CAPACITY PLANNING FOR AN INTEGRATED WASTE MANAGEMENT SYSTEM UNDER UNCERTAINTY: A NORTH AMERICAN CASE STUDY

Waste Management & Research (1997) 15, 523–546

CAPACITY PLANNING FOR AN INTEGRATED WASTE MANAGEMENT SYSTEM UNDER UNCERTAINTY: A NORTH AMERICAN CASE STUDY G. H. Huang1∗, B. W. Baetz2, G. G. Patry3 and V. Terluk4 1

Faculty of Engineering, University of Regina, Regina, SK S4S 0A2, Canada; 2Department of Civil Engineering, McMaster University, Hamilton, Ontario L8S 4L7, Canada; 3Faculty of Engineering, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada; and 4Environmental Services Department, The Regional Municipality of Hamilton–Wentworth, Hamilton, Ontario L8N 4A9, Canada (Received 21 January 1994, accepted in revised form 13 March 1996) In this paper, a grey integer-programming (GIP) formulation for the capacity planning of an integrated waste management system under uncertainty is applied to a North American case study. The GIP model is formulated by introducing concepts of grey systems and grey decisions into a mixed integer linear programming (MILP) framework. The approach has an advantage in that uncertain information (presented as interval numbers) can be effectively communicated into the optimization processes and resulting solutions, such that feasible decision alternatives can be generated through interpretation and analysis of the grey solutions according to projected applicable system conditions. Moreover, the GIP solution algorithm does not lead to more complicated intermediate models, and thus has lower computational requirements than other integer-programming methods that deal with uncertainties. The proposed model is used for the long-term planning of waste management facility expansion/utilization in the Regional Municipality of Hamilton–Wentworth (RMHW), Ontario, Canada. The binary decision variables in the model represent the ranges of facility expansion/development alternatives within a multi-period, multi-facility and multi-scale context, and the grey continuous variables represent waste flows along the routes connecting the municipalities and the waste management facilities. The results indicate that reasonable solutions have been generated through this grey mathematical programming approach. The case study results are potentially useful for MSW decision-makers in the RMHW for the long-term planning of the Region’s waste management activities and for formulating related local policies/ regulations regarding waste generation and management, and may stimulate the interest of waste management professionals in other jurisdictions on the use of this type of modelling approach for their specific long-range planning applications.  1997 ISWA

Key Words—Capacity planning, municipal solid waste management, uncertainty, systems analysis, grey integer programming, decision-making, Canada.

1. Introduction An integrated waste management system for a municipality may involve several facilities to meet the overall demand for waste processing, treatment, and disposal. A landfill may be utilized directly to satisfy waste disposal demand or, alternatively, to provide ∗ To whom correspondence should be addressed. 0734–242X/97/050523+24 $25.00/0

wm960106

 1997 ISWA

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capacity for other facilities’ residue disposal, and typically has an overall cumulative capacity limit. Other facilities, such as incineration plants, centralized composting/ recycling installations, and transfer stations, have daily operating capacity limits. From a long-term planning point of view, waste generation (including recyclable and compostable wastes) may keep increasing due to population increases and economic development. Therefore, municipal solid waste (MSW) managers may often face problems of insufficiency in available facility capacities to meet future waste disposal demand. In addition, because of the temporal variation of the relationships between waste generation and available facility capacities, the optimal schemes for the effective utilization of the facilities (i.e. optimal waste flow allocation patterns) may vary between different time periods (Baetz 1990). The above points emphasize the need for a systematic approach for the long-term capacity planning of a municipal solid waste management system. Previously, methods of mixed integer programming (MILP) and dynamic programming (DP) have been used for solving this type of waste managment planning problem (Rao 1975; Jenkins 1982; Baetz 1988, 1990; Baetz et al. 1989). Since many parameters in a waste management system can be uncertain, applicability of deterministic mathematical programming methods may be affected. Previously, there have been only studies of decision-making under uncertainty for hazardous waste management (Jennings & Suresh 1986; Koo et al. 1991; Lee et al. 1991), with no previous research relating to capacity planning under uncertainty for a MSW management system. In this study, a grey integer programming (GIP) model is formulated for this type of capacity planning problem and applied to the Regional Municipality of Hamilton–Wentworth (RMHW), Ontario, Canada. The GIP method improves upon the previous integer-programming methods that deal with uncertainties (fuzzy integer programming and stochastic integer programming) by incorporating concepts of grey systems and grey decisions within an MILP framework (Huang 1994). The approach can effectively communicate uncertain information (presented as grey or interval numbers, where the specification of a grey number ⊗(x), ⊗(x)=[a, b], implies that the assumed lower bound value of an uncertain parameter equals (a) and the assumed upper bound value of an uncertain parameter equals (b) into its optimization processes and resulting solutions, such that feasible decision alternatives can be generated through interpretation of the grey solutions according to projected applicable system conditions. Moreover, the approach has lower computational requirements than the other nondeterministic integer-programming methods. The grey binary variables in the model will represent the ranges of facility expansion/development alternatives within a multiperiod, multi-facility and multi-scale context, and the grey continuous variables will represent waste flows along the routes connecting the municipalities and waste management facilities. The MSW management system in the Regional Municipality of Hamilton–Wentworth is complicated and is affected by a number of impact factors, such as economic, technical, environmental, legislational and political issues, as well as the use and conservation of resources. Previously, studies of waste management activities in the Region have been conducted by engineering consulting companies. There has been no systematic planning for the entire Region over a long time horizon, and no planning that effectively incorporated uncertain information within the study framework. Consequently, solid waste managers in the Region desired to conduct long-term capacity planning for the Region’s waste management facilities, as well as the relevant planning

Capacity planning for a waste management system

525

Waste Generation Districts:

Watse Management Facilities:

District 1 = Township of Flamborough District 2 = Town of Dundas Districts 3 to 9 = City of Hamilton Districts 10 to 12 = Town of Stoney Creek Districts 13 to 16 = Town of Ancaster District 17 = Township of Glanbrook

DTS = Dundas transfer station KTS = Kenora transfer station MTS = Mountain transfer station SWARU = Waste incineration facility Third Sector = Waste recycling facility HHWD = Household hazardous waste depot ACF = Potential composting facility in Ancaster DCF = Potential composting facility in Dundas GCF = Potential composting facility in Glanbrook SCF = Potential composting facility in Stoney Creek Glanbrook Landfill New Landfill

N

Hamilton Harbour

DCF

1

DTS

3

2

4

5

Lake Ontario

HHWD KTS Third Sector 7 SWARU

11 9

8

10

6

12

SCF

MTS

16 13 17 14

ACF

15 New Landfill

Glanbrook Landfill GCF

Fig. 1. Study area and waste management facilities.

for facility utilization schemes during the different time periods, in order to achieve minimized total system cost. A GIP model was proposed as a suitable modelling approach for this type of facility capacity planning problem. The structure of the paper is as follows. In section two, aspects of the study area and its related waste management system are described. Material relating to the data collection and analysis for the case study is presented in section three. In section four, the mathematical programming formulation is briefly described with the full details of the model formulation being presented within a technical appendix. Modelling results are presented and discussed in section five, and concluding remarks are offered in section six. 2. The study area and the related waste management system 2.1 The study area The RHMW is situated in south-central Ontario, Canada. Its area is 1.1×103 km2, including six cities/towns (Hamilton, Dundas, Ancaster, Stoney Creek, Flamborough, and Glanbrook) (as shown in Fig. 1), and a population of 0.45×106. The Region is Canada’s largest steel producer and ranks high in industrial production, with two of Canada’s three largest steel firms (STELCO and DOFASCO) being located within the Region. The main residential areas are distributed in Hamilton, Dundas, north Ancaster, and west Stoney Creek. In terms of transportation, the Region is connected to Toronto and Niagara Falls via two highways (Queen Elizabeth Way (QEW) and Highway 403) (Marsh 1988; Sleightholm & Ruberto 1990).

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2.2 Solid waste management system 2.2.1 Waste management facilities The Region’s solid waste management system is required to satisfy the waste disposal needs of the 0.45×106 population who collectively produce more than 0.3×106 tonnes year−1 of residential, industrial, and commercial wastes. To manage these wastes effectively, an integrated system has been constructed, which incudes a waste-to-energy facility (named SWARU as an acronym for Solid WAste Reduction Unit), a Blue Box recycling program, a 550-acre (220 ha) landfill, three transfer stations, a backyard composting program and a household hazardous waste depot. (a) SWARU: The SWARU can burn up to 450 tonnes day−1 of waste and generates about 14×106 kW year−1 of electricity (the electricity is either used in plant or sold to Ontario Hydro where it provides for non-heating needs of approximately 2600 homes for an entire year). The remaining combustion by-products (residues) are divided into non-hazardous bottom ash and hazardous fly ash. The bottom ash, being the heavier component, falls to the boiler bottom and is removed by a conveyor belt. This type of material is inert and can be delivered directly to the Region’s landfill. The fly ash, being much lighter, is suctioned off, cooled, and then removed by conveyor. Finally, the fly ash is placed in covered containers and shipped to a licensed hazardous waste landfill. Currently, the majority of the waste inputs to the SWARU facility are from lower Hamilton and Stoney Creek. (b) Blue box recycling program: The Region’s recycling program is operated by Third Sector Employment Enterprises (abbreviated as Third Sector). The program is overseen by the Department of Environmental Services of the RHMW. The Ontario Ministry of Environment (MOE), the Ontario Multi-Materials Recycling Initiative (OMMRI), and local municipalities of the Region support the program by subsidizing the purchase of blue boxes, and providing funding to offset the operating costs. A typical Ontario household using a blue box diverts approximately 136 kg year−1 of recyclable materials from disposal. This figure converts to approximately 0.3 m3 year−1 household−1 of landfill space savings. Once a week, recyclable wastes are picked up on the regular garbage collection day. The contractor who picks up the recyclable materials in all cities/towns except Glanbrook is Third Sector itelf. In Glanbrook, the recyclable materials are picked up by Eggers Excavating who also collects curbside garbage. All recyclable materials are picked up and delivered to the Third Sector material recycling facility which is located in north-central Hamilton. Currently, this facility has an operating capacity of 100 to 110 tonnes day−1. (c) Landfill: The Region’s landfill is located at the southeast corner of Glanbrook with an area of 550 acres. Due to the expense and the time involved in siting and constructing a landfill, it is the Region’s objective to maximize the existing landfill’s life expectancy by prohibiting materials which may be feasibly diverted elsewhere. The landfill only accepts approved non-hazardous waste from the following sources: (i) waste generators in the Region via transfer stations (the landfill itself is not open to the public); (ii) bottom ash from SWARU; and (iii) grit from the sewage treatment plants of the Region. It is estimated that with the current capacity consumption rate, the landfill should be able to last for an additional 20 years.

Capacity planning for a waste management system

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(d) Transfer stations: The cities/towns are responsible for the collection of their own curbside wastes and the delivery of these wastes to the transfer stations or to SWARU. The Region has three strategically located transfer stations to receive wastes from municipal or individual sources and transfer them to downstream waste management facilities. They are located in Dundas [Dundas Transfer Station (DTS)], east Hamilton [Kenora Transfer Station (KTS)], and Hamilton mountain [Mountain Transfer Station (MTS)], respectively (Fig. 1). Presently, wastes collected through curbside pick-up from Flamborough, Dundas, and northwest Ancaster are delivered to the DTS, wastes from Glanbrook, Hamilton mountain, and southeast Ancaster go to the MTS, and wastes from lower Hamilton and Stoney Creek are directly delivered to SWARU. The DTS and MTS also receive individual deliveries from local industries, businesses, and institutions. No curbside collected waste is delivered to the KTS (only individual truck loads of industrial, commercial, and institutional wastes are accepted). Wastes received at the transfer stations are compacted into large, completely enclosed 75 yd3 trucks (transfer trailers), and then hauled to the Glanbrook landfill. 2.2.2 Waste management costs In 1992, approximately C$21 700 000 (Canadian dollars) was required to operate the Region’s solid waste management system. This cost was paid through both the municipal tax base and the tipping fees received at the transfer stations. Residents are allowed to bring in up to 300 kg of acceptable solid waste free of charge to the transfer stations (for loads of more than 300 kg, the charge is based on the entire load at C$180 tonne−1), while the commercial haulers are charged at a rate of C$180 tonne−1 (the first 300 kg are not free). The high tipping fee policy in the Region has the following attributes: (i) discourages importation of waste from other Regions; (ii) makes it financially attractive for companies and individuals to enhance their waste recycling, re-use, and reduction activities (e.g. the current cost of corrugated cardboard recycling ranges from C$25 to C$35 tonne−1, which is much lower than the tipping fee of C$180 tonne−1); (iii) provides revenue for operating and maintenance costs, as well as funds for supporting waste management initiatives (such as Blue Box programs, household hazardous waste management programs, backyard composting programs, and industrial waste reduction programs), or developing/expanding waste management facilities; and (iv) supplements public works and capital reserves. 3. Data collection and analysis The overall Region was divided into 17 waste generation districts for this waste management planning problem, based on characteristics relating to waste generation and transportation (Fig. 1). The study time horizon was 40 years, which was divided into five planning periods as shown in Table 1. Table 2 presents the curbside wastes generated forecasted for the five periods. It is indicated that, as time goes on, the waste generation in all of the 17 districts was assumed to increase. Over the 40-year planning horizon, due to the temporal variation of the relationships between waste generation and available facility capacities, the capacities of the Region’s waste management facilities may have to be increased. Table 3 shows the capacity expansion options and their capital costs for different waste management facilities for the five time periods. No expansion of SWARU was considered due to the existing restrictive waste-to-energy policies in the Province of Ontario. It is indicated that a

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TABLE 1 Five planning periods for the 40-year study time horizon Period k=1 k=2 k=3 k=4 k=5

Interval 1993–1998 1998–2003 2003–2013 2013–2023 2023–2033

new landfill may be developed with an area of [200, 300] acres ([80.9, 121.4] hectares) over the time horizon; a new composting facility could be developed/expanded by three different options in each of the five time periods with a maximum expansion limit of [550, 620] tonnes week−1; and Third Sector’s material recycling facility could be expanded once by a capacity of [810, 900] tonnes week−1. In terms of the potential locations of the new facilities, an unspecified location in southeast Ancaster was assumed to be a suitable site for the new landfill due to its satisfactory geological/geographical conditions (Fig. 1), while four potential locations were assumed to exist for the new composting facility [rural parts of Dundas, Ancaster, Stoney Creek, and Glanbrook (Fig. 1)]. Recently, Laidlaw Technology Inc. have submitted a proposal for a new composting facility in the Region, where a location at the Glanbrook landfill was suggested (Laidlaw Technologies Inc. 1992). Therefore, in order to better reflect the potential system condition variations, two cases were studied. These cases were: (i) when the composting facility is located in Glanbrook; and (ii) when there are four options for the composting facility location. The final decision for an optimal facility expansion/development scheme will depend on the consideration of many environmental, economic, and resource factors. Table 4 presents the operating costs and revenues for different waste management facilities over the five time periods. Generally, from Tables 2 to 4, it is seen that the majority of data obtained for the Region’s waste management activities are interval numbers, which can be easily incorporated within a grey mathematical programming model. 4. Formulation of the grey integer programming model Both the entire Region (Fig. 1) and the entire time horizon (40 years) are integrated as a general system. The decision variables in the system include two categories: discrete and continuous. The discrete variables represent the expansion options for waste management facilities in different time periods, and the continuous variables represent the waste flows from different districts to the waste management facilities via municipal collection (industrial/commercial wastes are not included in the model, and will be discussed separately). The objective is to minimize total system cost by achieving optimal facility expansion/development and optimal waste flow allocation for the entire time horizon. The constraints include all of the relationships between the decision variables and the waste generation, transportation, and management conditions. Thus, a grey integer programming (GIP) model for this capacity expansion planning problem can be formulated (Huang 1994). The model can be solved by an interactive algorithm developed by Huang (1994).

Flamborough

Dundas

Hamilton 403 West West Downtown Hamilton Downtown Hamilton East Downtown Hamilton East Hamilton West Mountain Hamilton East Mountain Hamilton

Lower Stoney Creek East Stoney Creek Mountain Stoney Creek

Northeast Ancaster Northwest Ancaster South Ancaster East Ancaster

Glanbrook

Flamborough

Dundas

Hamilton Hamilton Hamilton Hamilton Hamilton Hamilton Hamilton

Stoney Creek Stoney Creek Stoney Creek

Ancaster Ancaster Ancaster Ancaster

Glanbrook

∗ Including recyclable wastes.

Total

Name of district

City/Town

TABLE 2

j=17

j=13 j=14 j=15 j=16

j=10 j=11 j=12

j=3 j=4 j=5 j=6 j=7 j=8 j=9

j=2

j=1

District number

133] 139] 237] 376] 631] 324] 618]

[3035, 3421]

[64, 75]

[46, 58] [8, 17] [17, 29] [75, 87]

[231, 260] [6, 14] [69, 81]

[121, [121, [214, [341, [566, [289, [561,

[127, 145]

[179, 197]

k=1

138] 145] 247] 391] 657] 337] 643]

[3220, 3633]

[67, 78]

[52, 66] [9, 19] [19, 33] [85, 98]

[261, 294] [7, 16] [78, 92]

[126, [126, [223, [355, [589, [301, [584,

[137, 156]

[203, 223]

k=2

144] 151] 257] 407] 683] 351] 669]

74] 22] 37] 111]

[3421, 3862]

[69, 81]

[59, [10, [22, [96,

[296, 333] [8, 18] [88, 104]

[131, [131, [232, [369, [613, [313, [608,

[147, 156]

[229, 252]

k=3

156] 163] 278] 441] 740] 380] 725]

[3875, 4383]

[75, 88]

[75, 95] [13, 82] [28, 48] [123, 143]

[379, 426] [10, 23] [113, 133]

[142, [142, [251, [400, [664, [339, [658,

[171, 195]

[293, 323]

k=4

Waste generation rates, WGjk (tonnes week−1)

Curbside wastes generated in the five time periods∗

169] 177] 301] 478] 801] 412] 786]

[4414, 5002]

[81, 95]

[96, 122] [17, 36] [36, 61] [157, 183]

[485, 545] [13, 29] [145, 170]

[154, [154, [272, [433, [719, [367, [713,

[199, 227]

[376, 413]

k=5

Capacity planning for a waste management system 529

[810, 900] tonnes week−1 [2.60, 3.00]

[1.09, 1.74] [1.50, 2.02] [1.91, 2.66]

[70.0, 75.0]

k=1

[2.24, 2.59]

[0.94, 1.50] [1.29, 1.90] [1.65, 2.29]

[60.4, 64.7]

k=2

[1.93, 2.23]

[0.81, 1.29] [1.12, 1.64] [1.42, 1.98]

[52.1, 55.8]

k=3

[1.44, 1.66]

[0.60, 0.96] [0.83, 1.22] [1.06, 1.47]

[38.8, 41.5]

k=4

Expansion cost∗ (106 $)

∗ Present value (in Canadian dollars). † [200, 300] acres converts to [80.9, 121.4] hectares, as shown in Figs 2 and 4. ‡ i=5 when there is one option of the composting facility location, or i=5, 6, 7, 8 when there are four options of the composting facility location.

Third Sector, ⊗(ck)

[310, 345] tonnes week−1 [430, 485] tonnes week−1 [550, 620] tonnes week−1

Composting facility, ⊗(bimk)‡ Composting facility, ⊗(bimk) Composting facility, ⊗(bimk)

m=1 m=2 m=3

[200, 300] acres†

Expansion option Expansion capacity

Landfill, ⊗(ak)

Facility

TABLE 3

Capacity expansion options and their capital costs for the waste management facilities

[1.07, 1.24]

[0.45, 0.72] [0.62, 0.91] [0.79, 1.10]

[28.8, 30.9]

k=5

530 G. H. Huang et al.

k=1

∗ Costs in Canadian dollars.

SWARU Third Sector Composting facilities

Revenues from waste management facilities ($ tonne−1)∗:

Landfill SWARU Third Sector Composting facilities Dundas Transfer Station Kenora Transfer Station Mountain Transfer Station

[4.0, 5.5] [45.0, 55.0] [5.0, 10.0]

[37.0, 48.0] [60.0, 70.0] [100, 115] 40.0 [13.0, 16.0] [13.0, 16.0] [13.0, 16.0]

Operating costs of waste management facilities and transfer stations ($ tonne−1)∗:

Facility

TABLE 4

[3.5, 4.7] [38.8, 47.4] [4.3, 8.6]

[31.9, 41.4] [51.8, 60.4] [86.3, 99.2] 34.5 [11.2, 13.8] [11.2, 13.8] [11.2, 13.8]

k=2

[3.0, 4.1] [33.5, 40.9] [3.7, 7.4]

[27.5, 35.7] [44.6, 52.1] [74.4, 85.6] 29.8 [9.7, 11.9] [9.7, 11.9] [9.7, 11.9]

k=3

Period

[2.2, 3.1] [24.9, 30.5] [2.8, 5.5]

[20.5, 26.6] [33.2, 38.8] [55.4, 63.7] 22.1 [7.2, 8.9] [7.2, 8.9] [7.2, 8.9]

k=4

Operating costs and revenues of waste management facilities over the five time periods

[1.7, 2.3] [18.5, 22.7] [2.1, 4.1]

[15.2, 19.8] [24.7, 28.8] [41.2, 47.4] 16.5 [5.4, 6.6] [5.4, 6.6] [5.4, 6.6]

k=5

Capacity planning for a waste management system 531

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5. Results and discussion The GIP model contained more than 1000 constraints and more than 700 decision variables (25 binary and 715 continuous variables for the case when a single composting facility is assumed to be located in Glanbrook; 70 binary and 760 continuous variables for the case when there are four options for the composting facility location), which was solved on a 486 microcomputer using the MILP88 software package (Eastern Software Products 1989), with a typical single run taking approximately 50 hours. 5.1 Optimal solution when a single composting facility is located in Glanbrook 5.1.1 Facility expansion Table 5 and Fig. 2 show the facility expansion solutions for the landfill, Third Sector, and composting facilities obtained through the GIP model when the composting facility is assumed to be located in Glanbrook. It is indicated that a new landfill should be developed by a size of [200, 300] acres ([80.9, 121.4] hectares) at the start of period 4 (year 2014). A composting facility should be developed at a capacity of [430, 485] tonnes week−1 in Glanbrook at the start of period 1, and then expanded by an increment of [550, 620] tonnes week−1 at the start of period 2 (year 1999). The Third Sector material recycling facility is determined to be expanded by a capacity of [810, 900] tonnes week−1 at the start of period 5 (year 2024). 5.1.2 Waste flow allocation The waste flow allocation solutions for periods 1 to 5 are also shown in Table 5. It is indicated that the waste flow allocation patterns vary between different time periods due to the temporal variation of waste management conditions over the time horizon. In the following we will provide detailed interpretation and analysis of the period 1 solutions, which are graphically presented in Fig. 3. The solutions for the other periods can be similarly interpreted based on the results in Table 5. (a) Non-recyclable/non-compostable waste flows to transfer stations, SWARU, and landfill: The solution for period 1 (Fig. 3) indicates that all non-recyclable/non-compostable (NR/NC) MSW collected from districts 1, 2, and 3 ([132, 149], [89, 106], and [85, 96] tonnes week−1, respectively) should be delivered to the Dundas Transfer Station (DTS), and the majority of NR/NC MSW collected from districts 9 and 17 ([395, 624], and [39, 49] tonnes week−1, respectively) should be hauled to the Mountain Transfer Station (MTS), while no NR/NC MSW should go to the Kenora Transfer Station (KTS). The wastes entering the MTS should then be delivered to the landfill, while those from the DTS should be transported to SWARU. All NR/NC MSW collected from districts 4 to 7 and 10 to 16, and the majority of NR/NC MSW from district 8 should be directly hauled to SWARU. Curbside collected residential wastes are generally considered as suitable inputs for SWARU, while a very low percentage (less than 1%) of industrial/commercial wastes are considered to be acceptable. The majority of the districts (4 to 7, and 10 to 16) were determined to have their curbside wastes directly hauled to SWARU because this will: (i) avoid mixing the curbside waste with industrial/commercial wastes in the transfer stations; and (ii) reduce the operating costs of the transfer stations. The reasons why wastes from districts 1, 2, and 3 are first hauled to the DTS and then to SWARU via the QEW (a highway close to both the DTS and SWARU) are that the three

District number Facility

0 0 1 0 0

k=1

0 0 0 1 0

k=2

j=4, 5 j=6, 7 j=8 j=9 j=10 to 12 j=13 to 16

SWARU SWARU SWARU SWARU SWARU SWARU

j=1 j=2 j=3 j=4, 5 j=6, 7 j=8 j=9 j=10 to 12 j=13 to 16 j=17

Third Sector Third Sector Third Sector Third Sector Third Sector Third Sector Third Sector Third Sector hird Sector Third Sector

[17, [12, [12, 42 181 [28, [54, [31, [15, 13 32] 60] 36] 19]

19] 14] 13]

[259, 296] [635, 725] [139, 170] [0, 22] [245, 284] [117, 153]

[30, [20, [18, 87 236 [45, 144 [52, [25, 17 61] 32]

51]

33] 23] 20]

[209, 245] [566, 655] [181, 211] [0, 18] [242, 281] [99, 143]

[34, [21, [19, 109 295 [47, 174 [59, [28, 21

Flamborough Dundas Hamilton 403 West

j=1 j=2 j=3

DTS DTS DTS

[132, 149] [89, 106] [85, 96]

[123, 140] [83, 99] [76, 86]

318] 152]

237] 632] 201]

68] 37]

52]

37] 25] 21]

[200, [540, [172, 0 [274, [103,

0 0 0 0 0

k=3

[127, 146] [81, 99] [72, 84]

[176, 195] [103, 117] [86, 94]

[58, 64] [34, 39] [28, 31] [78, 88] [213, 236] [67, 75] [130, 143] [100, 116] [8, 62] [15, 17]

[236, 265] [638, 709] [19, 43] [0, 41] [301, 350] [143, 188]

1 0 0 0 0

k=4

Solutions for periods 1 to 5

Waste flow from municipalities to Dundas Transfer Station (DTS) (only non-zero flows are shown), ⊗(z1k) (tonnes week−1):

Flamborough Dundas Hamilton 403 West Downtown Hamilton East Hamilton West Mountain Hamilton East Mountain Hamilton Stoney Creek Ancaster Glanbrook

Waste flow from municipalities to Third Sector, ⊗(x3jk) (tonnes week−1):

Downtown Hamilton East Hamilton West Mountain Hamilton East Mountain Hamilton Stoney Creek Ancaster

Waste flow from municipalities to SWARU (only non-zero flows are shown), ⊗(x2jk) (tonnes week−1):

Landfill, ⊗(ak) Composter, ⊗(b1k) Composter, ⊗(b2k) Composter, ⊗(b3k) Third Sector, ⊗(ck)

Facility expansion/development scheme, ⊗(ak), ⊗(bmk), and ⊗(ck):

Name of district

TABLE 5 Solutions for the case when a single composting facility is located in Glanbrook

[227, 249] [120, 137] [93, 102]

[74, 81] [39, 45] [30, 33] [85, 96] [230, 256] [72, 81] [141, 155] [128, 149] [61, 80] [16, 19]

[256, 287] [692, 767] [0, 27] 0 [386, 447] [183, 241]

0 0 0 0 1

k=5

contd

Capacity planning for a waste management system 533

Facility

k=1

k=2

k=3

j=8 j=9 j=17

MTS MTS MTS

64 395, 424] [39, 49]

0 [293, 334] [34, 45]

DTS to Landfill, ⊗(y11k) MTS to Landfill, ⊗(y13k) DTS to SWARU, ⊗(y21k) MTS to SWARU, ⊗(y23k) 0 [497, 535] [305, 350] 0

0 [203, 253] [280, 324] 123

0 [145, 220] [279, 328] 132

[0, 3] [252, 313] [28, 40]

0 [624, 631] [363, 404] 0

185 396 [45, 53]

j=1 j=2 j=3

DTS′ DTS′ DTS′

29 25 24

50 34 31

69 44 39

[59, 64] [34, 39] [28, 31]

j=4, 5 j=6, 7 j=10 to 12

KTS′ KTS′ KTS′

[33, 37] [91, 101] [31, 36]

[52, 59] [142, 158] [52, 61]

[54, 61] [147, 164] [59, 68]

[79, 89] [213, 236] [100, 116]

West Mountain Hamilton East Mountain Hamilton Ancaster Glanbrook

j=8 j=9 j=13 to 16 j=17

MTS′ MTS′ MTS′ MTS′

58 112 [15, 19] 13

75 146 41 17

94 182 56 21

[68, 76] [132, 145] [48, 62] [15, 18]

Compostable waste flow from municipalities to the MTS compostable waste depot (only non-zero flows are shown), ⊗(wj3k) (tonnes week−1):

Downtown Hamilton East Hamilton Stoney Creek

Compostable waste flow from municipalities to the KTS compostable waste depot (only non-zero flows are shown), ⊗(wj2k) (tonnes week−1):

Flamborough Dundas Hamilton 403 West

Compostable waste flow from municipalities to the DTS compostable waste depot (only non-zero flows are shown), ⊗(wj1k) (tonnes week−1):

From From From From

Waste flow from transfer stations to facilities (only non-zero flows are shown), ⊗(yirk) (tonnes week−1):

West Mountain Hamilton East Mountain Hamilton Glanbrook

Waste flow from municipalities to Mountain Transfer Station (MTS) (only non-zero flows are shown), ⊗(zj3k) (tonnes week−1):

k=4

Solutions for periods 1 to 5

Waste flow from municipalities to Kenora Transfer Station (KTS), ⊗(zj2k): values from all districts were determined to be zero.

Name of district

District number

TABLE 5–contd

[73, 82] [143, 157] [61, 80] [16, 19]

[85, 95] [230, 256] [128, 149]

[75, 82] [40, 45] [31, 34]

256 [696, 748] [183, 231] 0

221 [429, 473] [49, 57]

k=5

Contd

534 G. H. Huang et al.

Facility

k=1

78 [155, 174] [198, 202]

System cost, ⊗(f) ($106 per 40 years):

SWARU Third Sector Composter [515.1, 699.1]

[425, 700] [28, 34] [34, 45]

Residues from SWARU, Third Sector, and Glanbrook Composter to the landfill (tonnes week−1):

DTS′ (r=1) KTS′ (r=2) MTS′ (r=3)

Compostable waste flow from transfer stations to Glanbrook Composter, ⊗(y4rk) (tonnes week−1):

Name of district

District number

TABLE 5–contd

[425, 700] [47, 56] [51, 67]

115 [246, 278] 279

k=2

[425, 700] [56, 67] [61, 80]

152 [260, 293] 353

k=3

[425, 700] [54, 70] [62, 88]

[121, 134] [392, 441] [263, 301]

k=4

Solutions for periods 1 to 5

425, 700] [61, 80] [71, 100]

[146, 161] [443, 500] [293, 338]

k=5

Capacity planning for a waste management system 535

536

G. H. Huang et al.

–1

Capacity (tonnes week )

Third Sector Glanbrook Composter 1,500

Landfill

1,000

500

Landfill

[80.9, 121.4] ha period 1

period 2

0 1990

2000

period 3

period 4

period 5

2010 2020 Time (year)

2030

Fig. 2. Facility expansion solutions for waste management facilities when a single composting facility is located in Glanbrook.

Municipal Collection

[1395, 1650]

[804, 888]

SWARU

[305, 350]

Transfer Stations (non-compostable)

[525, 569]

[425, 700]

Landfill

[431, 454] [2, 3] [28, 34]

[34, 45]

Blue Box [405, 429] Third Sector [431, 454] Transfer Stations (compostable)

Glanbrook Composter

Fig. 3. Optimal waste flow allocation pattern when the composting facility is located in Glanbrook (period 1). All values are expressed in tonnes week−1.

districts are close to the DTS and the “DTS→SWARU” routing avoids passing directly through the city of Hamilton. The majority of wastes collected from districts 9 and 17 should be first hauled to the MTS because of their close proximity to the transfer station. The distance from the MTS to SWARU is similar to that to the landfill, while the DTS has a much greater distance to the landfill than to SWARU. Therefore, it is more cost-effective to haul as much waste as possible from the DTS to SWARU, and deliver waste from the MTS to the landfill. No curbside collected waste should be delivered to KTS because, if the waste is to be disposed of in the landfill, it is more efficient to transport it via the MTS rather

Capacity planning for a waste management system

537

than the KTS since the KTS is located in northeast Hamilton and is distant from the landfill; on the other hand, if the waste is to be treated in SWARU, it is more convenient to directly transport it to SWARU which is directly adjacent to the KTS. Therefore, the KTS only accepts individual hauls of industrial/commercial wastes and residential wastes (minor), as well as residues from Third Sector. (b) Waste flow to Third Sector: Presently, about 23 000 tonnes year−1 (1992 data) of curbside by-product materials are recycled in the Region. In the period 1 solution, it is determined that districts 4 to 7 and 17 would have approximately 15–20% of their curbside wastes recycled, while the other districts would have somewhat lower recycling rates (approximately 10%). Districts 4 to 7 are in lower Hamilton, and have higher populations (thus lower collection costs due to economies of scale), and shorter haul distances to Third Sector (thus lower transportation costs). District 17 is Glanbrook, where both recyclable and non-recyclable curbside MSW are collected by Eggers Excavating in separate bins during a single collection trip. Thus, the associated collection and transportation costs are lower. Therefore, the Blue Box program could be promoted to a greater degree in these districts. For example, increased education programs could be conducted in these districts to increase the participation rates. Very low percentages of MSW in the transfer stations are recyclable (the recyclable flows from the transfer stations are less than 0.5% of the total amount of MSW recycled in the Region). Although there is presently a large bin at each transfer station for accepting recyclable wastes, few individuals respond. Typically, only about 50% of the wastes in the bins are recyclable, which leads to a low recycling rate and a high cost of collection and transportation for these materials from the transfer stations. (c) Waste flow to the Glanbrook Composter: The composting facility is assumed to be developed in Glanbrook at the start of period 1. According to the regional contractor’s design, the compostable wastes collected from the municipalities should first be delivered to the compostable waste depots in the Region’s three transfer stations, and then to the Glanbrook Composter by transfer trailer. The results indicate that all compostable MSW collected from districts 1 to 3 (78 tonnes week−1) should be delivered to the DTS compostable waste depot (DTS′), all compostable MSW from districts 4 to 7, and 10 to 12 ([155, 174] tonnes week−1) should go to the KTS compostable waste depot (KTS′), and all compostable MSW from districts 8, 9, and 13 to 17 ([198, 202] tonnes week−1) should go to the MTS compostable waste depot (MTS′), because of their close proximity to the relevant transfer stations. For each district individually, it is determined that districts 1 to 3, 8, 9, and 17 would have approximately 15–20% of their curbside wastes composted, while the other districts would have somewhat lower composting rates (approximately 10%). (d) Waste flow to the landfill: The residues from Third Sector, SWARU, and the Glanbrook Composter are [7, 8]% ([28, 34] tonnes week−1), [25, 35]% ([425, 700] tonnes week−1), and [8, 10]% ([34, 45] tonnes week−1) of their inputs, respectively. These residues are all hauled to the landfill. There are also [497, 535] tonnes week−1 of MSW flow from the MTS to the landfill. Thus, the total amount of curbside collected MSW (including residues) routed to the landfill is [984, 1314] tonnes week−1 ([51.2, 68.3]×103 tonnes year−1).

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(e) MSW from industrial and commercial sources: Based on 1992 data, the waste flow from industrial/commercial sources to the landfill is [32.8, 42.1]×103 tonnes year−1. These wastes are delivered to the landfill via the transfer stations, subject to a current tipping fee of $180 tonne−1. It is assumed that all industries and companies will deliver their wastes to a transfer station closest to the waste generation source. Therefore, the general distribution pattern of the industrial/commercial waste flow to the transfer stations will tend to remain constant. In 1992, the industrial/commercial wastes entering the DTS, KTS, and MTS were [15, 25], [75, 85], and [15, 25] tonnes day−1, respectively. (f) A comparison between the existing waste flow allocation and the period 1 solution: Compared with the existing waste flow allocation pattern, the major cause of the changes in the period 1 solution is the development of the Glanbrook Composter, which accepts compostable waste at a low operating cost, and thus may significantly reduce waste flows to other facilities. The major differences between the existing allocation and the optimized period 1 allocation are: (i) compostable MSW should be delivered to the transfer stations and then to the Glanbrook Composter in the optimized allocation; (ii) all NR/NC MSW collected from Ancaster (districts 13 to 16) and the majority of NR/NC MSW from West Mountain Hamilton (district 8) should be directly delivered to SWARU in the optimized allocation rather than to the DTS (districts 13 and 14) and MTS (districts 8, 15, and 16) in the existing allocation; (iii) all NR/NC MSW collected in district 3 (Hamilton 403 West) should be delivered to the DTS in the optimized allocation rather than to SWARU in the existing allocation; and (iv) all NR/NC MSW from the DTS should be hauled to SWARU in the optimized allocation, while a smaller fraction of the MSW from the DTS ([70, 100] tonnes week−1) is hauled to SWARU presently. (g) Waste flow allocation for periods 2 to 5: The major changes to the waste management conditions in periods 2 to 5 include: (i) waste generation continues to increase; (ii) the costs of waste management and facility expansion change with time; and (iii) the capacities of the waste management facilities change with time due to the facility developments/expansions and landfill capacity consumption. Therefore, the solutions for waste flow allocation patterns in the five periods are significantly different from each other (see Table 5 for detailed information). 5.1.3 System cost The system cost for the entire time horizon (40 years) under the optimal solution is C$[515.1, 699.1]×106 (in present value), with a total landfill utilization of [2.19, 2.93]×106 tonnes per 40 years. 5.2 Optimal solution when there are four options for the composting facility location 5.2.1 Facility expansion Table 6 and Fig. 4show the optimal facility expansion solutions for the landfill, Third Sector, and composting facilities obtained through the above GIP model when there are four options for the composting facility location (Glanbrook, Dundas, Ancaster, and Stoney Creek). It is indicated that a new landfill should be developed with a size of [200, 300] acres ([80.9, 121.4] hectares) at the start of period 4. The first composting

District number

0 0 0 0

m=1 m=2 m=3 m=1 m=2 m=3 m=1 m=2 m=3 m=1 m=2 m=3

Glanbrook Composter (i=5) Glanbrook Composter (i=5) Glanbrook Composter (i=5)

Dundas Composter (i=6) Dundas Composter (i=6) Dundas Composter (i=6)

Ancaster Composter (i=7) Ancaster Composter (i=7) Ancaster Composter (i=7)

Stoney Creek Composter (i=8) Stoney Creek Composter (i=8) Stoney Creek Composter (i=8)

0 0 1

0 0 0

0 0 0

0 0 0

0

0

k=2

Downtown Hamilton East Hamilton West Mountain Hamilton East Mountain Hamilton Stoney Creek Ancaster

j=4, 5 j=6, 7 j=8 j=9 j=10 to 12 j=13 to 16

SWARU SWARU SWARU SWARU SWARU SWARU

[268, 301] [726, 805] [60, 92] [0, 32] [245, 284] [102, 143]

[175, 217] [566, 655] [181, 211] [0 13] [242, 281] [99, 143]

Waste flow from municipalities to SWARU (only non-zero flows are shown), ⊗(x2jk) (tonnes week−1):

0 0 0

0 0 0

0 1 0

0

k=1

Third Sector (i=4)

Facility

Landfill (i=2)

Facility expansion/development scheme, ⊗(ak), ⊗(bimk), ⊗(ck):

Name of district

TABLE 6

[145, [540, [172, 0 [274, [103,

0 0 0

0 0 0

0 0 0

0 0 0

0

0

k=3

318] 152]

189] 632] 205]

[236, 265] [638, 709] [19, 43] [0, 41] [301, 350] [143, 188]

0 0 0

0 0 0

0 0 0

0 0 0

0

1

k=4

Solutions for periods 1 to 5

Solutions when there are four options for the composting facility location

[256, 287] [692, 767] [0, 11] 0 [386, 447] [183, 241

0 0 0

0 0 0

0 0 0

0 0 0

1

0

k=5

Contd

Capacity planning for a waste management system 539

−1

j=1 j=2 j=3 j=4, 5 j=6, 7 j=8 j=9 j=10 to 12 j=13 to 16 j=17

Third Third Third Third Third Third Third Third Third Third

[17, [12, [12, [34, [91, [28, [54, [31, [15, 13

19] 14] 13] 37] 101] 32] 60] 36] 19]

k=1

[30, [20, [18, 87 236 [45, 103 [52, [25, 17 61] 32]

51]

33] 23] 20]

k=2

[34, [21, [19, 109 295 [47, 174 [59, [28, 21 68] 37]

52]

37] 25] 21]

k=3

j=1 j=2 j=3

DTS DTS DTS

[126, 142] [89, 106] [85, 96]

[123, 140] [83, 99] [76, 86]

[127, 146] [81, 93] [72, 80]

j=8 j=9 j=17

MTS MTS MTS

142 [416, 435] [38, 49]

0 [334, 379] [33, 45]

From From From From

DTS to Landfill, ⊗(y11k) MTS to Landfill, ⊗(y13k) DTS to SWARU, ⊗(y21k) MTS to SWARU, ⊗(y23k)

0 [595, 625] [299, 343] 0

0 [208, 265] [280, 323] 157

Waste flow from transfer stations to facilities (only non-zero flows are shown), ⊗(yirk) (tonnes week−1):

West Mountain Hamilton East Mountain Hamilton Glanbrook

0 [90, 163] [279, 317] 187

0 [252, 313] [28, 40]

Waste flow from municipalities to Mountain Transfer Station (MTS) (only non-zero flows are shown), ⊗(zj3k) (tonnes week−1):

Waste flow from municipalities to Kenora Transfer Station (KTS), ⊗(zj2k): values from all districts were determined to be zero.

Flamborough Dundas Hamilton 403 West

0 [624, 631] [363, 404] 0

186 396 [45, 53]

[176, 194] [103, 117] [85, 94]

[58, 64] [34, 39] [28, 31] [78, 88] [213, 236] [67, 75] [130, 143] [100, 116] [48, 62] [15, 17]

k=4

Solutions for periods 1 to 5

Waste flow from municipalities to Dundas Transfer Station (DTS) (only non-zero flows are shown), ⊗(z1k) (tonnes week−1):

Flamborough Dundas Hamilton 403 West Downtown Hamilton East Hamilton West Mountain Hamilton East Mountain Hamilton Stoney Creek Ancaster Glanbrook

Sector Sector Sector Sector Sector Sector Sector Sector Sector Sector

Facility

Waste flow from municipalities to Third Sector, ⊗(x3jk) (tonnes week ):

Name of district

District number

TABLE 6–contd

153 [696, 764] [183, 247] 0

[221, 237] [429, 473] [49, 57]

[171, 200] [90, 113] [77, 89]

[74, 81] [39,45] [30, 33] [85, 96] [230, 256] [72, 81] [141, 155] [128, 149] [61, 80] [16, 19]

k=5

contd

540 G. H. Huang et al.

Facility

k=1

k=2

k=3 −1

k=4

Solutions for periods 1 to 5

j=1 j=2 j=3 j=4, 5 j=8 j=13 to 16

DTS′ DTS′ DTS′ DTS′ DTS′ DTS′

36 25 24 [33, 37] 58 29

[50, 51] [34, 35] [31, 32] 87 0 41

68 [44, 50] [39, 43] 109 0 56

[59, [34, [28, [79, 0 [48, 62]

65] 39] 31] 88]

j=6, 7 j=10 to 12

KTS′ KTS′

[91, 101] [31, 36]

[142, 157] [52, 60]

[147, 164] [60, 68]

[213, 236] [100, 116]

j=8 j=9 j=17

MTS′ MTS′ MTS′

0 91 13

75 146 17

Dundas Composter (i=5) Dundas Composter (i=5) Dundas Composter (i=5) Stoney Creek Composter (i=7) Stoney Creek Composter (i=7) Stoney Creek Composter (i=7)

[206, 209] [121, 137] 104 0 0 0

[425, 700] [21, 28] [34, 45] 0 [511.6, 694.9]

SWARU Third Sector Dundas Composter Stoney Creek Composter

System cost, ⊗(f) ($106 per 40 years):

Residues from SWARU, Third Sector, and composting facilities to the landfill (tonnes week−1):

DTS′ (r=1) KTS′ (r=2) MTS′ (r=3) DTS′ (r=1) KTS′ (r=2) MTS′ (r=3)

[425, 700] [44, 53] [34, 45] [20, 25]

245 [185, 211] 0 0 8 237

Compostable waste flow from transfer stations to composting facilities, ⊗yirk), i=5, 6, 7, 8 (tonnes week−1):

West Mountain Hamilton East Mountain Hamilton Glanbrook

[425, 700] [56, 67] [34, 47] [31, 39]

[317, 326] [113, 140] 0 0 92 297

94 182 21

153] 238]

286] 199]

[425, 700] [54, 70] [34, 49] [28, 39]

[248, [183, 0 0 [130, [215,

[68, 76] [132, 145] [15, 18]

Compostable waste flow from municipalities to the MTS compostable waste depot (only non-zero flows are shown), ⊗(wj3k) (tonnes week−1):

East Hamilton Stoney Creek

Compostable waste flow from municipalities to the KTS compostable waste depot (only non-zero flows are shown), ⊗(wj2k) (tonnes week−1):

Flamborough Dundas Hamilton 403 West Downtown Hamilton West Mountain Hamilton Ancaster

Compostable waste flow from municipalities to the DTS compostable waste depot (only non-zero flows are shown), ⊗(wj1k) (tonnes week ):

Name of district

District number

TABLE 6–contd

[425, 700] [61, 80] [34, 49] [44, 60]

[394, 423] [37, 62] 0 0 [321, 343] [232, 257]

[74, 82] [143, 157] [16, 19]

[230, 256] [128, 149]

131 69 47 [85, 95] 0 [61, 80]

k=5

Capacity planning for a waste management system 541

G. H. Huang et al. Third Sector Glanbrook Composter Stoney-Creek Composter

–1

Capacity (tonnes week )

542

1500

Landfill

1000

500 [80.9, 121.4] ha period 1

0 1990

period 2

2000

period 3

period 4

2010 2020 Time (year)

period 5

2030

Fig. 4. Facility expansion solutions for waste management facilities when there are four options for the composting facility location.

facility should be developed at a capacity of [430, 485] tonnes week−1 in Dundas at the start of period 1, and the second composting facility should be developed at a capacity of [550, 620] tonnes week−1 in Stoney Creek at the start of period 2. The Third Sector material recycling facility is determined to be expanded by a capacity of [810 900] tonnes week−1 at the start of period 5. Thus, the general facility expansion pattern for the four-option solution is similar to that from the solution when a single composting facility is located in Glanbrook (referred to here as the “single-option solution”), except for the development of the composting facilities. 5.2.2 Waste flow allocation The waste flow allocation solutions for periods 1 to 5 are also shown in Table 6. It is indicated that, generally, the waste flow allocation pattern for the four-option solution is similar to that for the single-option solution except for the waste flows to the composting facilities. In the following we will provide a detailed interpretation and analysis of the period 1 solutions, which are graphically presented in Fig. 5. The solutions for the other periods can be similarly interpreted based on the results in Table 6. (a) Non-recyclable/non-compostable waste flows to transfer stations, SWARU, and landfill: The solution for period 1 (Fig. 5) indicates that all NR/NC MSW collected from districts 1, 2, and 3 ([126, 142], [89, 106], and [85, 96] tonnes week−1, respectively) should be delivered to the DTS, and the majority of NR/NC MSW from districts 8, 9, and 17 (142, [416, 435], and [38, 49] tonnes week−1, respectively) should be hauled to the MTS, while no NR/NC MSW should go to the KTS. The wastes entering the MTS should then be delivered to the landfill, while those from the DTS should be transported to SWARU. All NR/NC MSW collected from districts 4 to 7 and 10 to 16 should be directly hauled to SWARU. The above waste flow allocation pattern is similar to that from the “single-option solution” because of the similar management conditions for NR/MC MSW.

Capacity planning for a waste management system Municipal Collection

[1401, 1657]

SWARU [299, 343]

[896, 970]

Transfer Stations (non-compostable)

543

[650, 698]

[425, 700]

Landfill

[431, 450] [1, 2] [21, 28]

Blue Box

[307, 344]

[34, 45] Third Sector

[431, 450] Transfer Stations (compostable)

0

Dundas Composter

0

Stoney-Creek Composter Fig. 5. Optimal waste flow allocation pattern when there are four options for the composting facility location (period 1). All values are expressed in tonnes week−1.

(b) Waste flow to Third Sector: The general recyclable material flow allocation pattern is similar to that from the single-option solution. The majority of the districts would have approximately 10% of their curbside waste recycled, except Glanbrook which would have a somewhat higher recycling rate. (c) Waste flow to Dundas Composter: The composting facility is determined to be developed in a rural part of Dundas at the start of period 1. The results indicate that all compostable MSW collected from districts 1 to 5, 8, and 13 to 16 ([206, 209] tonnes week−1) should be delivered to the DTS compostable waste depot (DTS′), all compostable MSW from districts 6, 7, and 10 to 12 ([121, 137] tonnes week−1) should go to the KTS compostable waste depot (KTS′), and all compostable MSW from districts 9 and 17 (104 tonnes week−1) should go to the MTS compostable waste depot (MTS′), because of their close proximity to the relevant transfer stations. For each district individually, it is determined that districts 1 to 3, 8, 9, and 13 to 17 should have approximately 15–20% of their curbside wastes composted, while the other districts should have somewhat lower composting rates (approximately 10%). (d) Waste flow to the landfill: The residues from Third Sector, SWARU, and the Dundas Composter are [7, 8]% ([21, 28] tonnes week−1, [25, 35]% ([425, 700] tonnes week−1), and [8, 10]% ([34, 45] tonnes week−1) of their inputs, respectively. These residues should all be hauled to the landfill. There are also [616, 653] tonnes week−1 of MSW flow from the MTS to the landfill. Thus, the total amount of curbside collected MSW (including residues) routed to the landfill is [1075, 1398] tonnes week−1 ([55.9, 72.7]×103 tonnes year−1). This pattern is similar to that from the single-option solution.

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(e) A comparison between the existing waste flow allocation and the period 1 solution: Compared with the existing waste flow allocation pattern, the major cause of the changes in the period 1 solution is the development of the Dundas Composter, which accepts compostable waste at a low operating cost, and thus may significantly reduce waste flows to other facilities. The major differences between the existing allocation and the optimized period 1 allocation are: (i) compostable MSW should go to the Dundas Composter in the optimized allocation; (ii) all NR/NC MSW collected in Ancaster (districts 13 to 16) and the majority of NR/NC MSW from West Mountain Hamilton (district 8) should be directly delivered to SWARU in the optimized allocation rather than to the DTS (districts 13 and 14) and MTS (districts 8, 15, and 16) in the existing allocation; (iii) all NR/NC MSW collected in district 3 (Hamilton 403 West) should be delivered to the DTS in the optimized allocation rather than to SWARU in the existing allocation; and (iv) all NR/NC MSW from the DTS should be hauled to SWARU in the optimized allocation, while a smaller fraction of the MSW from the DTS ([70, 100] tonnes week−1) is hauled to SWARU presently. (f) Waste flow allocation for periods 2 to 5: The solutions of waste flow allocation for periods 2 to 5 are significantly different from each other due to the development of the Stoney Creek Composter, and the variations in waste generation, available waste management capacities, and waste management costs over the time periods (see Table 6 for the detailed information). 5.2.3 System cost The system cost for the entire time horizon (40 years) under the optimal solution is C$[511.6, 694.9]×106 (which is C$[3.5, 4.2]×106 lower than that from the “singleoption solution”), with a total landfill utilization of [2.14, 2.88]×106 tonnes per 40 years (which is 0.05×106 tonnes per 40 years lower than that from the “single-option solution”). The results indicate that the “four-option solution” provides a better choice for the composting facility location by incorporating different location options within the GIP model as binary variables. However, the savings are lower than the system cost range by two orders of magnitude. This is due to the following facts: (i) transportation cost is part of total costs for MSW management (the others include capital and operating costs for MSW treatment/disposal/recycling facilities); (ii) even for transportation itself, the cost for waste/residue flows to/from the composting facilities is part of the total transportation cost for the system (the others include costs for waste/ residue flows to (and/or from) landfill, incinerator, recycling facilities, and transfer stations); and (iii) the differences between the two solutions are only related to some of the routes connected to the composting facilities. Generally, developing the composting facilities at the Dundas and Stoney Creek locations may be preferable to developing and expanding the Glanbrook Composter in terms of not only system cost but also landfill capacity consumption, although the differences in general percentage terms are not large. 5.3 Discussion The single-option solution provides an optimal alternative for facility expansion and relevant waste flow allocation when Glanbrook is considered to be the preferred composting facility location, as designed by Laidlaw Technologies Inc. (1992). However,

Capacity planning for a waste management system

545

if the consideration of other potential locations is allowed, the four-option solution may provide preferable options with both lower system cost and lower landfill capacity consumption. The major differences between the single-option and four-option solutions include: (i) the compostable waste flow allocation patterns are significantly different between the two solutions due to the different facility locations; (ii) more curbside collected wastes are determined to be composted in the four-option solution, because the two composting facility locations (Dundas and Stoney Creek) lead to lower transportation costs for the compostable waste flows and thus increased utilization of the composting facilities; and (iii) waste flows to Third Sector and the landfill are decreased in the fouroption solution due to the increased flows to the composting facilities. The uncertain input information did not cause variation in the solutions for the facility capacity binary variables for this case study (i.e. the output binary variables had the same value for both the lower and upper bounds). For the interpretation of grey solutions for the continuous flow allocation variables, it is indicated that lower flows to the landfill, SWARU, Third Sector, and the composting facilities are determined under the scheme for the lower bound cost [⊗(f)] than for the upper bound cost [⊗(f)]. The scheme for [⊗(f)] represents a set of decision options under the most advantageous system conditions, while that for [⊗(f)] represents a set of decision options under the most demanding system conditions. For system implementation, the decision variable values can be adjusted/shifted within their solution intervals to generate decision alternatives according to specific system objectives and conditions. 6. Conclusion In this paper, a grey integer programming (GIP) model for the capacity planning of a MSW management system has been formulated and applied to a North American case study regional municipality. The GIP approach has an advantage in that uncertain information (presented as grey interval numbers) can be effectively communicated into the optimization processes and resulting solutions, such that feasible decision alternatives can be generated through the interpretation and analysis of the grey solutions according to projected applicable system conditions. The results for the Regional Municipality of Hamilton–Wentworth, Ontario, Canada, indicate that reasonable solutions have been generated through the use of the GIP solution approach. This study is potentially useful for MSW decision-makers in the RHMW for long-term planning of the Region’s waste management activities and for formulating related local policies/regulations regarding waste generation and management. Waste management professionals in other municipalities may potentially consider the use of this type of systems modelling approach to generate facility capacity options for the long-range planning of their own municipal solid waste management systems. Acknowledgement This research has been supported by the Natural Sciences and Engineering Research Council of Canada. References Baetz, B. W. (1988) Capacity Planning for Production Facilities and Alternative Facilities with Consumable Capacity: Application to Waste Management Systems. Ph.D. Dissertaton, Duke University, U.S.A.

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