A fuzzy goal programming approach for the optimal planning of metropolitan solid waste management systems

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH ELSEVIER

European Journal of Operational Research 99 (1997) 303-321

A fuzzy goal programming approach for the optimal planning of metropolitan solid waste management systems N i - B i n C h a n g *, S.F. W a n g Department of Environmental Engineering, National Cheng-Kung University, Tainan, Taiwan, ROC

Received 15 July 1995; revised 4 January 1996

Abstract

The emphasis of waste reduction and recycling requirements prior to incineration and the protection of environmental quality during waste shipping, treatment, and disposal have resulted in a set of new solid waste management goals in system planning. However, the inherent uncertainties in the perception of both priority and scale of those economic and environmental goals may generate additional difficulties in management decision making. This paper applies a fuzzy goal programming approach for the optimal planning of solid waste management systems in a metropolitan region. In particular, it demonstrates how fuzzy, or imprecise, objectives of the decision maker can be quantified through the use of specific membership functions in various types of solid waste management alternatives. © 1997 Elsevier Science B.V. Keywords: Fuzzygoal programming;Solid waste management; Regional planning

1. Introduction

Multiple conflicting objectives characterize the current solid waste management systems such that integrated planning becomes essential and significant. It is frequently emphasized that both socioeconomic and environmental considerations need to be included simultaneously in solid waste management programs in order to provide a set of 'total solution' regarding waste recycling, facilities siting, and system operation. However, the inherent uncertainties in the perception of both priority and scale of those economic and environmental goals may generate additional difficulties in management decision making. Various deterministic multiobjective programming models have been applied for planning solid waste management systems. For instance, Perlack and Willis (1985) considered the application of a multiobjective programming model in a sludge disposal problem in the USA. Koo et al. (1991) accomplished the siting planning of a regional hazardous waste treatment center by using a fuzzy multiobjective programming technique in Korea. The efforts in combining the environmental objectives (i.e., air pollution, leachate, noise and traffic congestion) into a location/allocation model for solid waste management planning were established by Chang et al. in the USA and Taiwan (Chang and Wang, 1994, 1996a, b; Chang et al., 1993, 1994). A relevant study

* Corresponding author. 0377-2217/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PH S0377-2217(96)00024-0

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was also carried out by Chang and Wang (1995) in which a deterministic compromise programming model, including both considerations of economic and environmental objectives, was established in search of the long term optimal management alternatives in a typical solid waste management system. However, uncertainty plays an important role in most solid waste management problems. Fuzziness is one type of uncertainties especially embedded in those linguistic expressions in decision making, which is non-statistical in nature and generally cannot be described by traditional probability distribution. Such an impreciseness refers to the absence of sharp boundaries in information. It is found that the application of fuzzy sets theory to solving real-world decision making problems are urgently needed. The fuzzy mathematical programming is therefore viewed as an alternative to the stochastic one, where the parameters or objectives are modelled as fuzzy sets. There have been very few studies in the literature involving the use of fuzzy mathematical programming models for tackling real-world solid waste management problems. This research, serving as a continuing study of Chang and Wang 1995 illustrates the use of the fuzzy goal programming (FGP) approach (Zimmermann, 1978; Tiwari et al., 1978, 1986) to facilitate the long term planning of the solid waste management systems. The membership functions defined in fuzzy sets theory might provide one of the flexibility in the formulation of such uncertainty for the objective function and/or constraints to form the fuzzy mathematical programming model. It specifically demonstrates the fuzzy multicriteria decision making process, based on the considerations of economic and environmental impacts of noise, traffic congestion, air pollution, and material recycling within the long term planning program for siting landfills, incinerators, and transfer stations in a typical solid waste management system. Interactions among the effects of waste generation, source reduction, recycling, collection, transfer, processing, and disposal are tied together within such an analytical framework. The proposed FGP method has been applied to the solid waste management system in the city of Kaohsiung in Taiwan for the purpose of demonstration. It shows that the fuzzy optimal outputs may generate a set of flexible management alternatives for handling real-world, complex solid waste management problems. From the long term perspective, the optimal strategies obtained in this analysis are especially helpful for the sustainable development in a metropolitan region.

2. Model formulation

2.1. Basic structure of fuzzy goal programming Goal programming (GP) model is one type of multiobjective programming models. According to the priority of the goals, it can be classified in two categories: (1) non-preemptive (weighted) GP, and (2) preemptive (lexicographic) GP. Goals in the non-preemptive structure show roughly comparable importance. But there exists a hierarchy of priority level for the goals in the preemptive structure. To apply preemptive GP, the decision maker must rank his or her goals from most important to least important. Solution techniques of both types of goal programming focus on the minimization of the deviations from each goal, subject to the goal constraints and original functional constraints. In the formulations, each set of deviational variables, consisting of one slack a n d / o r surplus term, represents the distance from corresponding prespecified target value associated with each goal. Specifically, the weight factors corresponding to those deviational variables can be used to express their relative importance in decision making. However, the target value associated with each goal could be fuzzy in the real-world application. The fuzzy sets theory is frequently used in recent research. A fuzzy set A can be characterized by a membership function, usually denoted Ix, which assigns to each object of a domain its grade of membership in A (Zadeh, 1965). The more an element or object can be said to belong to a fuzzy set A, the closer to 1 is its grade of membership. Various types of membership functions can be used to support the fuzzy analytical

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framework although the fuzzy description is hypothetical and membership values are subjective. Membership functions, such as linear, piecewise linear, exponential, and hyperbolic functions, were used in different analysis. In general, the non-increasing and non-decreasing linear membership functions are frequently applied for the inequalities with 'less than or equal to' and 'greater than or equal to' relationships, respectively. Since the solution procedure of the fuzzy mathematical programming is to satisfy the fuzzy objective and constraints, a decision in a fuzzy environment is thus defined as the intersection of those membership functions corresponding to fuzzy objectives and constraints (Zimmermann, 1978, 1985). Hence, the optimal decision could be any alternative in such a decision space that can maximize the minimum attainable aspiration levels in decision making, represented by those corresponding membership functions (Zimmermann, 1985). The integrated use of goal programming and fuzzy sets theory has already been reported in the literature (Tiwari et al., 1978, 1986; Hannan, 1981; Rao et al., 1988; Inuiguchi et al., 1990). Lai and Huang (1992, 1994) further integrated several fuzzy linear and multiobjective programming techniques. The approach chosen in this study is similar to the method used by Zimmermann (1978) to formulate the FGP problem, but modified by the idea proposed by Tiwari et al. (1986). The reasons for choosing fuzzy goals with crisp constraints (asymmetric approach) to address the multiobjective solid waste management issue in this study can be summarized as: I. The uncertain information in solid waste management systems may not be fully identified by conventional probability theory; hence, the stochastic programming techniques are not suitable for such type of analysis. 2. Due to the impreciseness of the decision maker's preference associated with each goal, a conventional deterministic goal programming model cannot fully reflect such complexity. 3. Environmental goals, such as noise level, air pollution, and traffic congestion, are explicitly limited by the environmental law or regulation, which is crisp, such that the inherent vagueness of environmental impacts can be directly handled by the fuzzy goal constraints in the constraint set. 4. Although several parameters are very often imprecise or fuzzy in the constraint set, such as solid waste generation rate, the uncertainties of them can be limited if the conventional prediction technique, such as regression analysis, can be properly applied as the auxiliary tool.

2.2. Formulation of fuzzy goal programming for solid waste management Four fuzzy objectives, consisting of economics, noise control, air pollution control, and traffic congestion limitation, are considered in this analysis. 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 /3t ( = [(1 + f ) / ( 1 + r)] 1- I). The expression of the objective function is: T

Minimize C,( Sj,,) = ~_, ~,( C , - B,)

(1)

t=l

The cost components (C,) consist of: Total transportation cost =

[CTj,,Sik,],

(2)

[CC,,DC,, + Fk,Yk, ],

(3)

• (j,k)El,jq:k

Total construction cost =

~ k ~ ( J \ J I)

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r Total operating cost =

[COktY'~Sjk,[,

~'~

l (4)

k~(J\Jlt.JK\Ki) [

Total expansion cost =

[CEk,TEk, ] ,

]~

(5)

k~(J\JIOK\K 1)

Total recycling cost = ~

TRi,CRi,

(6)

i~R

The only two benefit components

(B t) considered here

are:

Total resource recovery income at the facilities = + ~]

Y'~

Y'~

[ PiktZiktSjkt],

(7)

i~R k~(MUK4UJ4 ) (j,k)~l I

Total household recycling income = __+_

~]

Y'~ [ Ieijt

°lijtGit ]"

(8)

iE(JIUKI) jER

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, and the average operating cost is assumed to be a constant. As usual, a fixed charge structure is employed in the formulation of total construction cost for the purpose of site selection. However, 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. But 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 assigned in the related 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 Cjk , and Vjk-~ is the passenger car unit (P.C.U.). 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., P.C.U.) through the use of a conversion factor, CU, associated with the number of standard garbage truck needed (i.e., SjkJP~). The expression of the objective function is: Minimize

Cz(Sik, ) = Y'~

Y'~

t~T' kE(J\JjUK\Kj)

CU

Y'~

SjkJP, + Vjk,.

(9)

jE(JIt3KI) , IEL

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 (i.e., from treatment and disposal facilities) and line sources of noise (i.e., increased traffic flow by the garbage truck). 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 the 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; Jung and Blaney, 1988; Ohta et al., 1980; Ohta and Mitani, 1987)). 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. An semi-empirical statistical regression model for noise impact assessment is independently developed by the authors, as illustrated below:

NLk=c'k +c2kln(Fk)-Dk'

Fk=CU[

jE(J,t.JKt),E

t~l~SJkt/Ptl + ~ '

(10)

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in which F is the noise impact created by the garbage truck fleet at the main entrance road of each treatment or disposal facility, c~k and Czk are regression coefficients. D is the spatial decay constant, an empirical number based on the local situation. The aggregate noise levels, at the most sensible neighboring community around the facility site, can then be estimated and compared with the acceptable noise level required in the environmental regulations. Temporal variations of noise are considered and evaluated through the integration of the noise impacts from those additional sources of waste shipping. Therefore, the objective function is: (11) kE(JXJIUKXKI ) tET'

jE(JIt.)KI), I~L

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 (i.e., ppm or }xg/m 3) of certain pollutants in the surrounding environment are controlled by the latter. The objective function is described as below: M i n i m i z e C4(Sjkt) =

E E Y'. kE(K3k)J3 ) pEP t~T'

(

~

SjktFGRENpAkbp),

(12)

(j,k)EIj

in which Akb p 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, 1982; Chang and Wang, 1994b). 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 A~bp ensures that the more 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 Akh~,, the long-term diffusion equation for a decay-pollutant (non-conservative pollutant) at ground level and at centerline of plume may be defined as (Jakeman and Simpson, 1982): C,,(x) =

q

d e t -

2zCO-zUX

2o-z2

exp(-kpt)

= qAkbl,,

(13)

in which:

Cl,(x) =

aggregate ambient air pollutant concentration of pollutant p at the downstream location x ( p . g / m 3 or ppm). the average wind speed (m/sec). R the effective height of plume release corresponding to the wind speed u (m). He first order reaction rate of pollutant p ( = 0 if the pollutant is conserved) (sec- ~). kp reaction time (sec). t~ q= emission rate of a particular air pollutant from the stack of incinerators (g/sec). vertical diffusion coefficient (m). ~z = Hence, the FGP model, based on the idea of weighted additive model (Tiwari et al., 1978), is described as below: max ~] i=l

wi/z i

(14)

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subject to: 1. Fuzzy goal constraint set 1.1. A goal constraint for cost minimization

U t -

>-

Ll

(15)

u.,.

1.2. A goal constraint for traffic congestion limitation u2 - c2(sj

,)

U2-L2

>-/~2"

(16)

1.3. A goal constraint for noise impacts control v3 - c 3 ( s j , , )

>_/z 3.

(17)

U3 -L 3

1.4. A goal constraint for air quality control U 4 -- C4(Sjkt) ~_~/tz4 .

(18)

U4 - L 4 1.5. A boundary constraint for membership degree 0_< tzi_< 1.

(19)

2. Basic functional constraint set 2.1. Mass balance constraint: 2.1.1. Point source: All solid waste generated in the collection district should be shipped to other treatment or disposal components. Furthermore, the 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),

V i ~ ( J , UKI), V t ~ T ' ,

(20)

k~(J\JzUK\KO Olit= E Olijt, j~R

V i E ( J , UKI), V t ~ T ' ,

(21)

0<_~Otijt<-~ Otijt.max, Vi~ (J~ UK~), V j ~ R , Vt~ T',

(22)

VRi, ~-

(23)

E aitolit , iE(JIUK j)

Vt~

Zt

2.1.2. 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.

E ( j,k)~l~

Sjk,(1--Rk)=

E

Sjk, V k ~ M , V t e T '

(24)

(kj)~l 2

2.2. 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. 2.2.1. New facility (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

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309

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

E

T

D C k y >- mink

y=l

~ Yky, Vk ~

(25)

( J 2 I,.J J 4 ) ,

y=l T

DCky+ E

NEXPkytNmaXkYky,

VkE(J2k-JJ4), V y E ( 1 , T -

1),

(26)

t=y+ 1 l

Y'~ NEXPkyt = TEXPk,, Vk e ( J2 U J4), Vt ~ T',

(27)

y=2

2.2.2. New facility (incinerators): The numbers of treatment train and associated size per each 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 reasonable for subsequent engineering design. Hence, the summation of the values of all binary variables Zkiy represents the number of combustor being initialized at a specific incinerator site in the time period y. Therefore, Eky. 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

Ni

E DCky=MCk E ~-,Zkiy, Vk~-J3, y=l

(28)

y = l i=1 T

N2

DCky+ E

~"-,MCkEkiyt
1),

(29)

t = y + l i=1

Y~MCkEkiyt = TEXPkt, V k E J 3, V t ~ T',

(30)

y=2 i=l Ni

EZkiy>__Yky,

Vk~J3, Vy~(1,T-1).

(31)

i=1

2.2.3. Old facility: T

DCk + E rEXPk, <_m a x

k,

Vke (K\K1).

(32)

t=l

2.3. Operating constraint: The accumulated waste inflow at each site should be less than, or equal to, the available capacity in each planning period. 2.3.1. New facility: '

+ ~.INEXPkyt t=y+

)

>_ }-", Sit t, V k E ( J \ J , ) , V t ' E T ' .

(33)

(j,k)~l I

2.3.2. Old facility: Time

(DCk+~,TEXPk, ' )~

E

1

(j,k)~l,

t=

Sjkt', V k ~ ( K \ K 1 ) , Vt'~T'.

(34)

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310

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

E Yk,<_~l, V k E (J21Jg31JJ4).

(35)

t=l

2.5. Site availability constraint: This constraint can also allow the planner to leave out some of the potential sites. T

~_, rk,
(36)

Y=I

2.6. 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.

C, < B, + TIPt[ ~

G,,1,

Lie(KiUJO

V t ~ T'.

(37)

J

3. Environmental quality constraint set 3.1. Traffic congestion constraint: 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 ( - ~ , as shown on the right hand side of the constraint below. Vjk, is the average value of background traffic flowrate before the inclusion of the garbage truck stream.

SLjk,

CU[ iE(j, Uki),E lGl SjkJt/Pl] +Vjk---~t
(38)

3.2. Noise control constraint:

c'k +c2kln{CU[ j~(J, UK,),E l e L

Sjkt//PI]+~jkt)--Dk
(39)

3.3. Air pollution control constraint: This analysis considers ambient air quality limitations for several pollutants at a set of prespecified sensitive area in Kaohsiung City. The constraints formulation are described as below:

f'[~(X3uJ,) ~-~ (j.k)et,Y]~(Sj~tFGRENpAkbP)l
(40)

(ENp)

f ' is a conversion factor regarding the time scale difference between the units of emission factor and National Ambient Air Quality Standard variable 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. It is known that the expression of each environmental objective in the above is the same as that in the left-hand side of the corresponding environmental quality constraint such that the consideration of fuzziness of the environmental impacts is required only in the fuzzy goal constraints. In this case, environmental constraints are prepared mainly to ensure that no matter how fuzzy the environmental impacts are, the crisp upper bound defined by related environmental law or regulations cannot be violated under any circumstance. In addition, the only source of uncertainty in the basic functional constraint set is the rate of waste generation and composition.

(Spt). The

Bbp,

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Such type of uncertainty could be reduced to a minimum if the prediction technique is reliable based on sufficient information.

3. Case study

3.1. Application background 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 Fig. 1. Twelve 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 as east and west subdistricts. The only existing landfill is the Shichinpu landfill, located at the northern boundary of Kaohsiung. In addition, there is an existing informal 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 land 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 disposal alternatives in the current solid waste management system. Several key questions frequently bother the public officials, which include: 1. Is it necessary to build two new transfer stations? 2. Are the construction schedule and planned capacity reasonable to meet the growing demand of waste treatment? 3. What is the impact of material recycling on the entire management system? 4. What is the long-term optimal waste management pattern once the environmental quality considerations are included in the next twenty years? 5. What is the impact if the uncertainty in decision making is included? These questions can be analyzed using this fuzzy multiobjective programming model. In this analysis, a hypothetical 20-year project with four planning time periods is conducted. The start-up year is 1993, when the system has only one landfill and one informal transfer station. The Shichinpu landfill is expected to be expanded and continuously used until the year 2003 (i.e., the end of 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, can be 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, all the potential sites of treatment and disposal facilities can be included into the system operation after the beginning of the second time period. The candidate sites for transfer stations are only prepared for shipping raw garbage. To establish such a fuzzy goal programming model, a lot of physical, economic, and environmental data for solid waste management have to be compiled together. Especially, various investigations for those supporting submodels required in environmental quality constraints have to be conducted before the optimization procedure is performed. In this analysis, economic database is mainly obtained from the government agencies, while most of the database of environmental quality is collected by the authors. Final selections of each parameter value need to 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

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TAIWAN

l

TAIPEICITY ]

~

I

Shichipullardfflls

1~ Nantzu resource recoveryplant

~t

Tsoyingtransferstation

Tsoymg t~

recover)'plant Kuslnn~

~gtwest

Chienchen transferstation Chienchen Tapindin 1 ~ ~ Legencl ~t

Sourcesof waste generation

•

Existing treatment facilities

•

Proposed sites of resource recovery plants

Taliapu resolllurce" gt n g /

Proposed site of samtary landfill Proposed sites of transfer stations Fig. 1. The georaphical location of solid waste management system in Kaohsiung. incinerators. Since there were no formal transfer stations in Taiwan, a database in the US was used after a careful economic calibration. 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, interest rate, inflation rate, operating cost of the treatment and disposal facilities, and the transportation cost were separately investigated or estimated as well.

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Besides the selection of those economic parameters, the estimation of several physical parameters are also required for building up the constraint set. For example, the treatment and conversion efficiency of material and energy recovery process were evaluated according to several engineering reports. According to the 5-year record of physical composition of solid waste in Kaohsiung City, the possible recycling ratio of paper, plastics, metal, and glass were predicted respectively. The historical records of solid waste generation were collected and waste generation rates were forecasted by statistical regression models. In addition, the maximum and minimum capacities of selected treatment and disposal sites were decided corresponding to the factors of land availability and technology. The classification of traffic service 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 location of each site ~cd 1

1 if CI ~ 38876 f = {(629108421)/590232if 38876
CI

o 38876

629108

( 1993 millions NT$) ~c2 1

1 if C2 =< 0.4523 f ~½= { (1 1409422)/0.6886 if 04523 < C2 < 1.1409 k 0 if C2 ~ 1.1409

C2

o 04523 1.1409 Traffic congestion index ~tc3,

(

1

= { (31 36423)/26 56 I. o

o1

if C3 < 4.80 if 4 80 < C3 < 3136 if C3 > 31 36

C3 480 (dBA)

3136

~C4

1 btc~ =

{,8:0894,8,4,c4s4482o89 0

if C4 ~ 820.89

C4

0 -14.75

82089

(rag/l) Fig. 2. The determination of membership functions in FGP model.

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Table 1 The planning scenarios for optimization analysis Cost minimization objective Traffic conjection objective Noise impact objective Air quality objective Membership degree Environmental constraints Basic constraints

Case 1

Case 2

Case 3

V * V V V

V(1) * * V(1) V(1) V(1)

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

Single

additive

additiue

V V

V V

V V

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

and related noise impacts were measured and summarized. The growth rates of background traffic flow over time periods can be assumed to be at the same speed as the estimated economic growth rate. The results can be used directly in the constraints for the control of traffic congestion and noise impacts. Background information of criteria air pollutants and related meteorological conditions at each designated site were obtained from several environmental impact assessment reports. To perform the optimization analysis, a pay-off table, as listed in Table 2, is needed. Fuzzy membership functions are therefore prepared with respect to the conventional pay-off table, as shown in Fig. 2. L I N D O software package is employed as a computer solver. The hardware required is an I B M PC or compatible machine with a 486 CPU and a microprocessor. 3.2. Optimization results and discussions

In this analysis, the decision maker may assign different weights as coefficients of the individual terms in the simple additive fuzzy achievement function to reflect their relative preference levels. However, the major difficulty is how to assess the planning alternatives based on different relative importance of the goals correctly. Therefore, three different cases are evaluated in this case study. As described in Table 1, case 1 represents the situation in which the consideration of different weights in the additive fuzzy achievement function is temporarily excluded, while all of the economic and environmental objectives and constraint sets are included. Case 2 thereby evaluates the impacts embedded in the decision m a k e r ' s preference levels by the inclusion of a specific weight associated with each fuzzy goal, assuming that all of the goals considered are equally important. But such a weighting arrangement implies that a priority structure is existing and environmental considerations are favored because o f the higher aggregate weight which is assigned to those objectives for environmental quality control. In order to avoid the exaggeration of the goal for environmental protection, case 3 therefore considers the economic and environmental goals with equally important weight in the decision making process, while all the other parts of the model remain the same.

Table 2 The pay-off table of the fuzzy goal programming model fl f2 f3 f4

Cost objective fl

Traffic objective )'~

Noise objective f3

Air objective 3'~

38,876 * 629,108 * * 620,236 562,894

1.15 * * 0.4523 * 0.47 0.61

31.36 * * I 1.32 4.80 ~ 10.17

820.89 * * 389.43 26.27 14.75 *

* Represent the lower bound of the objective Represent the upper bound of the objective

*

*

N.-B. Chang, S.F. Wang / European Journal of Operational Research 99 (1997) 303-321

315

Table 3 Optimization results in system analysis

Objective function value (1993 millions NT$) New incinerator sites included Initilization period Design capacity (TPD) Expansion capacity of Nantzu plant (TPD) Period 3 Period 4 Expansion capacity of Fudingjin plant (TPD) Period 3 Period 4 Expansion capacity of Talinpu plant (TPD) Period 3 Period 4 New transfer station included Initialization period Design capacity (TPD) Expansion capacity of Tsoying station(TPD) Period 3 Period 4 Expansion capacity of Chienchin station (TPD) Period 3 Period 4 New landfill included lnitilization period Design capacity (TPD) Expansion capacity (TPD) Period 3 Period 4 Tipping lee (NT$/ton) Period I Period 2 Period 3 Period 4 Recycling (TPD) Period 1 Period 2 Period 3 Period 4

Case 1

Case 2

Case 3

303, I 15 Nantzu Fudi ngjin 2 2 1 × 450 2 X 450

438,570 Fudingjin

85,240 Nantzu Fudingjin 3 2 2 × 450 1 X 450

4 1 X 450

0 0

0 1 × 450

0 0

0 0

1 X 450 0

Tsoying 2 693

-

-

0 0

-

-

-

-

Tapindin 2 2,939

Tapindin 2 2,798

Tapindin 2 2,974

0 0

102 100

25 0

2328 5914 4441 25839

2328 7225 20356 27213

2328 2209 1366 5475

0 161 199 1569

0 220 986 1615

0 0 0 306

To build up the fuzzy membership functions, a pay-off table, as shown in Table 2, might be used as a reference basis. Based on such an analytical scheme defined in Table 1, the optimization results, as shown in Table 3, unambiguously indicate that the emphasis of environmental quality objectives in case 2 would dramatically reduce the essential capacity of new waste incinerators, and inevitably increase the need of new landfilling capacity. Only the construction of Fudingjin incinerator is initialized in the fourth time period in case 2. In case 1, Tsyoing transfer station is selected as an essential facility in the second time period since Chienchen transfer station encounters worse situation from environmental perspective. It is worthwhile to point out that both proposed sites of transfer stations are excluded in cases 2 and 3. Part of the reasons might be the

316

N.-B. Chang, S.F. Wang~European Journal of Operational Research 99 (1997) 303-321

noise and traffic impacts generated by waste transferring process, which cannot be tolerated at these proposed sites due to the emphasis of environmental protection in these cases. Similarly, no transfer station is required in cases 2 and 3 due to the emphasis of environmental protection. However, Tapindin landfill is needed in all cases. The required tipping fee has generally increased over periods. While higher capacity of new incinerators

1

,/xr •q .

_

191.60(I11) - - "35g.~Pdk . . . .

~1 . / ~ ~,44.84(H)

,

111.52(1~

",

Tapind~

'

Tsoying

~3

Kushan

~4 gx5

Samrang east

~6

Yencheng

~7

Chienchin

gt 8

I-Isinhsing

Sanmmgv~st

~x9 Linya 10 Chienchen

kl 3.18(III)

,l~ ~

Nnatzu

~2

,16(IV)

11 Chichin 12 Hsiaokang

i i]

298.80(I1) 366.70(1II) 397.74(1V)

in 28p.93(IV) i i

366.33(1II7

~3. 2o79;~ 254.~](111;-.

05 ,

S

x

.4

4,3.02..

'L/''~, -~\ '£~,

I... ~9',,,

"'..'-.,.,,,,

~ \

(II)

140.54(111) 70.0~IV)

\

~x ~x ~ ~("~x

459.92(I1) 559.42(III) 616.26(IV)

. ", "x , x 24149(1I) . ~ "'. " , \ 'x/49.21(III) . f . ' - . ". ", \ '~" 49.20(I"4)

89.54(IV)

147.g5(IV) 206.26(II) 249.46(III) 273.63(IV)

.1o. l

Legend

101.02(II) 128.67(1II) 146.19(1V)

611.30(11)'-'~ "~, "7~t~"TCaTTIX

".

158.26(11),~ 191.00(III)'

i'

Sources of waste generation •

Existmg t r e a ~ t

•

Proposed sites of resource recov~y plants

•

Proposed site of sanitary landfill

m

2~.~s~, ~12

facilities

Proposed sites of transfer stations

Fig. 3. The optimal waste flow pattern in case 3 (unit TPD).

N.-B. Chmg, S.F. Wang/ European Journal of Operational Reseurch Table 4 The results of cost/benefit

analvsis

of each case

cost Case 1 Case 2 Case 3

Total cost

Transportation

Construction

Operating

Recycling

29,459 34,527 34,784

6,469 2,904 9,413

8,098 6,441 8,772

279,925 411,332 44,144

* Unit: 1993 millions NT$. * ’ The currency ratio is 26 NT$/l

323,95 1 455,204 97,113

Benefit Electricity

Recycling

7.09 I 417 7,769

13,745 16,217 4,106

cost q operating

cost H construction

cost IZ recycling

70% 60% 50%

-

40% 30% 20% 10%

-

case 1

case 2

Fig. 4. The comparative Cl electricity

income

case 3

cost structure of each case. kS!paper

q plastics

R glass

metal

100% 90% 80% S ‘s .$ z a S S 8

Net cost

20,836 16,634 I I.875

303,l I5 438,570 85,240

cost

80%

2 0

Total benefit

US. •i transportation

S ‘< g S 5

317

99 (1997) 303-321

70% 60% 50% 40% 30% 20% 10%

case

I

Fig. 5. The comparative

case 2 benefit structure of each case.

case 3

318

N.-B. Chang, S.F. Wang / European Journal of Operational Research 99 (1997) 303-321

1334

170 62

Traffic flo~ (P.CI l)

Air Quality TSP SI')x (~tg/m3) (ppb)

Noise Level (dBA)

Traffic fl.x~ (P.Cl l)

TSP (~tgim~)

S( )x (ppb)

Noise Level (dBA)

Fig. 6. The results of comparative impacts for environmental risk at the site of Nantzu incinerator (left) and Fudingjin incinerator (right).

is favored in case 3 with lower level of recycling activity, the required tipping fee reaches its minimum level. This implies that the benefit of energy recovery through the use of waste incineration facilities is overwhelming. In addition, because the option of incineration is favoured in case 3, the objective function value, that stands for the total cost incurred in the system, is much lower than the values in the other cases. For the purpose of demonstration, Fig. 3 illustrates the optimal pattern of waste stream allocation in case 3. Table 4 specifically expresses the cost and benefit distributions for all cases. Since recycling programs require relatively higher cost in Taiwan, it constitutes most of the expenditure. However, the avoided cost by recycling represents a specific type of indirect benefit which might be overwhelming in this system. To clearly understand the cost/benefit distribution, Fig. 4 and Fig. 5 illustrate the comparative structure of cost and benefit distributions for all cases. However, the most difficult estimation in such a large scale solid waste management system might be the environmental impacts in various types of planning alternatives. Fig. 6 therefore delineates such estimations of comparative impacts for two incineration sites selected in the optimization analysis. The outcome may provide a trade-off basis in the final decision making process.

4. Conclusions This analysis has verified that the proposed fuzzy goal mixed integer programming model is an effective tool for generating a set of more flexible optimal solutions in solving real-world complicated solid waste management issues. Although the environmental impacts and economic values are difficult to be compared with each other in the deterministic goal programming model, the fuzzy goal programming approach can successfully handle such an analysis. Both engineering considerations and management targets are tied together by using the fuzzy descriptions in the multi objective solid waste management system. The incorporation of grey systems theory in such a fuzzy analytical framework might be a valuable extension work in the future.

Appendix A. Notation

A.1. Definition of sets I I~

Set of linkages between system components in the transportation network in each period. Set of incoming waste stream at a specific site in each period.

N.-B. Chang, S.F. Wang/European Journal of Operational Research 99 (1997) 303-321

12 J JL J2 J3 J4 K KI K2 K3 K4 L R T' M

319

et of outgoing waste stream at a specific site in each period. et of all new system components (J~ t3 J2 U J3 U J4) in each period. Set of all new waste generation districts (point sources) in the system. Set of all new waste transfer stations in the system in each period. Set of all new waste treatment plants in the system in each period. Set of all new waste landfills in the system in each period. Set of all old system components (K~ U K z W K 3 t.) K4) in each period. Set of all old waste generation districts (point sources) in the system in each period. Set of all old waste transfer stations in the system in each period. Set of all old waste treatment plants in the system in each period. Set of all old waste landfills in the system in each period. Set of types of trucks used for shipping waste in the system. Set of resources recovered at facilities and households. Set of time period ({ 1. . . . . T}). Set of all intermediate facilities in each period.

A.2. Definition of input variable T

The number of total time periods in the planning horizon. Waste generation rate in municipal district i at time t. Unit transportation cost among system components at time period t. COk~ Unit operating cost at facility k at time period t. Variable construction cost at facility k at time period t. CCk t CRj~ Recycling cost of material i at time period t. Fixed cost for building new facility at site k at time period t. Fk, Recovery factor of resource i per unit waste processed at facility k at time period t. Tik~ Reduction ratio of waste destroyed by the processing at site k and time t. Rk max k The maximum allowable capacity at site k. The minimum required capacity at site k. min k N, The specified number of available potential sites in a time period t. The maximum number of treatment train for waste incineration which can be initialized in the NL optimization process. The maximum number of treatment train for waste incineration which can be expanded in the N2 optimization process. Time The length of time within one time period t (conversion factor). Discount factor for time period t. 13, Nominal interest rate. r Estimated inflation rate. f Net income per unit weight of secondary material j by household recycling in district i and at time Rijkt period t. The price of each resource i recovered at site k at time period t. Pikt oLijt.mnx Maximum fraction of recyclables which can be recovered in the waste stream G~i,. CU The conversion factor between the garbage truck unit and passenger car unit. The maximum designed traffic capacity on the main entrance road at each facility at time period t. C;k, The average background traffic flow on the main entrance road at each facility at time period t. V;k, Pl The allowable weight loading of different types of trucks. Required service level of main road connecting different system components at time period t. SL/k t Git CTjkr

320

N.-B. Chang, S.F. Wang~European Journal of Operational Research 99 (1997) 303-321

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. Limit k Total tolerance of pollutant p in the incoming waste stream at landfill k. The transport and transformation factor corresponding to the linkage between plant 'k' and receptor 'b' Akbp for pollutant ' p'. A conversion factor regarding the time scale difference between the units of emission factor (ENp) and f National Ambient Air Quality Standard (Sp). The flue gas production ratio, based on burning one ton of solid waste in the incinerator. FGR The emission standard of pollutant p in the time period t. s,,, The background concentration of air pollutant p at the location of a specific receptor a at the time Bbpt period t. Spatial decay constant at site j, based on the local situation. Dj NI j The acceptable noise level of site j in the environmental regulations.

A.3. Definition of decision variables The upper limit in the multiobjective pay-off table, prepared for the construction of fuzzy membershipfunction. Ll, L2, L3, L4 The upper limit in the multiobjective pay-off table, prepared for the construction of fuzzy membershipfunction. fuzzy membership degree. tzi C 1, C 2 , C 3, C 4 The fuzzy membership function corresponding to these four objectives, respectively. Optimal waste stream among system components at time period t. Sjk, Binary integer variable for the selection of facility at time period t. L, Binary integer variable for the selection the ith treatment train of facility k in the initialization Zkiy time period y. Binary integer variable for the selection the ith treatment train of facility k in the expansion time period t, initialized in the time period y. Design capacity of a new facility at site k at time period t. OCt, Expansion capacity at new site k at time t based on the initialization of facility operation at NEXPkyt time period y. Total expansion capacity of a new or an old facility at site k at time t. TEXPkl The total system costs and benefits respectively at time period t. Ct, Bt Tipping fee charged per unit amount of waste at time period t. TIPt Total recycling fraction corresponding to waste inflow Gir £Zit Recycling fraction of material j corresponding to waste Gir Olijt Total amount of household recycling at time period t. TR t

u,, u2, u3, u~

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