Solid Waste Management System Analysis by Multiobjective Mixed Integer Programming Model

Journal of Environmental Management (1996) 48, 17–43

Solid Waste Management System Analysis by Multiobjective Mixed Integer Programming Model Ni-Bin Chang and S. F. Wang Department of Environmental Engineering, National Cheng-Kung University, Tainan, Taiwan, R.O.C. Received 24 June 1995; accepted 17 October 1995

The conflict between economic optimization and environmental protection has received wide attention in recent research programs for solid waste management system planning. The purpose of this analysis is to apply multiobjective mixed integer programming techniques for reasoning the potential conflict between environmental and economic goals and for evaluating sustainable strategies for waste management in a metropolitan region. The information incorporated into the optimization objectives include economic impacts, characterized by operational income and cost for waste management, air quality impacts from discharges of target pollutants due to waste incineration, noise impacts from various types of facilities operation, and traffic flow increments by garbage truck fleets. The constraint set thereby consists of mass balance, capacity limitation, operation, financial and related environmental quality constraints. Optimal strategies obtained from such an analytical scheme may provide a set of total solutions for long-term waste stream allocation, siting, resource recovery and tipping fees evaluation. The case study in the city of Kaohsiung in Taiwan is included as a demonstration.  1996 Academic Press Limited

Keywords: solid waste management, system analysis, multiobjective programming, Taiwan.

1. Introduction Economic optimization for the system planning of solid waste management was first applied in the late sixties in California, U.S.A. (Anderson, 1968). Until the earlier eighties, the issue of increasing environmental concerns and the emphasis on material recycling have gradually changed the focus of solid waste management. Recent research programs into solid waste management system planning frequently emphasize that both socioeconomic and environmental considerations have to be evaluated simultaneously to provide a set of total solutions regarding waste recycling, facilities siting and systems operation. Various deterministic mathematical programming models have been applied for 17 0301–4797/96/090017+27 $18.00/0

 1996 Academic Press Limited

18

Solid waste management analysis

planning solid waste management systems. The spectrum of those deterministic modelling techniques include linear programming (LP), mixed integer programming (MIP), dynamic programming (DP) and multiobjective programming. For example, Hsieh and Ho (1993) and Lund and Tchobanoglous (1994) discussed the optimization of solid waste disposal and recycling systems by linear programming techniques. But location/ allocation models, by using mixed integer programming (MIP) techniques, mostly have been used in such applications. The MIP models applied for economic optimization of solid waste management systems includes Marks et al. (1970), Fuertes et al. (1974), Helms and Clark (1974), Walker and Schur (1974), Ku¨hner and Harrington (1975), Hasit and Warner (1981), Jenkins (1982), Gottinger (1986), Kirca and Erkip (1988) and Zhu and ReVelle (1990). The efforts in combining the environmental impacts, such as air pollution, leachate impacts, noise control and traffic congestion, into a location/ allocation model were established by Chang et al. (1993, 1994, 1995, 1996) in a single objective programming framework. In addition, Perlack and Willis (1985) presented the analysis of multiobjective decision-making in waste disposal planning. This paper represents the continuing effort of Chang et al.’s (1993, 1994, 1995, 1996) study. It specifically illustrates an extension work of multicriteria decision-making, based on the dynamic impacts of noise control, traffic congestion, air pollution and material recycling within a long-term planning framework during the siting of landfills, incinerators and transfer stations in a growing metropolitan region. Interactions among the effects of waste generation, source reduction, recycling, collection, transfer, processing and disposal are emphasized in a multiobjective mixed integer programming model. Compromise programming techniques are selected in search of the satisfactory solution. The practical implementation is assessed by the case study of the Kaohsiung solid waste management system in Taiwan. It shows that the incorporation of these environmental factors as part of the decision-making objectives does alter the pattern of waste allocation within metropolitan solid waste management systems, but reasoning the potential conflict between environmental and economic goals is feasible in the long term. 2. Model formulation Four objectives: economics, noise control, air pollution control and traffic congestion limitation, are considered in this analytical framework. Major variables are defined in the Appendix. The objective function for cost minimization is formulated for calculating the discounted cash flow of all quantifiable system benefits and costs over time. Discounted factors are equivalent to such an economic adjustment and provide the net system value for decision-making. Hence, the real discounted factor is defined simultaneously by the inflation rate (f) and the nominal interest rate (r), which is denoted as bt (=[(1+f)/(1+r)]t−1). The expression of the objective function is: T

Minimize

] b (C −B ) t

t

t=1

The cost components (Ct) consist of: total transportation cost=

]

(j,k)vI,jrk

[CTjktSjkt]

t

N.-B. Chang and S. F. Wang

19

]

total construction cost=

[CCktDCkt+FktYkt]

kv(J\J1)

total operating cost=

]

[COkt

]

[CEktTEXPkt]

kv(J\J1jK\K1)

total expansion cost=

]S

]

jkt

(j,k)vI1

kv(J\J1jK\K1)

] TR CR

total recycling cost=

it

it

ivR

The only two benefit components (Bt) considered here are: total resource recovery income at the facilities= ±

] ] ] [P

TiktSjkt]

ikt

ivR kv(MjK4jJ4) (j,k)vI1

total household recycling income= ±

] ] [IR a G ] ijt ijt

it

iv(J1jK1) jvR

In the expression, set subtraction is represented by the notation of a backslash (\). The total transportation costs are expressed as linearly proportional to unit waste loading. As usual, a fixed charge structure is employed in the formulation of total construction cost for the purpose of site selection. The average operating cost is assumed to be a constant. The facilities expansion cost does not have a fixed charge term, and only the variable cost is included. The possible recoverable resources (i.e. material and energy) consist of paper, glass, metal, plastics, steam and electricity. However, these secondary materials could be picked up directly at households or other places rather than in those treatment plants. Thus, a separate term, corresponding to the income from household recycling, is formulated. Since recyclables may not always have economic value in the secondary material market, the plus/minus sign is therefore used in these benefit expressions. The second objective to be maximized is the degree of traffic service at the main entrance road of each treatment or disposal facility. The degree of traffic congestion is conventionally classified as six different levels, each corresponding to a condition of the traffic flowrate relative to the original designed flowrate. The allowable traffic flow is thus equal to the multiplication of the selected service level and the designed flowrate at the main entrance road of each site (Cjkt). Vjkt is the average value of background traffic flowrate before the inclusion of the garbage truck fleet. The unit used to express Cjkt and Vjkt is the passenger car unit (PCU). Hence, the traffic impacts created by the operation of solid waste treatment can be expressed by converting the garbage truck fleet into a consistent unit (i.e. PCU) through the use of a conversion factor, CU, associated with the number of standard garbage trucks needed (i.e. Sjkt÷Pl).

20

Solid waste management analysis T

] ]

CU

tvT′ kv(J\J1jK\K1)

A

B

T

]

Sjkt÷Pl +Vjkt

jv(J1jK1),lvL

The third objective included is the minimization of noise impacts around each treatment facility. The major sources of noise in a typical solid waste management system include simple sources of noise (from treatment and disposal facilities) and line sources of noise (increased traffic flow caused by the garbage trucks). The former can be properly controlled by engineering technology, but the latter has to be regulated in the optimization process. Although the level of noise, its characteristics and the criteria used to assess noise impact differ from one environment to another, the method of doing so is similar (Johnson and Saunders, 1968; Jones, 1976; Jacobs et al., 1980; Ohta et al., 1980, 1987; Sannders et al., 1983; Jung and Blaney, 1988). In general, the Equivalent Noise Level (Leq) is the most prevalent approach used for the evaluation of traffic noise impacts. In Taiwan, the degree of noise control in a metropolitan region is classified at four different levels, and the unit used for the description of noise level is dBA. A semi-empirical regression model for noise impact assessment is independently developed by the authors, as illustrated below: NL=c1+c2 ln F−D and F=CU

C

]

D

Sjkt÷Pl +Vjkt

jv(J1jK1),lvL

in which F is the noise impact created by the garbage truck fleet at the main entrance road of each treatment or disposal facility. c1 and c2 are regression coefficients. D is the spatial decay constant, an empirical number based on the local situation. The aggregate noise levels, measured at the most affected community neighboring the facility site, can then be estimated and compared with the acceptable noise level required by environmental regulations. Temporal variations of noise are considered and evaluated through the integration of noise impacts from those additional sources of waste shipping. Therefore, the objective function is: Minimize

] ]

kv(J\J1jK\K1) tvT′

G

C A

]

c1k+c2k ln CU

B DH

Sjkt+Pl +Vjkt

jv(J1jK1),lvL

The fourth objective considered is the minimization of air pollution impacts. In Taiwan, air pollution control for municipal incinerators is regulated under the “Air Pollutants Emission Standards for Waste Incineration” and “National Ambient Air Quality Standards”. While the maximum allowable emission rates of criteria pollutants discharged from incinerators are limited by the former, the maximum concentrations (ppm or lg/m3) of certain pollutants in the surrounding environment are controlled by the latter. The objective function is described as below: Minimize

A

] ]] ] S

kv(K3jJ3) pvP tvT′

(j,k)vI1

B

FGR ENpAkbp

jkt

N.-B. Chang and S. F. Wang

21

in which Akbp is the transport and transformation factor that is dependent on the stability, wind speed, distance between emitter and receptor, effective stack height, diffusion coefficient in air, and half-life and decay rate of pollutant p (Wang et al., 1979; Jakeman and Simpson, 1985; Chang et al., 1995a). FGR is the flue gas production ratio, based on burning one ton of solid waste in the incinerator. ENp is the emission factor corresponding to the criteria pollutant p in the flue gas. The multiplication of FGR, ENp and Akbp ensures that the larger the amount of solid waste handled at an incineration site, the greater the amount of air pollution in a designated air quality control region. Such a formulation may yield maximum ground-level ambient concentrations at a set of receptors surrounding the municipal incinerators for air pollution assessment. To determine the value of Akbp, the long-term diffusion equation for a decay pollutant (non-conservative pollutant) at ground level and at the centerline of the plume may be defined (Jakeman and Simpson, 1982):

Cp(x)=

AB 2 p

0·5

A B

q −H2e EXP EXP(−kpt)=q Akbp 2prZux 2r2Z

in which: Cp(x)=aggregate ambient air pollutant concentration of pollutant p at the downstream location x (lg/m3 or ppm); u=the average wind speed (m/sec); He=the effective height of plume release corresponding to the wind speed u (m); kp=first-order reaction rate of pollutant p (=0 if the pollutant is conserved) per second; t=reaction time (sec); q=emission rate of a particular air pollutant from the stack of incinerators (g/ sec); rZ=vertical diffusion coefficient (m). The basic and environmental constraints are discussed sequentially, as follows: (1) Mass balance constraint: (a) Point source: all solid waste generated in the collection district should be shipped to other treatment or disposal components. Furthermore, waste reduction by household recycling can be taken into account in terms of the participation rate of residents, the recyclable ratio and the composition of waste. Recycling potential must be evaluated in advance, and the impact on system operations can be shown by including the following constraints.

]

Sikt=Git(1−ait) !iv(J1jK1), !tvT′

kv(J\J1jK\K1)

]a

ait=

ijt

!iv(J1jK1), !tvT′

jvR

0≤aijt≤aijt,max

!iv(J1jK1), !jvR, !tvT′

22

Solid waste management analysis

]

TRit=

Gitait

!tvT′

iv(J1jK1)

(b) System facility: for any system component, the rate of incoming waste must equal the rate of outgoing waste plus the amount deducted in the treatment process.

]S

(1−Rk)=

jkt

(j,k)vI1

]S

kjt

!kvM, !tvT′

(k,j)vI2

(2) Capacity limitation constraint: the treatment capacity planned during the procedure of construction and expansion should be less than, or equal to, the maximum allowable capacity and greater than, or equal to, the minimum capacity at one site. (a) New facilities (landfills and transfer stations): in the following expression, the binary integer variable is combined with the upper or lower bound of capacity such that the site selection can be performed by the binary choice of its value “one or zero”, which corresponds to the “inclusion or exclusion” of design capacities in the constraint and related cost/benefit terms in the objective function. The period of facility initialization is denoted by the symbol “y” that can avoid distortion of the later expansion schedule. T

]

T

]Y

DCky≥MINk

y=1

!kv(J2jJ4)

ky

y=1

T

DCky+

]

NEXPkyt≤MAXkYky !kv(J2jJ4), !yv(1, T−1)

t=y+1

t

] NEXP

=TEXPkt

!kv(J2jJ4), !tvT′

kyt

y=2

(b) New facilities (incinerators): the numbers of treatment trains and associated size per combustor in a municipal incinerator should be differentiated in the planning process. Otherwise, the planned size might not be consistent with the industrial specification and therefore not suitable for subsequent engineering design. Hence, the summation of the values of all binary variables Zkiy represents the number of combustors being initialized at a specific incinerator site in the time period y. Therefore, Ekyit stands for the choice of expansion in the time period t at an incinerator site, which has been initialized in the time period y. T

]

T

N1

]]Z

DCky=MCk×

y=1

T

DCky+

kiy

!kvJ3

y=1 i=1

N2

] ] MC ×E k

t=y+1 i=1

≤MAXk×Yky !kvJ3, !yv(1, T−1)

kiyt

N.-B. Chang and S. F. Wang

t

23

N2

] ] MC ×E k

=TEXPkt

!kvJ3, !tvT′

kyit

y=2 i=1

N1

]Z

≥Yky

!kvJ3, !yv(1, T−1)

kiy

i=1

(c) Old facility: T

] TEXP ≤MAX

DCk+

kt

k

!kv(K\K1)

t=1

(3) Operating constraint: the accumulated waste inflow at each site should be less than, or equal to, the available capacity in each planning period. (a) New facility:

C] A t′

TIME

BD

t′

DCky+

y=1

]

NEXPkyt ≥

t=y+1

]S

jkt

!kv(J\J1), !t′vT′

(j,k)vI1

(b) Old facility:

A

TIME DCk+

B

t′

] TEXP

kt

t=1

≥

]S

jkt′

!kv(K\K1), !t′vT′

(j,k)vI1

(4) Conditionality constraint: the conditional constraint ensures that the initialization of a new site in a system can occur only once in a multistage planning project. T

] Y ≤1 kt

!kv(J2jJ3jJ4)

t=1

(5) Site availability constraint: this constraint can also allow the planner to leave out some of the potential sites. T

] Y ≤N kt

t

!tvT′

y=1

(6) Financial constraint: the key point in the formulation is the use of an inequality, rather than equality, constraint. If the equality constraint holds, the solution will show that there will never be profits in operating these facilities in each period, and the accumulated income will be used up through the building of extra treatment capacity which is of no use in that period.

24

Solid waste management analysis

C] D

Ct≤Bt+TIPt

Git

!tvT′

iv(K1jJ1)

(7) Traffic congestion constraint: SLjkt represents the selected service level of traffic flow at each facility site. The allowable traffic flow is thus equal to the multiplication of the selected service level and the designed flowrate at the main entrance road of each site (Cjkt), as shown on the right-hand side of the constraint below. Vjkt is the average value of background traffic flowrate before the inclusion of the garbage truck stream. CU

C

]

D

Sjkjt÷Pl +Vjkt≤SLjktCjkt !jv(J\J1jK\K1), !tvT′

iv(J1jK1),lvL

(8) Noise control constraint:

G C

]

c1+c2 ln CU

D H

Sjkt÷Pl +Vjkt −Dk≤NLk !k, !tvT′

jv(J1jK1),lvL

(9) Air pollution control constraint: this analysis considers ambient air quality limitations for several pollutants at a set of prespecified sensitive areas in Kaohsiung City. The constraints formulation are described as below: f′

C]

] (S

D

FGR ENpAkbp) ≤Spt−Bbpt !b, !pvP, !tvT′

jkt

kv(K3jJ3) (j,k)vI1

f′ is a conversion factor regarding the time scale difference between the units of emission factor (ENp) and National Ambient Air Quality Standard (Spt). The variable Bbpt in the right-hand side of the constraint serves as an input variable to show the background concentration of air pollutant “p” at the location of a specific receptor “b” at time t. 3. Solution techniques In this analysis, the non-inferior solutions and trade-offs among the objectives are accordingly examined for several alternative planning scenarios using the distancebased compromise programming method (Zeleny, 1974, 1976). Due to the use of incommensurable formats and units in those objectives, rescaling is needed before the optimization analysis is performed so that their values are all confined to a given range, such as [0, 1]. Several scaling functions described in the literature can be applied. The recommended scaling function in this analysis is: Zk∗(x)−Zk(x) Zk∗

Z=

in which Zk∗ is the extreme value of each individual objective which can be obtained from the payoff table. This study assumes that both the objective and constraint functions are linear, and that the decision variables x are all non-negative. Linearization

N.-B. Chang and S. F. Wang

25

techniques may be applied if non-linear forms are encountered. Hence, the compromise programming problem is equivalent to solving the following dimensionless objective function (i.e. a distance-based function) which is the relative measure of a decisionmaker’s preference from the ideal solution point of view. If there are q objective functions in a multiobjective programming model, the distance-based formulation can be expressed as:

G] A q

Min da=Min

pak

k=1

Zk∗−Zk(x) Zk∗

BH

1/a

a

subject to: g(x)(≥, =, ≤)0 x≥0 where a is the distance parameter and 1≤a≤∞, pak>0 and Rqk=1 pak=1. The parameter pak is the corresponding weight of each objective. In general, the compromise programming algorithm couples three conditions as below: (i) For a=1, the objective function is defined as the Manhattan distance, and the problem becomes a linear programming as: q

Min d1=Max

] p Z (x) a k

k

k=1

subject to: g(x)(≥, =, ≤)0 x≥0 (ii) For 1
26

Solid waste management analysis

Taiwan Strait Taipei City

Taiwan Pacific Shichipul landfills Ocean Kaohsiung City Nnatzu Nnatzu resource recovery plant

Tsoying

Tsoying transfer station

Fudingjin resource recovery plant Kushan

Sanming west

Sanming east

Chienchin Hsinhsing

Yencheng

Linya

Chienchen transfer station Chichin

Chienchen Tapindin landfill

Talinpu Hsiaokang Legend resource Sources of waste generation recovery plant Existing treatment facilities Proposed sites of resource recovery plants Proposed site of sanitary landfill Proposed sites of transfer stations Figure 1. The geographical location of the solid waste management system in Kaohsiung.

is to apply compromise planning techniques if the environmental considerations are temporarily excluded, and the weight of each objective is assumed to be equally important in decision-making. The incorporation of those environmental protection objectives and environmental quality control constraints are then considered and the model is solved again using the compromise programming algorithm. Final comparison may be placed upon the differences of planning scenarios between the applications of a single objective and multiple objective scenarios in dealing with such a complex solid waste management planning issue. 4. Case study Kaohsiung City, located beside Kaohsiung harbor, is the largest city in the southern part of Taiwan. The geographical location of this system is shown in Figure 1. Twelve

N.-B. Chang and S. F. Wang

27

garbage collection teams are in charge of the clean up work in the eleven administrative districts. Only the Sanming district owns two collection teams, and the service area is separated by east and west divisions. The only existing landfill is in the Shichinpu landfill, located at the northern boundary of Kaohsiung. In addition, there is an existing transfer station in the Chichin district, which is a separate island on the other side of Kaohsiung harbor. The transportation to Chichin mainly relies on an underground tunnel across the bottom of the harbor connecting with the downtown area of Kaohsiung City. Three candidate sites—Fuhdingjin, Nantzu and Talinpu are planned for future resource recovery plants. Two proposed sites of transfer stations (Tsoying and Chienchen) and one new landfill (Tapindin) were selected in the preliminary screening procedure. But uncertainties still exist in the procurement of the landfill space and the agreement of local residents. The Shichinpu landfill is expected to be closed in 1995, but it has to be expanded in the near future due to the lack of other treatment alternatives in the current solid waste management system. Several key questions frequently bother the public officials, which include: (a) is it necessary to build two new transfer stations? (b) Are the construction schedule and planned capacity reasonable to meet the growing demand of waste treatment? (c) What is the impact of material recycling on the entire management system? and (d) What is the long-term optimal waste management pattern once the environmental quality considerations are included in the next twenty years? These questions can be analysed using this multiobjective programming model. In this analysis, a hypothetical 20-year project with four time periods is conducted. The start-up year was 1995, when the system had only one landfill and one transfer station. The Shichinpu landfill is expected to be expanded and continuously used until the year 2005 (i.e. the end of the second time period). The start-up date of operation of the Tapindin landfill is assumed to be at the beginning of the second time period. The Chichin transfer station, which only serves the Chichin district, is regarded as a point source. Construction or expansion of any facility is to be completed within the previous time period. If a facility is to be used in time period t, then it must be constructed in time period t−1 or before. Hence, the use of any facility in the dynamic optimization process represents the start-up date of its operation, whenever investments are incurred. Therefore, the potential sites of transfer stations and incinerators can be included into the system operation after the beginning of the second time period. The candidate sites for transfer stations are prepared for shipping raw garbage only. Many physical, economic and environmental data for solid waste management have to be compiled to build up the objective functions and constraints. Various investigations for supporting submodels in environmental quality constraints should be conducted before the optimization procedure is performed. The economic database is collected mostly from government agencies. The final selections of each parameter value should be reviewed by many disciplines. After such a series of investigations, an independent regression analysis for the determination of the fixed and variable costs in the construction cost functions is applied, based on a local database of landfills and incinerators. Since there were no formal transfer stations in Taiwan, U.S. data were used after a careful calibration (Booz-Allen and Hamilton Inc., 1976). Facility expansion costs are assumed to be the same as the variable costs in these construction cost functions. In addition, the prices of electricity and secondary materials, the interest rate and inflation rate, operating cost of the treatment and disposal facilities and the transportation cost were investigated separately and/or estimated. The waste reduction ratio and the conversion efficiency of

28

Solid waste management analysis

T 1. Planning scenarios for optimization analysis

Cost minimization objective Traffic congestion objective Noise impact objective Air quality objective Distance parameter, a Environmental constraints Basic constraints

Base

Case 1

V∗ — — — — — V

V — — — — V V

Case 2 V(1)∗∗ V(1) V(1) V(1) 1 V V

Case 3

Case 4

Case 5

V(1) V(1/3) V(1/3) V(1/3) 1 V V

V(1) V(1) V(1) V(1) infinity V V

V(1) V(1/3) V(1/3) V(1/3) infinity V V

∗: V represents the inclusion of an evaluation option. ∗∗: The number in the parentheses indicates the weight assigned to the objective.

energy recovery of the incineration process were selected according to several engineering reports. According to the 5-year record of the physical composition of solid waste in Kaohsiung City, possible and maximum recycling conditions of paper, plastics, metal and glass can be determined. The historical records of solid waste generation were collected and waste generation rates were forecast by a regression model. The maximum and minimum capacities of those treatment and disposal sites were decided corresponding to the land availability and technological information. The classification of traffic services of different types of roads in Taiwan was investigated and level C was chosen as the required service level in this analysis. Background traffic flow at the entrance to each site and related noise impacts were measured and summarized. The growth rates of background traffic flow over time can be assumed to occur at the same speed as the estimated economic growth rate. The results can be used directly in traffic congestion and noise impacts control constraints. Background information on air pollutants and related meteorological conditions at each designated site were obtained from several environmental impact assessment reports.

5. Optimization results and discussion The planning scenarios of the optimization analysis are arranged in Table 1, in which the base case represents the situation from which considerations of environmental protection are temporarily excluded to form a single objective programming model. Case 1 illustrates the impact caused by the inclusion of environmental quality constraints. Cases 2–5 perform the programming analysis. Case 2 specifically illustrates the effect of the inclusion of both environmental quality objectives and constraints under the conditions of distance parameter a=1, and the weight distribution is uniform for these four objectives. Case 3 indicates the outcome if the weight between environmental objectives and economic objective is equally important in decision-making. Cases 4–5 present a similar analytical framework except the distance parameter a is replaced by infinity. The numbers in parentheses in Table 1 represent the weight assigned to each objective in each case.

N.-B. Chang and S. F. Wang

29

T 2. Payoff table of the multiobjective programming model

f1 f2 f3 f4

Cost objective f1

Traffic objective f2

Noise objective f3

Air objective f4

38 876∗ 629 108∗∗ 620 236 562 894

1·15∗∗ 0·4523∗ 0·47 0·61

31·36∗∗ 11·32 4·80∗ 10·17

820·89∗∗ 389·43 26·27 14·75∗

∗: Represents the lower bound of the objective. ∗∗: Represents the upper bound of the objective.

A payoff table, Table 2, allows one to build up the analytical scheme of compromise programming. The LINDO software package is employed as a computer solver. Hence, optimization results, as shown in Table 3, unambiguously indicate that the inclusion of environmental quality objectives would reduce the number of new waste incineration projects and increase the need for recycling. Even though the weight of the environmental quality objectives is reduced in the non-compensatory condition in case 5, reducing the capacity of new incinerators is still favored. It is worth while to point out that both proposed sites for the transfer station are excluded in the multiobjective framework although they are included in the optimal solution in the base case and case 1. This is due to the consideration of noise and traffic impacts at these two potential sites that cannot be tolerated under current environmental regulations. In cases 2, 4 and 5, the order of magnitude of the objective function values are more than ten times higher than those in the other cases. This phenomenon reveals that the cost caused by the emphasis on environmental quality objectives is very high. Once the waste stream is directed mainly to the landfill, due to environmental considerations, tipping fees may increase dramatically compared to the outcomes in the base case and case 1. The recycling level reaches a maximum in case 4 due to the higher aggregate weights assigned to those environmental quality objectives. Figures 2–7 show the waste stream allocation pattern in each case based on the optimization analytical framework. 6. Cost/benefit analysis Cost and benefit distributions are major concerns in systems analysis. Table 4 therefore expresses the detailed cost and benefit information for each case. It obviously shows that the costs of waste recycling and transportation are the major expenditures in this multiobjective analytical scheme. If there is no recycling cost, transportation costs exceed 70% of the total expenditure. To clearly understand the cost/benefit distribution, Figures 8 and 9 delineate the comparative structure of cost and benefit distributions for each case. However, the most difficult estimation in such a large-scale solid waste management system is the cost avoided by waste recycling. This study is perhaps the first that applies optimization techniques to present the indirect benefit (avoided cost) of recycling in the solid waste management systems. Case 3 is thus selected for the purpose of demonstration. Based on the analytical framework in case 3, a simulated run is initialized to compare objective function values with and without the effect of waste recycling constraints. The net benefit of waste recycling is thus equal to the difference between these two objective function values. The avoided cost can then be

Design capacity (TPD)

Initialization period

New transfer station included

Expansion capacity of Nantzu plant (TPD) Period 3 Period 4 Expansion capacity of Fudingjin plant (TPD) Period 3 Period 4 Expansion capacity of Talinpu plant (TPD) Period 3 Period 4

Design capacity (TPD)

Initialization period

Objective function value (1993 millions NT$) New incinerator sites included

0 0

1∗450 0

Tsoying Chienchin 2 2 1052 103

0 0

0 0

Tsoying Chienchin 2 2 534 1376

0 0

38 876 Nantzu Fudingjin Talinpu 2 2 2 3∗450 2∗450 1∗450

Case 1

0 0

26 785 Nantzu Fudingjin Talinpu 2 2 2 2∗450 2∗450 4∗450

Base

—

—

—

—

0 0

—

1∗450

4

438 570 Fudingjin

Case 2

T 3. Optimization results in system analysis

—

—

—

—

1∗450 0

0 1∗450

2∗450 1∗450

3 2

85 240 Nantzu Fudingjin

Case 3

—

—

—

—

0 0

1∗450 0

1∗450 1∗450

3 2

233 516 Nantzu Fudingjin

Case 4

—

—

—

0 0

1∗450 0

0 1∗450

128 756 Nantzu Fudingjin Talinpu 3 2 3 1∗450 1∗450 1∗450

Case 5

30 Solid waste management analysis

Expansion capacity of Tsoying station (TPD) Period 3 Period 4 Expansion capacity of Chienchin station (TPD) Period 3 Period 4 New landfill included Initialization period Design capacity (TPD) Expansion capacity (TPD) Period 3 Period 4 Tipping fee (NT$/ton) Period 1 Period 2 Period 3 Period 4 Recycling (TPD) Period 1 Period 2 Period 3 Period 4 0 0 0 0 Tapindin 2 1466 766 766 2328 2617 633 836 0 0 0 0

47 0 124 191 Tapindin 2 153 245 710 2328 2406 0 97 0 0 0 0

0 220 986 1615

2328 7225 20 356 17 213 0 0 0 306

2328 2209 1366 5475

25 0

Tapindin 2 2974

Tapindin 2 2798 102 100

—

—

—

—

0 10 199 1107

2328 2468 4761 18 557

0 0

Tapindin 2 3000

—

—

0 0 199 427

2328 2209 5006 7440

0 0

Tapindin 2 3000

—

—

N.-B. Chang and S. F. Wang 31

32

Solid waste management analysis

1 Nnatzu 2 Tsoying 3 Kushan 4 Sanming east 76.60(II)

5 Sanming west 251.08(II) 317.32(III) 383.08(IV)

6 Yencheng 1

7 Chienchin

534.94(II) 582.67(III) 516.92(IV)

90.00(III) 90.00(IV)

Tapindin 2

8 Hsinhsing 9 Linya

90.00(II)

326.98(II) 413.18(III) 499.38(IV)

10 Chienchen 11 Chichin 12 Hsiaokang

207.96(II) 169.49(III) 26.43(III) 17.54(IV)

3

5

58.19(III) 282.72(IV)

135.33(IV)

6

298.80(II) 366.70(III) 299.27(IV)

4

188.18(II)

8

7

413.02(II) 506.87(III) 600.73(IV)

599.42(III)

9

188.18(II) 292.66(IV)

73.18(II) 84.42(III) 95.68(IV)

459.92(II) 559.42(III) 36.17(IV)

112.58(II)

90.00(III) 90.00(IV)

547.15(IV)

135.28(III) 157.98(IV) 611.30(II) 780.70(III) 950.10(IV)

101.02(II) 17.26(III)

11

10

111.41(III)

156.32(IV) 1376.08(II) 1500.00(III) 1500.00(IV)

Legend

153.43(II) 218.72(III) 255.00(IV)

Sources of waste generation Existing treatment facilities

12 158.26(II) 191.00(III) 223.76(IV)

Proposed sites of resource recovery plants Proposed site of sanitary landfill Proposed sites of transfer stations

Figure 2. The optimal waste flow pattern for the base case (measured in TPD).

N.-B. Chang and S. F. Wang

33

1 Nnatzu 2 Tsoying 3 Kushan 4 Sanming east 5 Sanming west 251.08(II) 297.50(III) 297.50(IV)

6 Yencheng 1

135.00(II) 135.00(III) 135.00(IV)

1052.80(II) 1050.50(III) 1052.50(IV)

Tapindin 2

8 Hsinhsing 9 Linya

326.98(II) 413.18(III) 499.38(IV)

10 Chienchen 11 Chichin 12 Hsiaokang

64.78(II)

207.96(II) 254.11(III) 499.38(IV)

7 Chienchin

27.06(II) 298.80(II) 366.70(III) 167.58(IV)

46.12(II)

3

5

413.02(II) 492.06(III) 492.06(IV)

4

127.22(II)

6

8

7

9

249.46(III) 292.66(IV)

14.81(III) 108.67(IV) 459.92(II) 559.42(III) 658.91(IV)

84.43(III) 95.68(IV)

49.21(II) 49.21(III) 49.21(IV)

47.80(II) 135.28(III) 157.98(IV)

103.70(II) 103.70(III) 103.70(IV)

Legend

11

101.22(II) 128.67(III) 156.32(IV)

10

103.70(II) 103.70(III) 103.70(IV)

507.60(II) 677.00(III) 846.40(IV)

Sources of waste generation

10.62(II) 10.62(III) 10.62(IV)

158.26(II) 191.00(III) 223.76(IV)

12

Existing treatment facilities Proposed sites of resource recovery plants Proposed site of sanitary landfill Proposed sites of transfer stations

Figure 3. The optimal waste flow pattern for case 1 (measured in TPD).

34

Solid waste management analysis

1 Nnatzu 2 Tsoying 3 Kushan 4 Sanming east 5 Sanming west 6 Yencheng 1

7 Chienchin 8 Hsinhsing 9 Linya

153.67(IV)

2 304.53(II) 310.62(III) 329.79(IV)

10 Chienchen

233.90(II) 238.44(III) 98.58(IV)

11 Chichin 12 Hsiaokang 278.33(II) 275.96(III) 287.62(IV)

3

5

4

193.65(II) 190.99(III) 198.50(IV)

6

384.84(II) 381.63(III) 397.22(IV)

8

7

9

428.44(II) 421.36(III) 434.41(IV)

68.12(II) 63.72(III) 63.38(IV)

15.37(IV)

104.88(II) 101.75(III) 104.68(IV) 192.17(II) 187.33(III) 192.52(IV)

11

10

569.47(II) 587.41(III) 627.07(IV)

94.20(II) 97.11(III) 103.02(IV)

Legend Sources of waste generation

147.47(II) 143.67(III) 147.88(IV)

12

Existing treatment facilities Proposed sites of resource recovery plants Proposed site of sanitary landfill Proposed sites of transfer stations

Figure 4. The optimal waste flow pattern for case 2 (measured in TPD).

N.-B. Chang and S. F. Wang

35

1 Nnatzu 2 Tsoying 3 Kushan 4 Sanming east 5 Sanming west 191.60(III) 358.22(IV)

6 Yencheng 1

60.48(III) 111.52(IV)

7 Chienchin

244.84(II) 125.73(III)

8 Hsinhsing 9 Linya

413.18(III) 467.16(IV)

Tapindin

10 Chienchen

2

11 Chichin 326.98(II)

12 Hsiaokang 298.80(II) 366.70(III) 397.74(IV)

280.93(IV)

366.33(III) 492.06(IV)

3

5

4

207.96(II) 254.11(III)

6

413.02(II) 140.54(III) 70.00(IV)

8

7

9

459.92(II) 559.42(III) 616.26(IV)

73.18(II) 84.43(III) 89.54(IV)

24.49(II) 49.21(III) 49.20(IV)

112.58(II) 135.28(III) 147.85(IV) 206.26(II) 249.46(III) 273.63(IV)

11

Legend

10

101.02(II) 128.67(III) 146.19(IV)

Sources of waste generation

611.30(II) 780.70(III) 888.72(IV)

158.26(II) 191.00(III) 209.34(IV)

12

Existing treatment facilities Proposed sites of resource recovery plants Proposed site of sanitary landfill Proposed sites of transfer stations

Figure 5. The optimal waste flow pattern for case 3 (measured in TPD).

36

Solid waste management analysis

1 Nnatzu 2 Tsoying 3 Kushan 4 Sanming east 5 Sanming west 6 Yencheng 1

7 Chienchin

38.30(III) 22.67(IV)

8 Hsinhsing 9 Linya

250.32(II)

Tapindin 2

10 Chienchen

234.03(II) 301.38(III) 9.40(III) 293.45(IV) 156.46(IV)

11 Chichin 12 Hsiaokang

91.96(II) 297.90(II) 348.36(III) 333.90(IV) 181.28(III) 42.15(IV)

3

5

4

207.33(II) 241.35(III) 230.55(IV)

6

8

7

411.78(II) 300.27(III) 416.15(IV) 458.53(II) 531.51(III) 505.11(IV)

9

72.96(II) 80.24(III) 73.55(IV)

23.40(II) 49.20(III) 49.20(IV)

112.24(II) 128.50(III) 121.46(IV) 205.64(II) 236.90(III) 224.05(IV)

11

Legend

10

100.72(II) 122.29(III) 119.80(IV)

Sources of waste generation

609.45(II) 741.63(III) 728.79(IV)

157.78(II) 181.44(III) 171.75(IV)

12

Existing treatment facilities Proposed sites of resource recovery plants Proposed site of sanitary landfill Proposed sites of transfer stations

Figure 6. The optimal waste flow pattern for case 4 (measured in TPD).

N.-B. Chang and S. F. Wang

37

1 Nnatzu 2 Tsoying 3 Kushan 4 Sanming east 5 Sanming west 6 Yencheng

348.43(IV)

1

7 Chienchin

37.22(III) 89.99(IV)

8 Hsinhsing 9 Linya

6.24(II)

383.05(III) 454.46(IV)

Tapindin

10 Chienchen

2

11 Chichin

244.84(III) 301.38(IV)

326.98(II)

12 Hsiaokang 298.80(II) 348.36(III) 314.70(IV)

97.03(IV)

181.28(III) 492.06(IV)

3

5

207.96(II) 241.35(III) 176.27(IV)

4 4113.02(II) 300.27(III) 54.76(IV)

80.97(IV)

6

8

7

9

73.18(II) 80.24(III) 87.12(IV)

459.92(II) 531.51(III) 599.45(IV) 24.48(II) 49.20(III) 49.20(IV)

112.58(II) 128.50(III) 143.86(IV) 206.26(II) 236.90(III) 266.14(IV)

11

Legend

101.02(II) 122.29(III) 142.20(IV)

10

611.30(II) 741.63(III) 864.54(IV)

Sources of waste generation

8.10(IV)

157.78(II) 181.44(III) 171.75(IV)

12

Existing treatment facilities Proposed sites of resource recovery plants Proposed site of sanitary landfill Proposed sites of transfer stations

Figure 7. The optimal waste flow pattern for case 5 (measured in TPD).

1 2 3 4 5

27 232 31 856 34 527 34 784 33 868 34 468

15 935 11 620 2904 9413 6317 9603

Construction

∗: Measured in 1994 millions NT$. ∗∗: The currency ratio was 26 NT$/1 US$ in 1994.

Base Case Case Case Case Case

Transportation

Cost

12 629 10 397 6441 8772 7848 8474

Operating 0 0 411 332 44 144 190 135 90 927

Recycling 55 796 53 873 455 204 97 113 238 168 143 472

Total cost 29 010 14 997 417 7769 4759 6836

0 0 16 217 4106 9977 7877

Recyclng

Benefit Electricity

T 4. The results of cost/benefit analysis of each case

29 010 144 997 16 634 11 875 14 736 14 713

Total benefit

26 785 38 876 438 240 85 240 223 516 128 756

Net cost

38 Solid waste management analysis

N.-B. Chang and S. F. Wang

39

100 90

12 629

10 397

Cost distribution (%)

80

44 144

70 60

11 620

90 927

15 935

190 135 411 332

50

8772

40

9413

30

31 856

7848

27 232 6441 2904

20

34 527

Base

Case 1

Case 2

9603

34 784

10 0

8474

Case 3

6317 33 868

34 468

Case 4

Case 5

Figure 8. The comparative cost structure of each case. Costs of: Φ transportation; Γ construction; Ε operating; recycling.

100 90

10 089

80

78

Cost distribution (%)

3380 7431

7256

70 3691

60 50

623

227 20 010

14 996 2361

40

1862 7769

30

684

16 218

20 4759

6836

10 0

Base

Case 1

Case 2

Case 3

Case 4

Case 5

Figure 9. The comparative benefit structure of each case. Φ Electricity income; Γ paper; Ε plastics; glass; ; metal.

calculated according to the net benefit, the cost of recycling and the corresponding electricity loss, as shown in Figure 10. 7. Conclusions This analysis aims to compare single objective and multiple objective programming analysis for solid waste management system planning in a metropolitan region. It can be shown that the inclusion of environmental quality constraints in a single objective programming model may result in quite different optimal planning compared to the results in the other cases with multiple objective considerations. Although multiple conflicting objectives exist, the regulated optimal waste flow pattern with regard to environmental quality requirements can be achieved using higher tipping fees. Moreover, this analysis shows that the efforts of material recycling exhibit very big indirect benefits

40

Solid waste management analysis

25 000

24 976

Cost

20 000 15 000 10 000

9093 avoided cost paper plastic glass

5000

Benefit

0 5000

recycling electricity cost loss

metal

201 5177

5917

10 000 10 447 15 000

12 327

Figure 10. Cost and benefit structure of material recycling in a simulated case. Units in 1994 million NT$. Net benefit=avoided cost+direct income−recycling cost−electricity loss. Total net benefit=8·5 billion NT$. Average net benefit=963 NT$/ton.

in an economic sense, although the emphasis of environmental quality as one of the objectives in decision-making may also inevitably drive the optimal solution toward pro-recycling programs. The enhancement of this modelling analysis by using the grey and fuzzy system theories as uncertainty analysis tools could be used in the future.

References Anderson, L. E. (1968). A mathematical model for the optimization of a waste management system. Sanitary Engineering Research Laboratory, SERL Report, No. 68-1. Berkeley: University of California. Baetz, B. W. (1990). Optimization/simulation modelling for waste management capacity planning. Journal of Urban Planning and Development, ASCE 116, 59–79. Booz-Allen and Hamilton Inc. (1976). Cost estimating handbook for transfer, shredding and sanitary landfilling of solid waste. No. PB 256444. Washington D.C.: USA, EPA, NTIS. Chang, N. B., Schuler, R. E. and Shoemaker, C. A. (1993). Environmental and economic optimization of an integrated solid waste management system. Journal of Resource Management and Technology 21, 87–100. Chang, N.-B. and Wang, S. F. (1994). A locational model for the site selection of solid waste management facilities with traffic congestion constraint. Civil Engineering Systems 11, 287–306. Chang, N.-B., Shoemaker, C. A. and Schuler, R. E. (1995). Solid waste management system analysis with air pollution and leachate impact limitations. Waste Management and Research (In press). Chang, N.-B., Yang, Y. C. and Wang, S. F. (1996). Solid waste management system analysis with noise control and traffic congestion limitations. Journal of Environmental Engineering, ASCE 122, 122–131. Fuertes, L. A., Hudson, J. F. and Mark, D. H. (1974). Solid waste management: equity trade-off models. Journal of Urban Planning and Development, ASCE 100, 155–171. Gottinger, H. W. (1986). A computational model for solid waste management with applications. Applied Mathematical Modelling 10, 330–338. Hasit, Y. and Warner, D. B. (1981). Regional solid waste planning with WRAP. Journal of Environmental Engineering, ASCE 107, 511–525. Helms, B. P. and Clark, R. M. (1974). Locational models for solid waste management. Journal of Urban Planning and Development, ASCE 97, 1–13. Hsieh, H. N. and Ho, K. H. (1993). Optimization of solid waste disposal system by linear programming technique. Journal of Resource Management and Technology 21, 194–201. Jacobs, L. J. M., Nijs, L. and Willigenburg, J. J. V. (1980). A computer model to predict traffic noise in urban situations under free flow and traffic light conditions. Journal of Sound and Vibration 72, 523–537. Jakeman, L. and Simpson, R. W. (1985). Assessment of air quality impact from an elevated point source. Journal of Environmental Management 20, 63–72.

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Jenkins, L. (1982). Parametric mixed integer programming: an application to solid waste management. Management Science 28, 1271–1284. Johnson, D. R. and Saunders, E. G. (1968). The evaluation of noise from freely flowing road traffic. Journal of Sound and Vibration 7, 287–309. Jones, I. D. (1976). Road Traffic Noise. New York: Pergamon Press. Jung, F. W. and Blaney, C. T. (1988). Highway traffic noise prediction for microcomputers: modeling of Ontario simplified program. TRB, TRR, 1176, 41–51. ¨ . and Erkip, N. (1988). Selecting transfer station locations for large solid waste systems. European Kirca, O Journal of Operational Research 38, 339–349. Ku¨hner, J. and Harrington, J. J. (1975). Mathematical models for developing regional solid waste management policies. Engineering Optimization 1, 237–256. Lund, J. R. and Tchobanoglous (1994). Linear programming for analysis of material recovery facilities. Journal of Environmental Engineering, ASCE 120, 1093–1095. Marks, D. H., ReVelle, C. S. and Liebman, J. C. (1970). Mathematical models of location: a review. Journal of Urban Planning and Development, ASCE 000, 81–93. Ohta, M. and Mitani, Y. (1987). A prediction method for road traffic flow based on an approach equivalent to that for a standard Poisson type traffic flow. Journal of Sound and Vibration 118, 11–22. Ohta, M., Yamaguchi, S. and Ikuta, A. (1980). Statistical estimation of road traffic noise in an arbitrary sound propagation environment by use of Stratonovich’s theory for a random points system. Journal of Sound and Vibration 69, 275–284. Perlack, R. D. and Willis, C. E. (1985). Multiobjective decision-making in waste disposal planning. Journal of Environmental Engineering, ASCE 111, 373–385. Sannders, R. E., Samuels, S. E., Leach, R. and Hall, A. (1983). An evaluation of the U.K. DOE traffic noise prediction method. ARR, No. 122. Sydney: Australian Road Research Board. Walker, W., Aquilina, M. and Schur, D. (1974). Development and use of a fixed charge programming model for regional solid waste planning. The 46th joint meeting of the Operation Research Society of America and the Institute of Management Sciences, Puerto Rico. Wang, N. H., Wang, L. K., Simmons, T. and Bergenthal, J. (1979). Computer-aided air quality management. Journal of Environmental Management 9, 61–87. Zeleny, M. (1974). Linear Multiobjective Programming. New York: Springer-Verlag. Zeleny, M. (1976). Multiple Criteria Decision Making. New York: McGraw-Hill. Zhu, Z. and ReVelle, C. (1990). A cost allocation method for facilities siting with fixed-charge cost functions. Civil Engineering Systems 7, 29–35.

Appendix: Notation used in the model    I=set of linkages between system components in the transportation network in each period. I1=set of incoming waste streams at a specific site in each period. I2=set of outgoing waste streams at a specific site in each period. J=set of all new system components (J1jJ2jJ3jJ4) in each period. J1=set of all new waste generation districts (point sources) in the system. J2=set of all new waste transfer stations in the system in each period. J3=set of all new waste treatment plants in the system in each period. J4=set of all new waste landfills in the system in each period. K=set of all old system components (K1jK2jK3jK4) in each period. K1=set of all old waste generation districts (point sources) in the system in each period. K2=set of all old waste transfer stations in the system in each period. K3=set of all old waste treatment plants in the system in each period. K4=set of all old waste landfills in the system in each period. L=set of types of trucks used for shipping waste in the system. R=set of resources recovered at facilities and households. T′=set of time period ({1, . . ., T}). M=set of all intermediate facilities in each period.

42

Solid waste management analysis

    T=the number of total time periods in the planning horizon. Git=waste generation rate in municipal district i at time t. CTjkt=unit transportation cost among system components at time period t. COkt=unit operating cost at facility k at time period t. CCkt=variable construction cost at facility k at time period t. CRjt=recycling cost of material i at time period t. Fkt=fixed cost for building new facility at site k at time period t. Tikt=recovery factor of resource i per unit waste processed at facility k at time period t. Rk=reduction ratio of waste destroyed by the processing at site k and time t. MAXk=the maximum allowable capacity at site k. MINk=the minimum required capacity at site k. Nt=the specified number of available potential sites during a time period. N1=the maximum number of treatment trains for waste incineration which can be initialized in the optimization process. N2=the maximum number of treatment trains for waste incineration which can be expanded in the optimization process. TIME=the length of time within one time period t (conversion factor). bt=discount factor for time period t. r=nominal interest rate. f=estimated inflation rate. IRijt=net income per unit weight of secondary material j by household recycling in district i and at time period t. Pikt=the price of each resource i recovered at site k at time period t. aijt,max=maximum fraction of recyclables which can be recovered in the waste stream Git. CU=the conversion factor between the garbage truck unit and passenger car unit. Cjkt=the maximum designed traffic capacity on the main entrance road at each facility at time period t. Vjkt=the average background traffic flow on the main entrance road at each facility at time period t. Pl=the allowable weight loading of different types of trucks. SLjkt=required service level of main road connecting different system components at time period t. MCk=the design capacity of a basic unit of a combustor in each treatment train at site k, which is consistent with the industrial specification. LIMITk=total tolerance of pollutant p in the incoming waste stream at landfill k. Akbp=the transport and transformation factor corresponding to the linkage between plant “k” and receptor “b” for pollutant “p”. f′=a conversion factor regarding the time scale difference between the units of emission factor (ENp) and National Ambient Air Quality Standard (Spt). FGR=the flue gas production ratio, based on burning one ton of solid waste in the incinerator. Spt=the emission standard of pollutant p in the time period t.

N.-B. Chang and S. F. Wang

43

Bbpt=the background concentration of air pollutant p at the location of a specific receptor a at the time period t. Dj=spatial decay constant at site j, based on the local situation. NLj=the acceptable noise level of site j in the environmental regulations.     Sjkt=optimal waste stream among system components at time period t. Ykt=binary integer variable for the selection of facility at time period t. Zkiy=binary integer variable for the selection of the ith treatment train of facility k in the initialization time period y. Ekiyt=binary integer variable for the selection of the ith treatment train of facility k in the expansion time period t, initialized in the time period y. DCkt=design capacity of a new facility at site k at time period t. NEXPkyt=expansion capacity at new site k at time t based on the initialization of facility operation at time period y. TEXPkt=total expansion capacity of a new or an old facility at site k at time t. Ct, Bt=the total system costs and benefits respectively at time period t. TIPt=tipping fee charged per unit amount of waste at time period t. aijt=total recycling fraction of material j corresponding to waste Git. TRt=total amount of household recycling at time period t.