روش تجزیه و تحلیل مبتنی بر فاصله برای شناسایی بلند مدت سیاست های مدیریت مواد زائد جامد شهری تحت عدم قطعیت

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.

For decades, many regions and nations have been paying attention to the planning of effective municipal solid waste (MSW) management systems due to the population growth and economic development. In MSW management systems, there are many processes that should be considered by decision makers, such as waste collection, transportation, treatment, and disposal (Wilson, 1985). Moreover, many system parameters (e.g., waste-generation rate, waste treatment cost, and facility–capacity), impact factors (e.g., energy price, labor fee, and management expenses) and their interactions are associated with uncertainties. Furthermore, the spatial and temporal variations of many system components may further multiply these uncertainties (Thompson and Tanapat, 2005). These complex uncertainties could result in difficulties in the long-term planning of MSW activities. Therefore, in response to these uncertainties and complexities, more effective systems analysis techniques are desired for managing MSW systems in a more efficient way. Previously, a number of inexact optimization techniques were developed to deal with such uncertainties and complexities in the MSW management systems, including fuzzy mathematical programming (FMP) (Chang and Wang, 1997; Wilson and Baetz, 2001a and Wilson and Baetz, 2001b; Cai et al., 2007, Nie et al., 2007, Li et al., 2008a, Guo and Huang, 2009, Xu et al., 2009 and Xu et al., 2010), stochastic mathematical programming (SMP) (Huang et al., 2001, Maqsood and Huang, 2003, Li and Huang, 2006a, Li et al., 2006, Li et al., 2008a and Li et al., 2008b), and interval–parameter programming (IPP) (Huang et al., 1992, Huang et al., 1997, Huang et al., 1998, Chanas and Kuchta, 1996, Davila and Chang, 2005, Su et al., 2008 and Liu et al., 2009). For example, Chang and Wang (1997) proposed a fuzzy interval multiobjective mixed integer programming model for the evaluation of solid waste management strategies in a metropolitan region, in which the uncertain information could be quantified by specific membership functions and combined through the use of interval numbers in a multiobjective linear programming framework. Huang et al. (1997) advanced an interval–parameter integer programming model for the long-term planning of waste management facility expansion/utilization in the Regional Municipality of Hamilton–Wentworth, Ontario, Canada; the proposed model could effectively reflect dynamic, interactive, and uncertain characteristics of the MSW management system in the study city. Wilson and Baetz, 2001a and Wilson and Baetz, 2001b presented a derived probability model for supporting municipal solid waste collection systems, where the stochastic aspects existing in waste-generation rate and vehicle capacity could be estimated. Davila and Chang (2005) proposed an interval–parameter mixed integer programming-based game theory approach for addressing optimization and cost-benefit analysis at two competing landfills in the Lower Rio Grande Valley, Texas, USA. Li and Huang (2006b) developed an interval–parameter two-stage mixed integer linear programming method for supporting long-term planning of waste management activities in the City of Regina, in which uncertainties expressed as both probability density functions and discrete intervals could be reflected. Guo and Huang (2009) proposed an inexact fuzzy-stochastic chance-constrained two-stage mixed integer linear programming method, where uncertainties existing in the MSW management systems were treated as intervals and dual probability distributions within a general optimization framework. In general, IPP has advantages in reflecting uncertainties expressed as interval numbers without knowing their distributions; the FMP and SMP methods can effectively reflect probabilistic and possibilistic uncertainties in the right-hand sides of a linear model. Nevertheless, the main limitations of the FMP methods remain in their difficulties in tackling uncertainties expressed as probabilistic distributions in a non-fuzzy decision space (Li et al., 2009); SMP requires probabilistic specifications for uncertain parameters, while in MSW management problems, it is often associated with difficulties in acquiring probability distribution for the date of waste generation. Minimax regret (MMR) analysis, which was proposed to determine the hedging alternatives under uncertainty but without probability information for the states of the world, was proved to be an effective method that could help to address the above shortcomings (Savage, 1954, Inuiguchi and Tanino, 2000, Li and Huang, 2006b, Chang and Davila, 2006, Chang and Davila, 2007 and Aissi et al., 2009). MMR only needs a list of possible scenarios without any assumption on their probabilities, and then seeks to minimize the maximum regret among all possible scenarios (Loulou and Kanudia, 1999). Each regret value corresponds to the difference between the cost of the alternative selected by decision makers and that of the best alternative for a special state of the world. Previously, several researchers employed MMR analysis to plan MSW management systems under uncertainty. For example, Chang and Davila (2006) introduced a grey minimax regret integer programming model for the management of MSW in the Lower Rio Grande Valley, South Texas, which could outline an optimal regional coordination of solid waste routing and possible landfill/incinerator construction under various forms of systematic and event-based uncertainty. Li and Huang (2006b) developed an interval minimax regret programming method for the planning of municipal solid waste management, which can address uncertainties expressed as interval values in MSW management systems and make the final decision based on inexact minimax regret analysis. Li and Huang (2009) developed an inexact minimax regret integer programming method and applied it to a real case study in the City of Regina, Canada. However, Regina is a very small city with around 100 km2 and has low population of about 195,000; transfer stations and multiple districts were not considered in the modeling formulation. In comparison, Changchun City covers an area of approximately 379.9 km2 and has high population of about 2.78 million, including five main districts. In addition, a number of transfer stations that can decrease vehicle traffic going to-and-from the facility, recycle various useful wastes, and contribute to a reduction in the waste volumes because of the compaction process considered. Therefore, the complexities of MSW management in the City of Changchun are much higher than those in the City of Regina, which drive the local decision makers to look for effective and forward-looking solutions to address various waste management issues. However, many big cities in China lack effective systems analysis techniques for MSW management planning (e.g., the City of Changchun). Therefore, as an extension of previous efforts, this study aims to develop an interval-based regret-analysis (IBRA) model for planning municipal solid waste (MSW) management in the City of Changchun, China. In this study, transfer stations and multiple districts will be considered in the modeling formulation, which is different from that proposed by Li and Huang (2009) and applied to the City of Regina. The IBRA model will reflect the complex nature of the waste management system in the City of Changchun and make the final decisions based on minimax regret analysis. The detailed tasks of IBRA model include: (i) tackling uncertainties expressed as interval-random variables without knowing their probability distributions, (ii) analyzing all possible scenarios associated with different system costs and risk levels, (iii) identifying the optimal regional coordination of solid waste routing among districts, transfer stations and waste disposal facilities, (iv) reflecting dynamic complexities in waste management systems in planning capacity–expansion schemes for waste management facilities, and (v) generating alternatives under different decision criterions for supporting the real-world (i.e., Changchun City) MSW management and planning. The paper is organized as follows: Section 2 describes the statement of MSW management problems for the City of Changchun; Section 3 formulates an interval-based regret-analysis (IBRA) model for supporting MSW management of the study city; Section 4 provides the results analysis for all possible scenarios, based on IBRA model; Section 5 provides discussion for the results under different risk attitudes or different decision criterions; and Section 6 presents conclusions of the work.

In this study, an interval-based regret-analysis (IBRA) model has been developed for supporting long-term planning of municipal solid waste (MSW) management. The IBRA model incorporates approaches of interval–parameter programming (IPP) and minimax–regret (MMR) analysis within an integer programming framework. It can deal with uncertainties presented as both interval values and random variables while assumptions on their probabilities are not needed. It can also be used for analyzing all scenarios that are associated with different system costs under various predefined policies. Moreover, a regret matrix with interval elements can be generated based on a matrix of interval system costs, such that desired decision alternatives can be identified according to the IMMR criterion. The developed IBRA method has been applied to tackling the dynamic, interactive and uncertain characteristics of the solid waste management system in the City of Changchun, China. Reasonable solutions have been generated, demonstrating complex tradeoffs among system cost, regret level, and system-failure risk. Solutions based on the IMMR criterion can help (i) identify the desired alternatives regarding waste generation and management; (ii) facilitate dynamic analysis of capacity–expansion planning under uncertainty, (iii) provide desired alternatives for waste-flow allocation, (iv) adjust the existing MSW disposal-routing patterns, and (v) undertake sensitivity analyses to demonstrate the effects of variations among the alternatives. Although this study is the first attempt for planning waste management system in the City of Changchun through the application of the IBRA model, the results suggest that this hybrid model is an effective tool for decision makers of the long-term MSW management planning. The IBRA model can also be incorporated within other optimization techniques to handle various types of uncertainties in the MSW management systems.