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

Transcription

1 Journal of Environmental Management 81 (2006) An inexact two-stage mixed integer linear programming method for solid waste management in the City of Regina Y.P. Li a, G.H. Huang b,c, a Environmental Systems Engineering Program, Faculty of Engineering, University of Regina, Regina, SK, Canada S4S 0A2 b Sino-Canada Center of Energy and Environmental Research, North China Dianli University, Beijing, China c University of Regina, Regina, SK, Canada S4S 0A2 Received 22 February 2005; received in revised form 12 July 2005; accepted 17 October 2005 Available online 5 May 2006 Abstract In this study, an interval-parameter two-stage mixed integer linear programming (ITMILP) model is developed for supporting longterm 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. r 2006 Elsevier Ltd. All rights reserved. Keywords: Decision making; Environment; Inexact; Two-stage; Planning; Probability; Solid waste; Uncertainty 1. Introduction Management of municipal solid waste (MSW) is a priority for many urban communities throughout the world (Yeomans and Huang, 2003). Many MSW management systems in North America consist of garbage trucks and a landfill. They are complicated with a number of economic, technical, environmental, legislational, and political factors. Due to the potential for groundwater contamination, the scarcity of land near urban centers, and the growing opposition from the public with regard to landfill disposal, many cities are making efforts on waste diversion through an integrated solid waste management (ISWM) approach to change the current practice of relying solely on a landfill for its waste disposal. However, complexities exist in such a diversion effort, including the collection techniques to be used, the levels of service to be Corresponding author. Tel.: ; fax: address: gordon.huang@uregina.ca (G.H. Huang). offered, and the facilities to be adopted; moreover, many related processes and/or factors are complex with multiperiod, multi-layer, and multi-objective features (Thomas et al., 1990; Zeng and Trauth, 2005). Thus, systems analysis techniques can be employed to assist in developing a longterm MSW management and diversion plan, which will be helpful for analyzing tradeoffs among various socioeconomic and environmental objectives. Previously, Chi (1997) proposed an inexact mixed integer linear programming (IMILP) model for the planning of waste diversion in the City of Regina, Canada. The IMILP model could effectively reflect uncertainties that exist as intervals. However, the model could not deal with distributional information for the right-hand side constraints; consequently, when the right-hand side stipulation values fluctuated within wide intervals, highly uncertain solutions might be generated, which would be of limited practical use to decision makers. Sae-Lim (1999) developed an inexact fuzzy stochastic mixed integer linear programming model for the planning of waste management /$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi: /j.jenvman

2 Y.P. Li, G.H. Huang / Journal of Environmental Management 81 (2006) Methods of chance-constrained programming and fuzzy linear programming were introduced into a general IMILP framework. This method could reflect probabilistic and possibilistic uncertainties in a linear model s right-hand sides. However, it permits multiple tolerable levels of system constraint violation, with the generated solutions being unable to satisfy all of the model s original constraints; moreover, the method could not support the analysis of various policy scenarios that are associated with different levels of economic penalties when the promised constraints (or policy targets) are violated. The two-stage programming (TSP) method is an effective alternative for tackling problems where an analysis of policy scenarios is desired and the related data are mostly uncertain (Luo et al., 2003). It is useful when the right-hand side coefficients are random with known probability distributions. In TSP, a decision is first undertaken before values of random variables are known and, then, after the random events have happened and their values are known, a second decision is made in order to minimize penalties that may appear due to any infeasibility (Loucks et al.,1981; Birge and Louveaux, 1988, 1997; Ruszczynski, 1993). The TSP methods were widely explored over the past decades (Pereira and Pinto, 1991; Schultz et al., 1996; Ruszczynski and Swietanowski, 1997; Huang and Loucks, 2000; Seifi and Hipel, 2001; Maqsood and Huang, 2003; Ahmed et al., 2004). However, these previous methods were incapable of reflecting dynamic complexities in waste management systems, such as the timing, sizing and siting in terms of capacity expansions for waste-management facilities. In fact, an integrated MSW management system may involve multiple facilities to meet the overall demand for waste processing, treatment, and disposal (Huang and Chang, 2003; Yeomans et al., 2003). Capacity expansions for individual waste management facilities are needed to satisfy increasing waste management demands, where a related optimization analysis will typically require the use of integer variables to indicate whether or not particular facility development or expansion options are to be undertaken. Mixed integer linear programming (MILP) is a useful tool for this purpose (Huang et al., 1995, 1997). Therefore, one potential approach for better accounting for the complexities and uncertainties of capacity expansion and economic penalty is to link the TSP within the interval-parameter MILP framework. Therefore, the objective of this study was to develop an interval-parameter two-stage mixed integer linear programming (ITMILP) model for supporting solid waste management in the City of Regina. In the ITMILP, both TSP and interval linear programming (ILP) would be introduced into a general MILP framework. Uncertainties expressed as not only probability density functions but also discrete intervals would be reflected. In detail, this research would: (i) tackle the dynamic, interactive and uncertain characteristics of the solid waste management system in the City of Regina; (ii) analyze various policy scenarios that are associated with different levels of economic penalties when the promised policy targets are violated; (iii) apply the proposed ITMILP method to supporting the City s longterm solid waste management planning and address issues concerning plans for cost-effective waste diversion and landfill prolongation. 2. Solid waste management in the City of Regina 2.1. Waste generation The City of Regina is the capital of the Province of Saskatchewan, and is located in the heart of western Canada. The population of the city is about 190,400, where the households generate residential wastes of about 70,000 tonne (City of Regina, 2000). Solid waste management in the City covers many areas, ranging from garbage collection to environmental protection. It involves the provision of specific and personal services to most of the residents (through waste collection and recovery) as well as indirect services to the whole community (through waste disposal and recovery). Recent population projections assumed a growth rate of 0.7% per year in the City (Sae- Lim, 1999). The results of a waste characterization study for the City indicated that the residential sector of Regina generated waste at a rate of approximately 1.17 kg/capita/ day (Barlishen, 1996; Chi and Huang, 1998). The municipal solid wastes generated typically include paper, yard waste, food waste, plastics, metals, glass, wood, and other items. Therefore, for the long-term planning exercise, a general waste generation rate of kg/capita/day will be used for the residential sector of the City Waste collection Residential waste collection service is provided to 52,000 households (76% of the total) in Regina (City of Regina, 2002), as part of the general city services that are funded by property taxes. The remaining 17,000 homes (24% of the total), consisting primarily of high-density multi-family dwellings, pay for their garbage to be removed by private companies or the City. The city has been putting into execution a high level of generator satisfaction at low cost. The average frequency of collection is about once per week. Since the mid-1980s, two different types of city collection operations have evolved. Where back alley access to a home existed, automated collection was used. Those residential neighborhoods without back alleys were mostly serviced by manual collection. A small proportion of homes in these neighbourhoods received automated collection with individual roll-out containers. The manual collection system was provided to about 22,000 suburban homes in Regina, and the average amount of garbage produced per property was 18 k/week and the pick-up cost was about $0.90 per visit (City of Regina, 2000). Automated city collection was provided to 31,000 homes in mostly older neighborhoods where large containers were

3 190 Y.P. Li, G.H. Huang / Journal of Environmental Management 81 (2006) shared by a number of homes. The average amount of garbage produced by a property serviced by automated collection was 26 k/week. However, the superior efficiency of the system actually resulted in a lower pick-up cost of about $0.75 per visit (City of Regina, 2000). The average garbage collection/transportation cost was [32, 53] $/tonne for manual collection or [21, 37] $/tonne for automated collection (City of Regina, 2000). Costs for waste collection and transportation were estimated based on the existing conditions in the collection areas; the average container size, collection frequency, collection mode (automatic and manual), and collection time (per load) were considered. The collection costs have been decreasing since the number of households served by the automated collection system continued to increase since the mid-1980s, leading to an increased collection efficiency (City of Regina, 2000). Furthermore, Since the City is relatively small in size (about 100 km 2 ), the impact of spatial factor (i.e., locations of the subareas) becomes insignificant. Therefore, in this study, a projected interval of [32, 37] $/tonne was used for approximating the collection and transportation costs for waste flow to the landfill over the planning horizon. This approximation was based on the following facts: (a) The garbage collection/ transportation cost was between 32 and 53 $/tonne for manual collection (with an average of 37.1 $/tonne), or between 21 and 37 $/tonne for automated collection (with an average of 31.8 $/tonne) (City of Regina, 2000). (b) The average cost for both manual and automated collections was 34.6 $/tonne. Therefore, the average collection and transportation costs for waste flow to the landfill could be approached by using the average of automated collection (E32 $/tonne) as the lower bound, and that of manual collection (E37 $/tonne) as the upper bound, with the mid value (i.e for the interval [32, 37]) being close to the average cost for both manual and automated collections (34.6 $/tonne) Waste management facilities Landfill: Consistent with many communities in western Canada, the City relies mostly on a sanitary landfill for disposing of its MSW. The landfill is located in the northeastern part of the city, occupying 97 h with the actual landfill area being 60 h. Approximately 160,000 tonne per year of garbage were buried at the landfill, where the industrial, commercial and institutional (IC&I) sector produced 61% (or 97,000 tonne) of the total waste flow, and the residential sector generated approximately 39% (or 63,000 tonne). The existing landfill is facing two major problems: firstly, it is expected to be able to accept waste till 2011 or 2012 (City of Regina, 2000, 2002), and thus a new landfill will be built before the expiry date of the existing one; secondly, the existing landfill is proximal to the aquifer such that groundwater contamination is a special concern. From a long-term planning point of view, the contribution of the residential sector to the City s landfill is assumed to fall within an interval of [35, 40]%. Recycling: The City is operating a number of recycling programs to encourage residents to reduce the amounts of waste that end up at the landfill. The programs include a big blue bin paper recycling project (BBBPRP), a used oil recycling program (UORP), a paint-it-recycled program, a white goods recycling program (WGRP), and a backyard composting program. The City started the BBBPRP in A total of 14 depots were placed at high traffic locations such as shopping and recreation centers with easy automobile access. The depots were available to all 69,000 residences in the City and accepted about 5000 tonne of paper per year (about 40% of residential waste in Regina consists of paper products) (City of Regina, 2000). In the City, about 80% of respondents responded that they made use of the city s big blue bin recycling program (Barlishen, 1996; City of Regina, 2000). Potentially recyclable material constituted approximately 41.79% of the waste stream, while the observed recycling rate of residential waste was only 8.72% in Regina, indicating a high potential for further improvements. Composting: The City is operating a backyard composting program to naturally process grass clippings (by leaving them on the lawns). The households backyard composting diverted approximately 2400 tonne per year of wastes from the landfill, which were approximately 3% of the residential waste stream (Sae-Lim, 1999). However, the waste stream generated in the City contained a high percentage of compostable materials, including 20,000 tonne of yard wastes (25.64%) and 20,900 tonne of organic wastes (26.79%); the potentially compostable material constituted approximately 52.43% of the waste stream (Chi and Huang, 1998). Over 50% of residential garbage was yard waste in summer months, with the majority of them being grass clippings. This implied that most of the compostable yard and organic wastes were currently disposed of at the City s landfill. From a long-term planning point of view, over one-third of all residential waste could be eliminated through the composting operation (City of Regina, 2000). Therefore, development of a centralized composting program would help obtain increased waste diversion and prolong the life of the existing landfill Waste diversion In 1988, the Canadian Council of the Ministers of Environment (CCME) adopted a policy guidance for MSW diversion and recycling. In Canada, establishment of defined waste diversion targets and relevant regulations was currently a growing trend. Such regulations typically focused on mandating recovery of specific materials (e.g., dry recyclables and yard wastes), and supporting decisions of appropriate collection systems (e.g., depot, curbside or deposit). In April 1995, the City of Regina established the Regina Round Table on Solid Waste Management (RRTSWM), in order to obtain community inputs about

4 Y.P. Li, G.H. Huang / Journal of Environmental Management 81 (2006) the development of a long-term solid waste management plan. In June 2000, The RRTSWM developed a 20-year solid waste management strategy for the City. The Round Table produced 31 basic recommendations in the areas of waste collection, diversion and disposal. It was the view of the Round Table that, starting in 2001, 50% diversion of residential waste landfilled would be achievable within 10 years, and 65% diversion woud be feasible over 20 years. However, in 2000, the amount of residential waste diverted from landfill was 12% and that diverted from the industrial, commercial, and institutional sectors was 20% (Cheng et al., 2002). Although the city had implemented a number of diversion programs since 1997, realization of the CCME goal would be still a daunting task (Environment Canada, 2000) Waste management cost Solid waste management is complex and the collection and disposal of waste are costly. The cost could be estimated as high as $ per tonne in some communities (City of Regina, 2002). The net system costs mainly included the costs for waste collection, transportation and processing, as well as the capital costs for developing/ expanding waste management facilities. In the City of Regina, the average cost of garbage collection for each household was about $38.00 per year, while the total waste management cost was $74.00 per year (City of Regina, 2000). In 2000, approximately $4.4 million were incurred for the City s waste collection, landfill operation, and waste minimization, while the revenues generated from waste management were about $3.0 million. This resulted in a net cost of about $1.4 million for the City s waste management practices. About 80% of the City s waste management budget was spent on the collection and disposal, while the remaining was used for waste diversion programs (City of Regina, 2000) Statement of problems The MSW collection and disposal system may normally consist of garbage trucks and a landfill. However, a recent development in solid waste management is the increasing realization that conventional single-choice management, such as reliance on landfills for waste disposal, is inadequate. Due to the potential of environmental damage from landfill sites, the scarcity of land near urban centers and the growing public opposition, the current trend for disposal of solid waste is toward implementing waste diversion and creating an integrated MSW management system. Thus, increasing the waste diversion rate and thus prolonging the useful life of the landfill are becoming an important objective. Presently, the City of Regina relies on landfilling, recycling and composting (backyard) facilities for managing its solid wastes. The landfill is used directly to satisfy waste disposal demand or alternatively to provide capacity for the other facilities residue disposals; it typically has an overall cumulative capacity limit. The other facilities have daily operating capacity limits. From a long-term planning point of view, waste generation rates in the City will keep increasing due to the population increase and economic development. Therefore, not only the landfill but also other existing facilities will face problems of insufficiency in their capacities to meet the City s overall waste disposal demand in the future. Because of the temporal variation of the relationships between waste generation (demand) and available facility capacities (supply), the optimal schemes for effective utilization of the facilities (i.e., optimal waste flow allocation patterns) will also vary between different time periods. Many impact factors and their interactions must be systematically evaluated in planning an integrated waste management system within a multi-period and multidistrict context. These lead to a number of challenging questions such as (i) What is the least-cost means for meeting the reduction and/or diversion goals? (ii) If a new landfill is needed during the next 25-year period, where should it be located? (iii) What new facilities should be developed or expanded? (iv) What capacity of expansion (or new development) should be undertaken? and (v) In each period, how to effectively use the facilities and allocate the relevant waste flows? 3. Development of ITMILP model In this study, an ITMILP model will be developed for supporting the City s long-term solid waste management planning. Issues concerning planning for cost-effective diversion and prolongation of the landfill will be addressed. It is expected that the results would provide useful information and decision-support for waste management and planning in the study City Data collection and analysis The study time horizon is 25 years, which is divided into five planning periods. Table 1 presents the waste generation rates and the associated probabilities of occurrence in the five planning periods, indicating that the waste generation amounts are highly uncertain, presented by intervals and probabilities and vary among different periods. Tables 2 and 3 contain regular costs for allowable waste flows, operating costs for waste management facilities, and penalty costs for surplus waste flows, as well as revenues from recycling and composting facilities over the five planning periods. It is indicated that the penalty costs for the excess waste flows (associated with infeasibilities for the relevant constraints) are significantly higher than the regular ones for the allowable waste flows. Over the 25-year planning horizon, due to the temporal variations of relationships among waste generation, collection, transportation and disposal, the overall capacity of the City s waste management facilities will have to be

5 192 Y.P. Li, G.H. Huang / Journal of Environmental Management 81 (2006) Table 1 Waste-generation rates and the associated probabilities Level of waste generation Probability Waste-generation rate, w kh (tonne/week) k ¼ 1 k ¼ 2 k ¼ 3 k ¼ 4 k ¼ 5 h ¼ 1 (low) 0.1 [1373, 1423] [1418, 1469] [1465, 1517] [1513, 1567] [1563, 1619] h ¼ 2 (low-medium) 0.2 [1423, 1478] [1469, 1525] [1517, 1574] [1567, 1624] [1619, 1678] h ¼ 3 (medium) 0.4 [1478, 1543] [1525, 1595] [1574, 1649] [1624, 1705] [1678, 1761] h ¼ 4 (medium-high) 0.2 [1543, 1598] [1595,1651] [1649,1706] [1705, 1762] [1761, 1820] h ¼ 5 (high) 0.1 [1598, 1648] [1651,1702] [1706,1758] [1762, 1816] [1820, 1876] Table 2 Costs and revenues for allowable waste flows Planning period k ¼ 1 k ¼ 2 k ¼ 3 k ¼ 4 k ¼ 5 Operating costs of waste management facilities, OP ik ($/tonne) Landfill [9, 17] [6.9, 13.02] [5.83, 11.02] [4.94, 9.32] [4.18, 7.89] Composting facility [21, 26] [16.09, 19.92] [13.61, 16.85] [11.52, 14.26] [9.74, 12.06] Material recovery facility [61, 67.8] [46.74, 51.95] [39.54, 43.95] [33.45, 37.18] [28.30, 31.46] Collection and transportation costs, TR ik ($/tonne) To landfill [32, 37] [24.52, 28.35] [20.74, 23.98] [17.55, 20.29] [14.85, 17.17] To composting To material recovery facility Revenues from waste management facilities, RE ik ($/tonne) Composting facility [5.0, 10.0] [3.83, 7.66] [3.24, 6.48] [2.74, 5.48] [2.32, 4.64] Material recovery facility [45.0, 55.0] [34.48, 42.14] [29.17, 35.65] [24.68, 30.16] [20.88, 25.52] Residue costs, FT ik ($/tonne) Composting [8, 10]% [1.68, 2.1] [1.287, 1.609] [1.089, 1.36] [0.92, 1.152] [0.779, 0.974] Recycling [7, 8]% [1.47, 1.68] [1.126, 1.287] [0.953, 1.089] [0.806, 0.92] [0.68, 0.779] Table 3 Costs and revenues for excess waste flows Planning period k ¼ 1 k ¼ 2 k ¼ 3 k ¼ 4 k ¼ 5 Operating costs of waste management facilities, DP ik ($/tonne) Landfill [18, 34] [13.79, 26.05] [11.67, 22.04] [9.87, 18.65] [8.35, 15.78] Composting facility [34, 42] [26.05, 32.18] [22.04, 27.23] [18.65, 23.03] [15.78, 19.49] Material recovery facility [104, 115.3] [79.69, 88.34] [67.41, 74.74] [57.04, 63.23] [48.25, 53.50] Collection and transportation costs, DR ik ($/tonne) To landfill [48, 55.5] [36.77, 42.52] [31.11, 35.98] [26.32, 30.27] [22.27, 25.75] To composting To material recovery facility Revenues from waste management facilities, RM ik ($/tonne) Composting facility [5.0, 10.0] [3.83, 7.66] [3.24, 6.48] [2.74, 5.48] [2.32, 4.64] Material recovery facility [45.0, 55.0] [34.48, 42.14] [29.17, 35.65] [24.68, 30.16] [20.88, 25.52] Residue costs, DT ik ($/tonne) Composting [8, 10]% [2.52, 3.15] [1.93, 2.41] [1.63, 2.04] [1.38, 1.73] [1.17, 1.46] Recycling [7, 8]% [2.21, 2.52] [1.69, 1.93] [1.43, 1.63] [1.21, 1.38] [1.03, 1.17] increased. There will be potentially one material recovery facility (MRF), one composting facility, and three landfill expansion options being taken into account for the longterm planning. The capacity-expansion options and the relevant capital costs for different waste management facilities are shown in Table 4. In detail, for the landfill, either a new development (located at the southern or northern site) or an expansion based on the existing one

6 Y.P. Li, G.H. Huang / Journal of Environmental Management 81 (2006) Table 4 Capacity expansion options and their capital costs for waste management facilities Expansion option Total capacity Capacity for residential waste Expansion cost ($10 6 ) K ¼ 1 k ¼ 2 k ¼ 3 k ¼ 4 k ¼ 5 Landfill (FLC ik and DLC i ) Expansion ði ¼ 1Þ 71.3 ha 28.5 ha North site ði ¼ 2Þ 71.3 ha 28.5 ha [9.60, 10.45] [8.69, 9.46] [7.35, 8.01] [6.22, 6.77] [5.26, 5.73] South site ði ¼ 3Þ 71.3 ha 28.5 ha [6.44, 14.94] [5.83, 13.53] [4.93, 11.45] [4.17, 9.69] [3.53, 8.20] Composting facility (FTC 4mk and DTC 4mk ) Option 1 ðm ¼ 1Þ 189 t/wk 132 t/wk [2.12, 2.54] [1.92, 2.30] [1.62, 1.95] [1.37, 1.65] [1.16, 1.39] Option 2 ðm ¼ 2Þ 385 t/wk 270 t/wk [4.23, 5.08] [3.83, 4.60] [3.24, 3.89] [2.74, 3.29] [2.32, 2.79] Option 3 ðm ¼ 3Þ 483 t/wk 338 t/wk [5.29, 6.35] [4.79, 5.75] [4.05, 4.86] [3.43, 4.12] [2.90, 3.48] Material recovery facility (FTC 5mk and DTC 5mk ) Option 1 ðm ¼ 1Þ 350 t/wk 140 t/wk [4.51, 5.00] [4.08, 4.53] [3.46, 3.83] [2.92, 3.24] [2.47, 2.74] Option 2 ðm ¼ 2Þ 700 t/wk 280 t/wk [9.02, 10.01] [8.17, 9.06] [6.91, 7.67] [5.85, 6.49] [4.95, 5.49] Option 3 ðm ¼ 3Þ 875 t/wk 350 t/wk [10.86, 12.51] [9.83, 11.33] [8.32, 9.58] [7.04, 8.11] [5.96, 6.86] Table 5 Allowable waste flow levels and diversion rates under scenario 1 Time period k ¼ 1 k ¼ 2 k ¼ 3 k ¼ 4 k ¼ 5 Allowable waste flow level, T ik (t/wk) To landfill [1068, 1093] [925, 947] [759, 776] [580, 592] [567, 579] To composting facility [142, 146] [250, 256] [379, 388] [517, 529] [534, 546] To MRF [213, 219] [294, 301] [379, 388] [470, 481] [518, 529] Waste diversion rate, DG ik To landfill 75% 63% 50% 37% 35% To composting facility 10% 17% 25% 33% 33% To MRF 15% 20% 25% 30% 32% will be undertaken, with an area of [71.3, 92.7] ha over the planning horizon (City of Regina, 1989, 2000); for the recycling facility, three desired capacity-expansion schemes (i.e., 350, 700 and 875 tonne/wk) will be considered in correspondence to the varying waste diversion policies under the rising waste-generation rates; the City will plan to develop a large-scale windrow composting facility to mainly divert residential yard waste, where a capacity of 10,000, 20,000 or 25,000 tonne/year (i.e., 189, 385 or 483 tonne/week) would be considered with a possibility of expansion in each of the five periods. Since the planning problem under consideration is dynamic and includes multiple periods, discount factors are considered for each planning period to obtain the total present value for the objective function. Based on the local waste management policy, the diversion goals are interpreted as constraints for the ITMILP model. The allowable waste flow to the landfill can be regulated with dynamic reduction in correspondence with the increasing waste diversion goal along with time. Conversely, the allowable waste flows to the composting and recycling facilities will be required to increase along with time. Three typical scenarios are considered in this study. Tables 5 7 show the allowable waste flows from the City to the three waste management facilities as well as the relevant waste diversion goals as required in scenarios 1 3, respectively. These scenarios can be described as follows: Scenario 1 is based on an aggressive policy for waste minimization and diversion (Table 5). The City will consider developing/expanding the landfilling, composting and recycling facilities. In addition, 50% diversion of residential waste should be achieved within 10 years, and 65% diversion over 20 years. Therefore, this scenario corresponds to decisions with significant efforts for capacity development/expansion in order to satisfy the Round Table s diversion goals. In Scenario 2, the City s waste management practices are based on the existing policy over the next 25 years (Table 6). In the current practice, households utilizing the drop-off depots and the curbside collection program divert approximately 9% of their waste streams. Also, the yard-composting programs divert about 3% of the wastes. Thus the total diversion rate for the residential waste is approximately 12%.

7 194 Y.P. Li, G.H. Huang / Journal of Environmental Management 81 (2006) Table 6 Allowable waste flow levels and diversion rates under scenario 2 Time period k ¼ 1 k ¼ 2 k ¼ 3 k ¼ 4 k ¼ 5 Allowable waste flow level, T ik (t/wk) To landfill [1238, 1268] [1278, 1309] [1319, 1350] [1363, 1394] [1408, 1439] To composting facility [43, 44] [44, 45] [46, 47] [47, 48] [49, 50] To MRF [142, 146] [147, 150] [152, 155] [157, 160] [162, 165] Waste diversion rate, DG ik To landfill 88% 88% 88% 88% 88% To composting facility 3% 3% 3% 3% 3% To MRF 9% 9% 9% 9% 9% Table 7 Allowable waste flow levels and diversion rates under scenario 3 Time period k ¼ 1 k ¼ 2 k ¼ 3 k ¼ 4 k ¼ 5 Allowable waste flow level, T ik (t/wk) To landfill [1030, 1060] [893, 920] [733, 753] [560,576] [547, 563] To composting facility [137, 141] [241, 248] [366, 377] [499, 514] [516, 531] To MRF [206, 212] [284, 291] [366, 377] [454, 467] [500, 515] Waste diversion rate, DG ik To landfill 75% 63% 50% 37% 35% To composting facility 10% 17% 25% 33% 33% To MRF 15% 20% 25% 30% 32% Scenario 3 provides an analysis based on varied policies for allowable waste-flow levels to different facilities under an aggressive waste diversion goal (Table 7). Generally, a policy with low allowable waste-flow levels corresponds to a relatively low system cost under advantageous conditions but, at the same time, it implies a high penalty when such allowances are violated. Thus, a tradeoff exists between the wastemanagement cost and the allowance-violation risk Modeling formulation In formulating the ITMILP model for the study problem, the decision variables are sorted into two categories: discrete and continuous. The discrete variables represent the expansion options for waste management facilities in different periods, while the continuous ones represent the optimized waste flows from the City s residences to the waste management facilities. The objective is to minimize the total expected system cost by achieving optimal plans for facility expansion/development and waste flow allocation over the entire planning horizon. The constraints include all of the relationships among decision variables, waste generation rates, waste diversion goals, and waste-management-facility capacities. In detail, the problems under consideration include: (a) how to achieve minimum system costs under uncertainty, (b) how to select an optimal facility-expansion scheme, (c) how to allocate the relevant waste flows to suitable waste disposal facilities, (d) how to achieve the waste diversion goal and thus lengthen the life of the landfill, and (e) how to reflect policies in terms of allowable waste-flow levels with a minimized risk of system disruption. Consequently, the ITMILP technique is considered applicable for tackling these problems. Thus, we have Minimize f ¼ X5 X 5 i¼1 k¼1 þ X5 X 5 i¼4 k¼1 þ X5 X 5 X 5 i¼1 k¼1 h¼1 þ X5 X 5 X 5 i¼4 k¼1 h¼1 X5 X 5 X 5 i¼4 k¼1 h¼1 þ X3 X 5 i¼1 k¼1 L k T ik ðtr ik þ OP ik Þ L k T ik FE i FT ik X5 X 5 i¼4 k¼1 p h L k X ikh ðdr ik þ DP ik Þ p h L k X ikh FE i DT ik p h L k X ikh RM ik FLC k Y ik þ X5 L k T ik RE ik X 3 X 5 FTC imk Z imk i¼4 m¼1 k¼1 ð3:1þ

8 Y.P. Li, G.H. Huang / Journal of Environmental Management 81 (2006) X k0 subject to: ( ) X 3 L k ðt ik þ X ikh ÞþX5 FE i ðt ik þ X ikh Þ LC 1 k¼1 i¼1 þ X3 X k0 i¼1 k¼1 DLC i Y ik, i¼4 8 h; k 0 ¼ 1; 2; 3; 4; 5; i ¼ 1; 2; 3 ð3:2þ (Landfill capacity constraints), T 4k þ X 4kh TC 4 þ X3 X k0 m¼1 k¼1 DTC 4mk Z 4mk, 8 h; k 0 ¼ 1; 2; 3; 4; 5; i ¼ 4 ð3:3þ (Composting capacity constraints), T 5k þ X 5kh TC 5 þ X3 X k0 m¼1 k¼1 DTC 5mk Z 5mk, 8 h; k 0 ¼ 1; 2; 3; 4; 5; i ¼ 5 ð3:4þ (Recycling capacity constraints), X 5 i¼1 ½T ik þ X ikh Šw kh ; 8k; h (3.5) (Waste disposal demand constraints), X 3 i¼1 ½T ik þ X ikh ŠDG ik w kh ; 8k; h (3.6) (Diversion rate of waste flow to the landfill), T 4k þ X 4kh DG 4k w kh ; 8k; h (3.7) (Diversion rate of waste flow to the composting facility), T 5k þ X 5kh DG 5k w kh ; 8k; h (3.8) (Diversion rate of waste flow to the recycling facility), T ik max T ik X ikh 0 (3.9) (Non-negativity and technical constraints), 8 >< 1; Y 0; ik>: integer; i ¼ 1; 2; 3; 8k; Z imk 8 >< 1; 0; >: integer; i ¼ 4; 5; 8m; k (Binary constraints), X 3 X 5 i¼1 k¼1 (3.10) (3.11) Y ik 1 (3.12) (Landfill expansion/development may only be considered once in the planning horizon), X 3 Z imk m¼1 1; i ¼ 4; 5; 8k (3.13) (Expansions for composting and recycling facilities may occur in any given time period), where f is the net system cost ($); i the type of waste management facility, i ¼ 1, 2, 3, 4, 5, where i ¼ 1 for the existing landfill, 2 and 3 for two new landfill options, 4 for composting facility, and 5 for recycling facility; L k the length of time period k (week); k the time period, k ¼ 1, 2, 3, 4, 5; m the name of expansion option for composting and recycling facilities, m ¼ 1, 2, 3; h the level of waste generation in the city, where h ¼ 1, 2, 3, 4 and 5 when the waste generation rate is low, low-medium, medium, medium-high and high, respectively; DG ik the diversion rate of waste flow to facility i regulated by the City s authority in period k, i ¼ 1, 2, 3, 4, 5; DP ik the operating cost of facility i for excess waste flow during period k ($/tonne) (the second-stage cost parameter), where DP ik OP ik, i ¼ 1, 2, 3, 4, 5; DR ik the cost of collecting and transporting excess waste from the City to facility i during period k ($/tonne) (the second-stage cost parameter), where DR ik TR ik, i ¼ 1, 2, 3, 4, 5; DT ik the disposal cost for excess waste residues generated by composting or recycling facility during period k ($/tonne) (the second-stage cost parameter), where DT ik FT ik, i ¼ 4, 5; FE i the residue flow from facility i to the landfill (% of incoming mass to the facility i), i ¼ 4, 5; FLC ik the capital cost for landfill expansion/development in period k ($/tonne), i ¼ 1, 2, 3; FT ik the disposal cost for allowable waste residues generated by processing facility i during period k ($/tonne), i ¼ 4, 5; FTC imk the capital cost of expanding composting or recycling facility by option m in period k ($/tonne) i ¼ 4, 5; LC 1 the existing landfill capacity (tonne); DLC i the amount of capacity expansion/ development for the landfill (tonne), i ¼ 1, 2, 3; OP ik the regular operating cost of waste management facility i during period k ($/tonne), i ¼ 1, 2, 3, 4, 5; p h the probability of waste-generation rate equaling w kh ; RE ik the revenue generated by processing allowable waste flows in composting or recycling facility during period k ($/tonne), i ¼ 4, 5; RM ik the revenue generated by processing excess waste flows in composting or recycling facility during period k ($/tonne) (the second-stage revenue parameter), i ¼ 4, 5; T ik the allowable waste flow to facility i during period k (tonne/week) (the first-stage deterministic variable), i ¼ 1, 2, 3, 4, 5; T ik max the maximum allowable waste flow to facility i during period k (tonne/week); TC i the existing capacity of composting or recycling facility (tonne/week), i ¼ 4, 5; DTC imk the amount of capacity expansion option m for composting or recycling facility at the start of period k (tonne/week), i ¼ 4, 5; TR ik the cost of collection and transportation for allowable waste flow to facility i during period k ($/tonne), i ¼ 1, 2, 3, 4, 5; w kh the residential waste generation rate with probability p h in period k (tonne/week); X ikh the amount by which the allowable waste flow level is exceeded when the waste-

9 196 Y.P. Li, G.H. Huang / Journal of Environmental Management 81 (2006) generation rate is w kh the with probability p h (tonne/week) (the second-stage decision variable); Y ik the binary decision variable for landfill expansion/development at the start of period k, i ¼ 1, 2, 3; Z imk the binary decision variable for composting or recycling facility with expansion option m at the start of period k, i ¼ 4, 5. Several assumptions are made when formulating this model, including: (1) based on the local waste management policies, a promised allowable waste-flow level from the City to different facilities is predefined (violation of this limit will lead to penalties in terms of raised transportation and operation costs); (2) all solid wastes have to be shipped to a disposal site within a certain period after its generation, and no mass loss is incurred in the transportation process; (3) construction or expansion of any facility should be completed within the time period during which it was initiated; (4) waste collection and disposal serve only the City s households, while industrial, commercial and institutional wastes are not considered in this study. With regards to assumption (4), the main constraint in extending the developed model to industrial, commercial and institutional sectors is due to the fact that waste management for the non-residential sectors is not under the supervision of the municipal government. Therefore, each industrial, commercial or institutional organization has flexibility in choosing and/or changing waste-management contractors, with dynamic and random features. It is thus hard for a municipal government to incorporate activities of the non-residential sectors within its framework for waste-management planning; instead, management of wastes from the non-residential sectors would mainly rely on the related regulations and by-laws. 4. Results and discussion The ITMILP method can effectively deal with uncertainties presented as both probabilities and intervals, within a multi-facility, multi-period, multi-waste-level, and multi-option context. Solutions of the model provide an effective linkage between the predefined environmental policies and the associated economic implications (e.g., losses and penalties caused by improper policies). The solutions contain a combination of deterministic, interval and distributional information, and can thus facilitate the reflection for different forms of uncertainties. The interval solutions can help managers obtain multiple decision alternatives, as well as provide bases for further analyses of tradeoffs between waste-management cost and systemfailure risk; the binary-variable solutions represent the decisions of facility expansion, where several alternatives are generated; the continuous-variable solutions are related to decisions of waste-flow allocation Solution under Scenario Facility expansion: Table 8 and Fig. 1 present the optimal solution for facility expansions under this scenario (i.e., solution of binary decision variables). Fig. 2 shows the remaining landfill capacity at the end of each period. The results indicate that the landfill should be expanded at the start of period 2, with an incremental capacity of 71.3 ha, where 28.5 ha (i.e., approximately 40% of the total capacity) will be dedicated to the City s residential waste. A large centralized composting facility should be developed with a capacity of 483 tonne/week at the start of period 1, with 70% of the capacity (i.e., 338 tonne/week) being dedicated to the residential waste; then this facility should be expanded by an increment of 189 tonne/week at the starts of periods 3 and 4, respectively. Thus, the composting capacity for residential wastes would eventually be increased to [647, 651] tonne/week. The MRF should be expanded by a capacity of 700 tonne/week at the start of period 1 (and thus 280 tonne/week for residential waste); then this facility would be expanded by 350 tonne/week at the starts of periods 2 and 5, respectively. Thus, the MRF capacity for residential waste would eventually be [721, 742] tonne/week Waste flow allocation: Table 9 shows the solution of optimized waste-flow allocation during periods 1 5. Generally, the solutions present as interval and probabilistic forms, demonstrating that the related decisions should be sensitive to the Table 8 Solution of capacity development/expansion (Scenario 1) Facility Symbol Expansion capacity Capacity for residential waste Period Capacity-expansion solution Landfill Y 12opt 71.3 ha ha. 1 [1, 1] Composting Z 431 opt 483 t/wk 338 t/wk 1 [1, 1] Z 413 opt 189 t/wk 132 t/wk 3 [1, 1] Z 414 opt 189 t/wk 132 t/wk 4 [1, 1] Material recovery facility Z 521 opt 700 t/wk 280 t/wk 1 [1, 1] Z 512 opt 350 t/wk 140 t/wk 2 [1, 1] Z 515 opt 350 t/wk 140 t/wk 5 [1, 1]

10 Y.P. Li, G.H. Huang / Journal of Environmental Management 81 (2006) Fig. 1. Capacity planning for waste-management facilities (Scenario 1). Fig. 2. Remaining landfill capacity at the end of each period (Scenario 1). uncertain modeling inputs. Based on the local wastemanagement policy, there would be [1134, 1193] 10 3 tonne of waste flows (including residues) allocated to the landfill, including [1086, 1125] 10 3 tonne of allowable flow and [48, 68] 10 3 tonne of excess flow. There would be [495.2, 514.5] 10 3 tonne of waste flows diverted to the composting facility, including [474, 485] 10 3 tonnenes of allowable flow and [21.2, 29.5] 10 3 tonne of excess flow. The flow diverted to the MRF would be [509.0, 528.7] 10 3 tonne, including [487, 499] 10 3 tonne of allowable flow and [22.0, 29.7] 10 3 tonne of excess flow. Fig. 3 presents waste flows allocated to the landfill, composting facility and MRF during the entire planning horizon. It is indicated that the flow to the landfill

11 198 Y.P. Li, G.H. Huang / Journal of Environmental Management 81 (2006) Table 9 Solution of waste flow allocation (Scenario 1) Period Facility Waste generation rate Probability (%) Allowable waste Excess waste flow (t/wk) Optimized waste 1 Landfill Low 10 [1068, 1093] 0 [1068, 1093] 1 Composting Low 10 [142, 146] 0 [142, 146] 1 MRF Low 10 [213, 219] 0 [213, 219] 1 Landfill Low-medium 20 [1068, 1093] [0.0, 15.5] [1068.0, ] 1 Composting Low-medium 20 [142, 146] [0.0, 1.8] [142.0, 147.8] 1 MRF Low-medium 20 [213, 219] [0.0, 2.7] [213.0, 221.7] 1 Landfill Medium 40 [1068, 1093] [40.5, 64.3] [1108.5, ] 1 Composting Medium 40 [142, 146] [5.8, 8.3] [147.8, 154.3] 1 MRF Medium 40 [213, 219] [8.7, 12.5] [221.7, 231.5] 1 Landfill Medium-high 20 [1068, 1093] [89.3, 105.5] [1157.3, ] 1 Composting Medium-high 20 [142, 146] [12.3, 13.8] [154.3, 159.8] 1 MRF Medium-high 20 [213, 219] [18.5, 20.7] [231.5, 239.7] 1 Landfill High 10 [1068, 1093] [130.5, 143] [1198.5, 1236] 1 Composting High 10 [142, 146] [17.8, 18.8] [159.8, 164.8] 1 MRF High 10 [213, 219] [26.7, 28.2] [239.7, 247.2] 2 Landfill Low 10 [925, 947] 0 [925, 947] 2 Composting Low 10 [250, 256] 0 [250, 256] 2 MRF Low 10 [294, 301] 0 [294, 301] 2 Landfill Low-medium 20 [925, 947] [0.0, 13.8] [925.0, 960.8] 2 Composting Low-medium 20 [250, 256] [0.0, 3.3] [250.0, 259.3] 2 MRF Low-medium 20 [294, 301] [0.0, 4.0] [294.0, 305.0] 2 Landfill Medium 40 [925, 947] [35.8, 57.9] [960.8, ] 2 Composting Medium 40 [250, 256] [9.3, 15.2] [259.3, 271.2] 2 MRF Medium 40 [294, 301] [11.0, 18.0] [305.0, 319.0] 2 Landfill Medium-high 20 [925, 947] [79.9, 93.1] [1004.9, ] 2 Composting Medium-high 20 [250, 256] [21.2, 24.7] [271.2, 280.7] 2 MRF Medium-high 20 [294, 301] [25.0, 29.2] [319.0, 330.2] 2 Landfill High 10 [925, 947] [115.1, 125.3] [1040.1, ] 2 Composting High 10 [250, 256] [30.7, 33.3] [280.7, 289.3] 2 MRF High 10 [294, 301] [36.2, 39.4] [330.2, 340.4] 3 Landfill Low 10 [759, 776] 0 [759, 776] 3 Composting Low 10 [379, 388] 0 [379, 388] 3 MRF Low 10 [379, 388] 0 [379, 388] 3 Landfill Low-medium 20 [759, 776] [0.0, 11.0] [759.0, 787.0] 3 Composting Low-medium 20 [379, 388] [0.0, 5.5] [379.0, 393.5] 3 MRF Low-medium 20 [379, 388] [0.0, 5.5] [379.0, Landfill Medium 40 [759, 776] [28.0, 48.5] [787.0, 824.5] 3 Composting Medium 40 [379, 388] [14.5, 24.3] [393.5, 412.3] 3 MRF Medium 40 [379, 388] [14.5, 24.3] [393.5, 412.3] 3 Landfill Medium-high 20 [759, 776] [65.5, 77] [824.5, 853] 3 Composting Medium-high 20 [379, 388] [33.3, 38.5] [412.3, 426.5] 3 MRF Medium-high 20 [379, 388] [33.3, 38.5] [412.3, 426.5] 3 Landfill High 10 [759, 776] [94.0, 103.0] [853.0, 879.0] 3 Composting High 10 [379, 388] [47.5, 51.5] [426.5, 439.5] 3 MRF High 10 [379, 388] [47.5, 51.5] [426.5, 439.5] 4 Landfill Low 10 [580, 592] 0 [580, 592] 4 Composting Low 10 [517, 529] 0 [517, 529] 4 MRF Low 10 [470, 481] 0 [470, 481] 4 Landfill Low-medium 20 [580, 592] [0.0, 8.9] [580.0, 600.9] 4 Composting Low-medium 20 [517, 529] [0.0, 6.9] [517.0, 535.9] 4 MRF Low-medium 20 [470, 481] [0.0, 6.2] [470.0, 487.2] 4 Landfill Medium 40 [580, 592] [20.9, 38.9] [600.9, 630.9] 4 Composting Medium 40 [517, 529] [18.9, 33.7] [535.9, 562.7] 4 MRF Medium 40 [470, 481] [17.2, 30.5] [487.2, 511.5] 4 Landfill Medium-high 20 [580, 592] [50.8, 59.9] [630.8, 651.9] 4 Composting Medium-high 20 [517, 529] [45.7, 52.5] [562.7, 581.5] 4 MRF Medium-high 20 [470, 481] [41.5, 47.6] [511.5, 528.6] 4 Landfill High 10 [580, 592] [71.9, 79.9] [651.9, 671.9] 4 Composting High 10 [517, 529] [64.5, 70.3] [581.5, 599.3]

12 Y.P. Li, G.H. Huang / Journal of Environmental Management 81 (2006) Table 9 (continued ) Period Facility Waste generation rate Probability (%) Allowable waste Excess waste flow (t/wk) Optimized waste 4 MRF High 10 [470, 481] [58.6, 63.8] [528.6, 544.8] 5 Landfill Low 10 [567, 579] 0 [567, 579] 5 Composting Low 10 [534, 546] 0 [534, 546] 5 MRF Low 10 [518, 529] 0 [518, 529] 5 Landfill Low-medium 20 [567, 579] [0.0, 8.3] [567.0, 587.3] 5 Composting Low-medium 20 [534, 546] [0.0, 8.0] [534.0, 553.7] 5 MRF Low-medium 20 [518, 529] [0.0, 7.7] [518, 537] 5 Landfill Medium 40 [567, 579] [20.3, 37.4] [587.3, 616.4] 5 Composting Medium 40 [534, 546] [19.7, 35.1] [553.7, 581.1] 5 MRF Medium 40 [518, 529] [19.0, 34.5] [537.0, 563.5] 5 Landfill Medium-high 20 [567, 579] [49.4, 58] [616.4, 637.0] 5 Composting Medium-high 20 [534, 546] [47.1, 54.6] [581.1, 600.6] 5 MRF Medium-high 20 [518, 529] [45.5, 53.4] [563.5, 582.4] 5 Landfill High 10 [567, 579] [70.0, 77.6] [637.0, 656.6] 5 Composting High 10 [534, 546] [66.6, 73.1] [600.6, 619.1] 5 MRF High 10 [518, 529] [64.4, 71.3] [582.4, 600.3] Fig. 3. Optimal waste-flow allocation pattern (Scenario 1). would be decreasing with time, while those to the composting and recycling facilities would keep increasing. Consequently, under this waste-flow allocation pattern, the City would achieve the 47% diversion rate within the upcoming 25 years, indicating that the waste-management plan based on the policy as predefined in scenario 1 could satisfy the required diversion goal System cost: Under this scenario, the resulting system cost is $[108.8, 135.1] million, which is associated with a total landfill capacity consumption of [1134.0, ] 10 3 tonne and 65% diversion goal at the end of the planning horizon. The system cost includes expenses for handling fixed allowable waste flows, probabilistic excess flows, and expansions/ developments of landfilling, composting and recycling facilities. The results indicate that the cost for facility expansions is $[14.3, 16.2] million (or [12.0, 13.2]% of the total system cost); the regular cost for disposing/diverting allowable waste flows is $[87.8, 108.0] million (or [79.9, 80.7]% of the total system cost); the penalty cost for handling excess waste flows is $[6.7, 10.9] million (or [6.2, 8.1]% of the total system cost). In addition, the cost for waste landfilling is $[35.0, 47.4] million (or [35.1, 38.0]% of the total system cost); the costs for waste composting and recycling are $[31.8, 37.5] million (or [27.8, 29.2]% of the total system cost) and $[42.0, 50.2] million (or [37.1, 38.6]% of the total system cost), respectively. In general, 62.5 to

13 200 Y.P. Li, G.H. Huang / Journal of Environmental Management 81 (2006) Fig. 4. Capacity planning for waste-management facilities (Scenario 2). Fig. 5. Remaining landfill capacity at the end of each period (Scenario 2). 68.2% of the total system cost is used for waste diversion, demonstrating the economic implication of raised environmental requirements Solution under Scenario Facility expansion: Figs. 4 and 5 show the results of capacity-expansion planning and the remaining landfill capacity at the end of each period under this scenario. It is indicated that only the landfill would be expanded at the start of period 2, while the composting and recycling facilities should not be developed or expanded over the planning horizon Waste flow allocation: Table 10 shows the solution of optimized waste flow allocation during periods 1 5. It can be seen that the allocation plan is significantly different from that in scenario 1, due to the different waste management policies. There would not be any excess flows to composting and recycling facilities (in reference to the allowable flows) under all waste-generation levels. This is due to the following facts: (i) the required diversion rate (12%) is low; (ii) the composting and recycling facilities would remain the status quo, while the landfill would be expanded; (iii) since the composting and recycling facilities have higher collection/transportation and disposal costs,