.     

Violation analysis for solid waste management systems: an interval fuzzy programming approach

This paper introduces a violation analysis approach for the planning of regional solid waste management systems under uncertainty, based on an interval-parameter fuzzy integer programming (IPFIP) model. In this approach, several given levels of tolerable violation for system constraints are permitted. This is realized through a relaxation of the critical constraints using violation variables, such that the model's decision space can be expanded. Thus, solutions from the violation analysis will not necessarily satisfy all of the model's original constraints. Application of the developed methodology to the planning of a waste management system indicates that reasonable solutions can be generated through this approach. Considerable information regarding decisions of facility expansion and waste flow allocation within the waste management system were generated. The modeling results help to generate a number of decision alternatives under various system conditions, allowing for more in-depth analyses of tradeoffs between environmental and economic objectives as well as those between system optimality and reliability.     

FSILP: fuzzy-stochastic-interval linear programming for supporting municipal solid waste management

Although many studies on municipal solid waste management (MSW management) were conducted under uncertain conditions of fuzzy, stochastic, and interval coexistence, the solution to the conventional linear programming problems of integrating fuzzy method with the other two was inefficient. In this study, a fuzzy-stochastic-interval linear programming (FSILP) method is developed by integrating Nguyen's method with conventional linear programming for supporting municipal solid waste management. The Nguyen's method was used to convert the fuzzy and fuzzy-stochastic linear programming problems into the conventional linear programs, by measuring the attainment values of fuzzy numbers and/or fuzzy random variables, as well as superiority and inferiority between triangular fuzzy numbers/triangular fuzzy-stochastic variables. The developed method can effectively tackle uncertainties described in terms of probability density functions, fuzzy membership functions, and discrete intervals. Moreover, the method can also improve upon the conventional interval fuzzy programming and two-stage stochastic programming approaches, with advantageous capabilities that are easily achieved with fewer constraints and significantly reduces consumption time. The developed model was applied to a case study of municipal solid waste management system in a city. The results indicated that reasonable solutions had been generated. The solution can help quantify the relationship between the change of system cost and the uncertainties, which could support further analysis of tradeoffs between the waste management cost and the system failure risk.     

Sustainable pattern analysis of a publicly owned Material Recovery Facility in a fast-growing urban setting under uncertainty

Sustainable development goals are achievable through the installation of Material Recovery Facilities (MRFs) in certain solid waste management systems, especially those in rapidly expanding multi-district urban areas. MRFs are a cost-effective alternative when curbside recycling does not demonstrate long-term success. Previous capacity planning uses mixed integer programming optimization for the urban center of the city of San Antonio, Texas to establish that a publicly owned material recovery facility is preferable to a privatized facility. As a companion study, this analysis demonstrates that a MRF alleviates economic, political, and social pressures facing solid waste management under uncertainty. It explores the impact of uncertainty in decision alternatives in an urban environmental system. From this unique angle, waste generation, incidence of recyclables in the waste stream, routing distances, recycling participation, and other planning components are taken as intervals to expand upon previous deterministic integer-programming models. The information incorporated into the optimization objectives includes economic impacts for recycling income and cost components in waste management. The constraint set consists of mass balance, capacity limitation, recycling limitation, scale economy, conditionality, and relevant screening restrictions. Due to the fragmented data set, a grey integer programming modeling approach quantifies the consequences of inexact information as it propagates through the final solutions in the optimization process. The grey algorithm screens optimal shipping patterns and an ideal MRF location and capacity. Two case settings compare MRF selection policies where optimal solutions exemplify the value of grey programming in the context of integrated solid waste management.     

A multi-objective location-allocation optimization for sustainable management of municipal solid waste

The location problem of treatment and service facilities in municipal solid waste (MSW) management system is of significant importance due to the socioeconomic and environmental concerns. The consideration of waste treatment costs, environmental impact, greenhouse gas (GHG) emissions, social fairness as well as other relevant aspects should be simultaneously taken into account when a MSW management system is planned. Development of sophisticated decision support tools for planning MSW management system in an economic-efficient and environmental friendly manner is therefore important. In this paper, a general multi-objective location-allocation model for optimally managing the interactions among those conflicting factors in MSW management system is proposed. The model is comprised of a three-stage conceptual framework and a mixed integer mathematical programming. The inclusion of environmental impact and GHG emission objectives push the output of the model tightening toward more environmentally friendly and sustainable solutions in MSW management. The application of this model is demonstrated through an illustrative example, and the computational efficiency of the programming is also tested through a set of incremental parameters. Latter in this paper, a comparison with previous case studies of MSW system design is presented in order to show the applicability and adaptability of the generic model in practical decision-making process, and the perspectives of future study are also discussed.     

Landfill space consumption dynamics in the Lower Rio Grande Valley by grey integer programming-based games

The Lower Rio Grande Valley (LRGV) region in South Texas emerges as a warehouse and transportation center between Central America and the US with positive growth impacts due to the North American Free Trade Agreement (NAFTA). In 10 years time, a 39.8% population increase has resulted in a 25% boost in solid waste per capita disposal rate in the region. A landfill space shortage drives a need for landfill operators to understand their optimal management strategies in this highly-competitive market. Initially, a strategic plan for optimal solid waste pattern distribution minimizes net costs for cities. This is accomplished through a grey integer programming algorithm that encapsulates all uncertainty present in the solid waste system. Secondly, a series of grey integer submodels construct payoff matrices for a zero-sum two-person game. The ensuing game theoretic analysis is critical for evaluating optimal pricing strategies for tipping fees available to the most significant regional landfills (e.g. Browning-Ferris Industries (BFI) and City of Edinburg) as they compete over disposal contracts. The BFI landfill intrinsically benefits from its competitive pricing policy and central location to solid waste generators. The City of Edinburg landfill, on the other hand, wishes to secure its lucrative solid waste management revenue. It desires a gaming strategy backed by optimality that integrates ambiguity in solid waste generation, design capacity boundaries, and unitary shipping costs. Results show that a two-tiered analysis via grey integer programming-based games may pave the way for 'grey Nash equilibria' pricing tactics that will help the Edinburg landfill maintain its waste contracts.     

Two-stage planning for sustainable water-quality management under uncertainty

In water-quality management problems, uncertainties may exist in a number of impact factors and pollution-related processes (e.g., the volume and strength of industrial wastewater and their variations can be presented as random events through identifying a statistical distribution for each source); moreover, nonlinear relationships may exist among many system components (e.g., cost parameters may be functions of wastewater-discharge levels). In this study, an inexact two-stage stochastic quadratic programming (ITQP) method is developed for water-quality management under uncertainty. It is a hybrid of inexact quadratic programming (IQP) and two-stage stochastic programming (TSP) methods. The developed ITQP can handle not only uncertainties expressed as probability distributions and interval values but also nonlinearities in the objective function. It can be used for analyzing various scenarios that are associated with different levels of economic penalties or opportunity losses caused by improper policies. The ITQP is applied to a case of water-quality management to deal with uncertainties presented in terms of probabilities and intervals and to reflect dynamic interactions between pollutant loading and water quality. Interactive and derivative algorithms are employed for solving the ITQP model. The solutions are presented as combinations of deterministic, interval and distributional information, and can thus facilitate communications for different forms of uncertainties. They are helpful for managers in not only making decisions regarding wastewater discharge but also gaining insight into the tradeoff between the system benefit and the environmental requirement.     

An inexact reverse logistics model for municipal solid waste management systems

This paper proposed an inexact reverse logistics model for municipal solid waste management systems (IRWM). Waste managers, suppliers, industries and distributors were involved in strategic planning and operational execution through reverse logistics management. All the parameters were assumed to be intervals to quantify the uncertainties in the optimization process and solutions in IRWM. To solve this model, a piecewise interval programming was developed to deal with Min-Min functions in both objectives and constraints. The application of the model was illustrated through a classical municipal solid waste management case. With different cost parameters for landfill and the WTE, two scenarios were analyzed. The IRWM could reflect the dynamic and uncertain characteristics of MSW management systems, and could facilitate the generation of desired management plans. The model could be further advanced through incorporating methods of stochastic or fuzzy parameters into its framework. Design of multi-waste, multi-echelon, multi-uncertainty reverse logistics model for waste management network would also be preferred.     

A mixed integer linear programming model for optimisation of organics management in an integrated solid waste system

In this paper, the authors propose a mixed integer linear programming model for designing an Integrated Solid Waste Management System (ISWMS) to meet specific economic goals. The model refers to a set of municipalities, known as ‘local basin’, which have to share a common waste management system. At the municipal level the model allows for an identification of the optimal collection service option; at the local basin level, the model provides the optimal waste flow appropriate to the collection service option of each municipality. The model has been applied to a full-scale case study of an area located in southeast Italy. A scenario analysis was carried out to investigate alternative municipal solid waste management options, which fundamentally differ in the organic flow mass rate to be either collected and composted or landfilled. Findings show that an increase in the cost of landfilling determines the optimal collection scenario and the configuration plants tend to recover higher rates of organics in separate collection and thus higher refuse derived fuel productions. The results obtained validate the application of the model in both the strategic planning and operational phases, by supporting public administrators at both municipality and local basin level in decision making and evaluation of technical and economic performances of ISWMSs.     

A two-stage inexact joint-probabilistic programming method for air quality management under uncertainty

A two-stage inexact joint-probabilistic programming (TIJP) method is developed for planning a regional air quality management system with multiple pollutants and multiple sources. The TIJP method incorporates the techniques of two-stage stochastic programming, joint-probabilistic constraint programming and interval mathematical programming, where uncertainties expressed as probability distributions and interval values can be addressed. Moreover, it can not only examine the risk of violating joint-probability constraints, but also account for economic penalties as corrective measures against any infeasibility. The developed TIJP method is applied to a case study of a regional air pollution control problem, where the air quality index (AQI) is introduced for evaluation of the integrated air quality management system associated with multiple pollutants. The joint-probability exists in the environmental constraints for AQI, such that individual probabilistic constraints for each pollutant can be efficiently incorporated within the TIJP model. The results indicate that useful solutions for air quality management practices have been generated; they can help decision makers to identify desired pollution abatement strategies with minimized system cost and maximized environmental efficiency.     

Toward quantifying the effectiveness of water trading under uncertainty

This paper presents a methodology for quantifying the effectiveness of water-trading under uncertainty, by developing an optimization model based on the interval-parameter two-stage stochastic program (TSP) technique. In the study, the effectiveness of a water-trading program is measured by the water volume that can be released through trading from a statistical point of view. The methodology can also deal with recourse water allocation problems generated by randomness in water availability and, at the same time, tackle uncertainties expressed as intervals in the trading system. The developed methodology was tested with a hypothetical water-trading program in an agricultural system in the Swift Current Creek watershed, Canada. Study results indicate that the methodology can effectively measure the effectiveness of a trading program through estimating the water volume being released through trading in a long-term view. A sensitivity analysis was also conducted to analyze the effects of different trading costs on the trading program. It shows that the trading efforts would become ineffective when the trading costs are too high. The case study also demonstrates that the trading program is more effective in a dry season when total water availability is in shortage.     

A dual-interval fixed-mix stochastic programming method for water resources management under uncertainty

In this study, a dual-interval fixed-mix stochastic programming (DFSP) method is developed for planning water resources management systems under uncertainty. DFSP incorporates interval-parameter programming (IPP) and fuzzy vertex analysis (FVA) within a fixed-mix stochastic programming (FSP) framework to address uncertain parameters described as probability distributions and dual intervals. It can also be used for analyzing various policy scenarios that are associated with different levels of economic consequences since penalties are exercised with recourse actions against any infeasibility. A real case for water resources management planning of Zhangweinan River Basin in China is then conducted for demonstrating the applicability of the developed DFSP method. Solutions in association with α-cut levels are generated by solving a set of deterministic submodels, which are useful for generating a range of decision alternatives under compound uncertainties. The results can help to identify desired water-allocation schemes for local sustainable development that the prerequisite water demand can be guaranteed when the available water resource is scarce.     

Inexact fuzzy-stochastic mixed integer programming approach for long-term planning of waste management–––Part B: Case study

In this study, a solid waste decision-support system was developed for the long-term planning of waste management in the City of Regina, Canada. Interactions among various system components, objectives, and constraints will be analyzed. Issues concerning planning for cost-effective diversion and prolongation of the landfill will be addressed. Decisions of system-capacity expansion and waste allocation within a multi-facility, multi-option, and multi-period context will be obtained. The obtained results would provide useful information and decision-support for the City's solid waste management and planning. In the application, four scenarios are considered. Through the above scenario analyses under different waste-management policies, useful decision support for the City's solid waste managers and decision makers was generated. Analyses for the effects of varied policies (for allowable waste flows to different facilities) under 35 and 50% diversion goals were also undertaken. Tradeoffs among system cost and constraint-violation risk were analyzed.Generally, a policy with lower allowable waste-flow levels corresponded to a lower system cost under advantageous conditions but, at the same time, a higher penalty when such allowances were violated. A policy with higher allowable flow levels corresponded to a higher cost under disadvantageous conditions. The modeling results were useful for (i) scheduling adequate time and capacity for long-term planning of the facility development and/or expansion in the city's waste management system, (ii) adjusting of the existing waste flow allocation patterns to satisfy the city's diversion goal, and (iii) generating of desired policies for managing the city's waste generation, collection and disposal.     

Optimal Land Use Management for Soil Erosion Control by Using an Interval-Parameter Fuzzy Two-Stage Stochastic Programming Approach

Soil erosion is one of the most serious environmental and public health problems, and such land degradation can be effectively mitigated through performing land use transitions across a watershed. Optimal land use management can thus provide a way to reduce soil erosion while achieving the maximum net benefit. However, optimized land use allocation schemes are not always successful since uncertainties pertaining to soil erosion control are not well presented. This study applied an interval-parameter fuzzy two-stage stochastic programming approach to generate optimal land use planning strategies for soil erosion control based on an inexact optimization framework, in which various uncertainties were reflected. The modeling approach can incorporate predefined soil erosion control policies, and address inherent system uncertainties expressed as discrete intervals, fuzzy sets, and probability distributions. The developed model was demonstrated through a case study in the Xiangxi River watershed, China’s Three Gorges Reservoir region. Land use transformations were employed as decision variables, and based on these, the land use change dynamics were yielded for a 15-year planning horizon. Finally, the maximum net economic benefit with an interval value of [1.197, 6.311] × 10⁹ $ was obtained as well as corresponding land use allocations in the three planning periods. Also, the resulting soil erosion amount was found to be decreased and controlled at a tolerable level over the watershed. Thus, results confirm that the developed model is a useful tool for implementing land use management as not only does it allow local decision makers to optimize land use allocation, but can also help to answer how to accomplish land use changes.     

Formalising informal solid waste recycling at the Pomona dumpsite in Harare,Zimbabwe

The role of informal recycling in poverty alleviation and solid waste management in cities in developing countries has been receiving increased attention. This study explores the integration of the informal recycling sector with the Harare City Council's solid waste management system, focusing on the Pomona dumpsite. The extent of this integration was compared with interventions proposed in InteRa, a new way of evaluating the integration of informal recyclers with the waste management systems of cities in developing countries. Our results suggest that the Harare City Council, which had the vision of transforming itself into a world‐class city, failed to fully integrate the informal recycling sector. We suggest to policymakers that complete integration of the informal sector will not necessarily prevent cities from achieving such visions. Rather, addressing the neglected interventions may help in achieving their visions.