fuzzy parametric programming model for multi-objective integrated solid waste management under...

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Integrated solid waste management systemLong term planningMulti-objective and multi-period planningFuzzy parametric programming

increasing waste quantities, changing waste composition, decreasing land availability for waste disposalsites and increasing awareness about the environmental risk associated with the waste management

plore the various alternatives in order to identify an optimal man-agement strategy. It is to be noted that the planning for an ISWMsystem for any urban centre is done for a long term, i.e., 20 or 25years.

The basic input for municipal solid waste (MSW) managementis the solid waste quantities which changes with respect to time

using interval programming, stochastic modelling and/or fuzzysystems. A number of researchers have applied these techniquesto consider the effect of uncertainty in the ISWM models. In inter-val programming approach the upper and lower bounds of coef-cients are determined and then deterministic model is used toaddress these upper and lower bounds. Interval programminghas been widely used by researchers to incorporate uncertaintyin ISWM (e.g. Cheng, Chan, & Huang, 2003; Huang, Baetz, & Party,1994, 1995a, 1995b; Huang, Baetz, Patry, & Terluk, 1997; Huang,Chi, & Li, 2005; Maqsood, Huang, & Zeng, 2004). It is to be notedthat, the output of interval programming method is with upper

Corresponding author.E-mail addresses: [email protected] (A.K. Srivastava), [email protected].

Expert Systems with Applications 39 (2012) 46574678

Contents lists available at

w

.eac.in (A.K. Nema).The regional solid waste management (SWM) system comprisesof many interrelated components including transportation, treat-ment and disposal. These interrelated components must be consid-ered in integration in order to arrive at an optimal wastemanagement plan. Mathematical models can be used to describethe objective, component interactions and available managementoptions. The mathematical models can be subjected to rigorousmethods of systems analysis for planning the integrated solidwaste management system (ISWM). The mathematical modelsprovide a systematic means by which the decision-maker can ex-

facilities is increasingly becoming a scarce resource due to growingawareness about the associated environmental risk in the proxim-ity to these facilities. In order to cope with the uncertainties in-volved in the solid waste quantities and available capacities ofwaste management facilities, an efcient and sustainable solidwaste management plan is required.

2. Literature review

In an optimization model, the uncertainty can be addressed by1. Introduction0957-4174/$ - see front matter 2011 Elsevier Ltd. Adoi:10.1016/j.eswa.2011.09.022facilities. The present study focuses on the optimum selection of the treatment and disposal facilities,their capacity planning and waste allocation under uncertainty associated with the long-term planningfor solid waste management. The fuzzy parametric programming model is based on a multi-objective,multi-period system for integrated planning for solid waste management. The model dynamically locatesthe facilities and allocates the waste considering fuzzy waste quantity and capacity of waste manage-ment facility. The model addresses uncertainty in waste quantity as well as uncertainties in the operatingcapacities of waste management facilities simultaneously. It was observed that uncertainty in wastequantity is likely to affect the planning for waste treatment/disposal facilities more as compared withthe uncertainty in the capacities of the waste management facilities. The relationship between increasein waste quantity and increase in the total cost/risk involved in waste management is found to be non-linear. Therefore, it is possible that a marginal change in waste quantity could increase the total cost/risksubstantially. The information obtained from the analysis of modeling results can be effectively used forunderstanding the effect of changing the priorities and objectives of planning decisions on facility selec-tions and waste diversions.

2011 Elsevier Ltd. All rights reserved.

at an increasing rate. Also the land available for the waste disposalKeywords:Solid waste management

Solid waste management is increasingly becoming a challenging task for the municipal authorities due toFuzzy parametric programming model fowaste management under uncertainty

Amitabh Kumar Srivastava a,, Arvind K. Nema baBundelkhand Institute of Engineering & Technology, Kanpur Road, Jhansi 284128, IndibDepartment of Civil Engineering, Indian Institute of Technology Delhi, Huaz Khas, New

a r t i c l e i n f o a b s t r a c t

Expert Systems

journal homepage: wwwll rights reserved.multi-objective integrated solid

hi 110016, India

SciVerse ScienceDirect

ith Applications

lsevier .com/locate /eswa

Nomenclature

IndicesT total planning periodS total number of solid waste source nodes, i.e. population

centersI total number of transfer stations cum segregation/

sorting facilitiesJn total number of new landllsJe total number of existing landllsJ total number of landllsRe total number existing recycling facilitiesRn total number new recycling facilitiesR total number recycling facilitiesKe total number of existing compost facilitiesKn total number of new compost facilitiesK total number of compost facilitiesM total number of waste componentst index for time (1, . . . , t)s index of solid waste source nodes, i.e. population cen-

tersi index of transfer stations cum segregation/sorting facil-

itiesjn index of new landllsje index of existing landllsj index of existing landlls (j = je [ jn)re index of existing recycling facilitiesRn index of new recycling facilitiesR index of recycling facilities (r = re [ rn)ke index of existing compost facilitieskn index of new compost facilitiesk index of compost facilitiesm index for solid waste composition (m = 1 for paper; m

= 2 for plastic; m = 3 for food; m = 4 for metals; m = 5for glass and m = 6 for others mainly inert)

Input dataTCsit unit transportation cost for unit quantity of waste be-

tween source/population center and transfer stations(in s i t matrix)

TCijt unit transportation cost for unit quantity of waste be-tween transfer stations and landlls (in i j t matrix)

TCilt unit transportation cost for unit quantity of waste be-tween transfer stations and incinerators (in i l t ma-trix)

TCikt unit transportation cost for unit quantity of waste be-tween transfer stations and compost plants (in i k tmatrix)

TCirt unit transportation cost for unit quantity of waste be-tween transfer stations and recyclingcenters (in i r tmatrix)

TCrjt unit transportation cost for unit quantity of waste be-tween recycling centers and landlls (in r j tmatrix)

TCrlt unit transportation cost for unit quantity of waste be-tween recycling centers and incinerators (in r l tmatrix)

TCkjt unit transportation cost for unit quantity of waste be-tween compost plants and landlls. (in k j t matrix)

TCklt unit transportation cost for unit quantity of waste be-tween compost plants and incinerators (in k l tmatrix)

TCljt unit transportation cost for unit quantity of wastebetween incinerators and landlls (in l j t matrix)

OCit operating cost of transfer stations cum segregation ifacilities during time t (in i t matrix)

OCrt operating cost of recycling centers r during time t (inr t matrix)

OCkt operating cost of compost plant k during time t (ink t matrix)

OClt operating cost of incinerators l during time t (in l tmatrix)

OCjt operating cost of landlls j during time t (in j t ma-trix)

CCjnt capital cost of new landlls jn during time t (in jn tmatrix)

CCknt capital cost of new compost plants kn during time t (inkn t matrix)

CClnt capital cost of new incinerators ln during time t (inln t matrix)

ICtm unit selling rate of waste material m during time t (int m matrix)

IKt unit selling rate of compost during time t (in t 1 ma-trix)

Gst quantity of waste generated at populationcenter/sources during time period t (in s t matrix)

Ljs air attenuation factor from landll j to source/populationcenter s for dispersion of risk through air (in j s ma-trix)

Ljs sub attenuation factor from landll j to source/populationcenter s for dispersion of risk through subsurface med-ium (in j s matrix)

Lls attenuation factor from incinerator l to source/popula-tion center s for dispersion of risk (in l s matrix)

Rjair risk factor from landll j through air medium (in j 1matrix)

Rjsub risk factor from landll j through air medium (in j 1matrix)

Rlair risk factor from landll l through air medium (in l 1matrix)

Hst population at source/population centers s during timet (in s t matrix)

HVm caloric value of individual waste component m (inm 1 matrix)

RHVl rated heating value of incinerator l (in l 1 matrix)CQj cumulative capacity of landll j (in j 1 matrix)Qujt maximum operating capacity of landll j during time t

(in j t matrix)Qult maximum operating capacity of incinerator l during

time t (in l t matrix)Qukt maximum operating capacity of compost k during time

t (in l t matrix)Qljt minimum operating capacity of landll j during time t

(in j t matrix)Qllt minimum operating capacity of incinerator l during

time t. (in l t matrix)Qlkt minimum operating capacity of compost k during time

t (in k t matrix)x ratio of rejects and incoming waste at recycling centers

(in single number)n ratio of rejects and incoming waste at compost plants

(in single number)w ratio of residue and incoming waste at incinerators (in

single number)dij direct radial distance between locations i and j (in i j

matrix)aj exponent term depends on site conditions such as wind

speed, turbulence (in j 1 matrix)/j angle between directions of plume centerline from the

reference axis (in j 1 matrix)

4658 A.K. Srivastava, A.K. Nema / Expert Systems with Applications 39 (2012) 46574678

ms w#ij angle between line joining to point j and i (in i j ma-trix)

R summation of the risk due to various sources (singlenumber)

Tr1 individual risk from source 1 (single number)Tr2 individual risk from source 2 (single number)Trn individual risk from source n (single number)pj tolerance in maximum capacity of landll j (in j 1

matrix)pl tolerance in maximum capacity of incinerator l (in l 1

matrix)pk tolerance in maximum capacity of compost k (in k 1

matrix)pj tolerance in minimum capacity of landll j (in j 1

matrix)pl tolerance in minimum capacity of incinerator l (in l 1

matrix)pk tolerance in minimum capacity of compost k (in k 1

matrix)ast lower extreme deviation in waste quantity at source s

during time t (in s t matrix)bst upper extreme deviation in waste quantity at source s

during time t (in s t matrix)

Decision variables/outputsWsit quantity of waste to be transported from source s to

transfer station i during time t

A.K. Srivastava, A.K. Nema / Expert Systeand lower bounds, but it does not reect the distribution of uncer-tainty within the upper and lower bounds. However, the fuzzy lin-ear programming can effectively reect uncertainties due tohuman impreciseness with the distribution represented by anappropriate membership function. The optimization techniqueswith fuzzy theory have been used for addressing the solid wastemanagement problems by various researchers, e.g. Chang, Chen,and Wang (1997) and Chang and Wang (1997).

Minimax regret optimization technique is a technique whichcan reduce a problem with uncertainty into a number of sub-problems with certainty. These sub-problems are subjected to analgorithm where the regret (of not achieving the objective, in caseof the prevailing uncertainty) is minimized (Igor, 2000). This tech-nique has been used for addressing the solid waste managementproblems under uncertainty by researchers including Chang andDavila (2006, 2007) and Li and Huang (2006a).

The interval programming technique was improved by Li andHuang (2006b) and Li, Huang, Nie, and Huang (2006) by proposinga two-stage programming technique in which uncertainties can beexpressed as discrete values at certain intervals instead of proba-bility distribution functions. The two stage interval programmingwas further modied using chance-constrained programming byLi, Huang, Nie, and Qin (2007). The chance constraint interval pro-gramming can address to the uncertainties represented by a givenprobability distributions within the given discrete intervals.

Nie, Huang, Li, and Liu (2007) used an interval-parameter fuzzy-robust programming, in which the input parameters are repre-sented as interval numbers of fuzzy membership functions. In thistechnique it is assumed that the complexity of the real world canbe effectively handled using the fuzzy boundary intervals.

Wijtm quantity of waste material m to be transported fromtransfer station i to landll j during time t

Wkjtm quantity of waste material m to be transported fromcompost plant k to landll j during time t

Wljt quantity of waste to be transported from incinerator lto landll j during time tWrjtm quantity of waste material m to be transported fromrecycling centers r to landll j during time t

Wiltm quantity of waste material m to be transported fromsource i to incinerator l during time t

Wrltm quantity of waste material m to be transported fromrecycling centers r to incinerator l during time t

Wkltm quantity of waste material m to be transported fromcompost plant k to incinerator l during time t

Wiktm quantity of waste material m to be transported fromtransfer stations i to compost plants k during time t

ajet binary variable if equal to 1 then existing landll je is inoperation during time t otherwise 0

alet binary variable if equal to 1 then existing incinerator leis in operation during time t otherwise 0

aket binary variable if equal to 1 then existing compost ke isin operation during time t otherwise 0

bjnt binary variable if equal to 1 then new landll jn is inoperation during time t otherwise 0

blnt binary variable if equal to 1 then new incinerator ln isin operation during time t otherwise 0

bknt binary variable if equal to 1 then new compost kn is inoperation during time t otherwise 0

b0jnt binary variable if equal to 1 then new landll jn isstarted during time t otherwise 0

b0lnt binary variable if equal to 1 then new incinerator ln isstarted during time t otherwise 0

b0knt binary variable if equal to 1 then new compost kn isstarted during time t otherwise 0

ith Applications 39 (2012) 46574678 4659Inexact semi innite programming technique (He and Huang,2004) takes input parameters in given intervals which are repre-sented as the functions of time. This technique is applied to solidwaste management problem by He, Huang, Zeng, and Lu (2008),Guo, Huang, He, and Sun (2008) and Guo, Huang, and He (2008).The inexact semi innite programming is proved more useful thanthe interval programming approach because it reected the dy-namic feature of the input variables (e.g., changing waste quanti-ties with respect to time) (Guo, Huang, He, & Zhu, 2009).

Li, Huang, Yang, and Nie (2008) used two stage linear program-ming with fuzzy robust optimization. In two stage programming,initially waste allocation is decided based on the denite quantityof waste generation at the source then the deviated waste quantityis allocated to an available facility. The excess cost due to theseadditional waste quantities is calculated and termed as the penaltycosts (Li, Huang, Nie, & Nie, 2008).

The techniques based on fuzzy linear programming enables usto consider uncertainties in the values of decision variables in amore natural and direct way (Zimmermann, 1987). The fuzzy lin-ear programming is suitable in the situation where uncertaintiesin some of the parameters can be consciously assumed by the deci-sion-maker (Liang, 2008; Pramanik & Roy, 2008). Fuzzy linear pro-gramming formulations can be solved using the approachsuggested by Bellman and Zadeh (1970). In this approach a maxi-mization problem can be reduced to a deterministic (non-fuzzy)linear programming problem enabling the use of the simplexmethod. A certain disadvantage of this approach is the fact thatone obtains only the maximizing alternative losing the informationon the fuzzy decision. A fuzzy decision should provide informationon other alternatives which are close to the optimal solutions.

yjt cumulative waste quantity reaching landll j till timet

h possibility level of uncertainty in waste quantityc threshold level of uncertainty in capacityl~Git membership function for waste quantityl~kjt membership functions for capacity

Chanas (1983) proposed a method to overcome the limitationsof BellmanZadehs approach by using the fuzzy parametric pro-gramming approach. Chanass approach identies a complete fuzzydecision for the fuzzy mathematical programming problem. Theefcient application of fuzzy parametric programming over theother fuzzy linear programming techniques has been demon-strated by Carlson, Tavares, and Formigoni (1998) and Fung, Tang,and Wang (2003) for long term production planning problems.

In the present study, fuzzy parametric programming has beenused for addressing the uncertainty involved in the solid wastemanagement planning. The fuzzy parametric programming is hav-ing denite advantage while addressing to the uncertainties in-volved in the waste quantities and the capacity constraints ontreatment and disposal facilities. Also this approach is uniquedue to the fact that it gives a set of alternatives which are closeto the optimal solutions rather than suggesting a unique solutionas the optimal solution. A brief description of the fuzzy parametricprogramming approach is given in the subsequent section.

2.1. The fuzzy parametric programming approach

Eq. (2) can be rewritten asXnj1

aijxj 6 bi u qi; i 1;2; . . .m 4

where parameter u0 6 u 6 1 can be interpreted as the degree ofconstraints violation. Chanas (1983) has demonstrated that theminimum value of objective function of Eq. (1) can be representedas analytically dependent on u and is a continuous, piece-wise lin-ear and concave function in u. Therefore, above fuzzy linear pro-gramming is converted into Eq. (1) and Eq. (4) and can be solvedby substituting different values of u between 0 and 1. The fuzzyparametric programming approach for the planning of ISWM isshown in Fig. 1.

3. Developing the model

3.1. Denition of the system

The proposed model formulation addresses to the waste man-agement problem consisting of a number of waste generationsources with changing waste quantities and characteristics, a set

4660 A.K. Srivastava, A.K. Nema / Expert Systems with Applications 39 (2012) 46574678Let us consider the following fuzzy linear programmingproblem:

min cx; 1

Xnj1

aijxj 6 ~bi; i 1;2; . . . ;m; 2

where x are decision variables, a and c are coefcient. In this prob-lem, constraints b are fuzzy number therefore, denoted as ~b. Let themembership function of fuzzy constraint is

lix 1 siqi if

Pnj1

aijxj bi si

1 ifPnj1

aijxj 6 bi

8>>>>>: 3where qi is the maximum value of the violation si admissible in theith constraints.

The fuzzy linear programming problem given in Eqs. (1)(3) canbe solved by fuzzy parametric programming approach (Chanas,1983) as explained below.Fig. 1. Proposed fuzzy parametric programof existing treatment and disposal facilities at given locations, aset of candidate sites for the treatment and disposal facilities andtransportation routes (Fig. 2). The aim of the ISWM planning is toship the solid waste generated in the region to a suitable treatmentor disposal site within a certain period of time after its generation.

The set of waste generation sources and transfer stations arerepresented by s and i, respectively. j represents the set of land-lls in which jn are the new landlls and je are the existing landlls(j = je [ jn). The set of recycling facilities is represented by r,whereas, k and l represent the sets of compost and incineratorsrespectively. For each of the waste management facilities, the sub-script e and n shows the existing facilities and the new facilitiesrespectively (i.e. r = re [ rn, k = ke [ kn, l = le [ ln). The total planningperiod T in divided in the steps of t periods (t e T).

3.2. Objective function

The objectives considered in the model for optimization are (i)total cost and (ii) environmental riskming approach for ISWM planning.

k for proposed model formulation.

ms with Applications 39 (2012) 46574678 4661Minimize f1 Total Cost 5Minimize f2 Environmental Risk 6The details of methodology used to calculate the total cost andenvironmental risk are summarized below.

3.3. Estimation of cost

The total cost is estimated as the sum of the cost of transporta-tion, operating cost of treatment, and the xed cost for opening of anew facility minus the income from recycling and compost facili-ties. The transportation cost include cost will be incurred in trans-portation of waste from population center or source nodes totransfer station cum segregation facilities, then from segregationfacilities to treatment or disposal facilities. The cost incurred inthe transportation of waste residue from treatment facilities to dis-posal facilities has also been included. The operating cost of facili-ties is cost of processing the waste at treatment and disposalfacilities. All the cost components have been converted into thesame base year by discounting all the costs at their present worth

Total cost Transportation cost Operating cost Capital cost for new facilities Income from sale of recyclables and compost;

6whereas,

Transportation cost Xs

Xi

Xt

Wsit TCsit

Xi

Xj

Xt

Xm

Wijtm TCijt !

XXX X !

Fig. 2. The waste ow networ

A.K. Srivastava, A.K. Nema / Expert Systei l t m

Wiltm TCilt

Xi

Xk

Xt

Xm

Wiktm TCikt !

Xi

Xr

Xt

Xm

Wirtm TCirt !

Xr

Xj

Xt

Xm

Wrjtm TCrjt !

Xr

Xl

Xt

Xm

Wrltm TCrlt !

Xk

Xj

Xt

Xm

Wkjtm TCkjt !

Xk

Xl

Xt

Xm

Wkltm TCklt !

Xl

Xj

Xt

Wljt TCljt

; 7whereas TCsit is the transfer cost for unit waste quantity from sourcenodes/population centers to transfer stations cum segregation facil-ities. Similarly, TCijt is the transportation cost for unit quantity ofwaste to be transported between source, i and landll j and Wijtmis the quantity of m type waste to be transported from source iand landll j during time period t. Similarly other terms can bedened.

Total operating cost and capital cost of the waste managementfacilities are computed using Eqs. (8) and (9), respectively

Operation cost Xs

Xi

Xt

Wsit OCit

Xj

Xt

Xi

Xm

Wijtm Xk

Xm

Wkjtm

Xr

Xm

Wrjtm Xl

Wljt

!

OCjt Xk

Xt

Xi

Xm

Wiktm

!

OCkt Xr

Xt

Xi

Xm

Wirtm

!

OCrt Xl

Xt

Xi

Xm

Wiltm Xk

Xm

Wkltm

Xr

Xm

Wrltm

! OClt; 8

where OC is the operating cost of facility for unit waste quantity, e.g.OCjt is the capital cost needed to start new landll jn during time t

Capital cost CCj t b0j t CCknt b0k t CClnt b0l t

; 9

n n n n

sta0

1

stG stb

stG

i

sitW

Fig. 3. Membership function for solid waste quantities.

ms wwhere CC is the capital cost required to start new facility, e.g. CCjnt isthe operating cost of landll j during time t and b0 is binaryvariable.

It is assumed that some of the facilities already exist before theplanning, therefore, the capital cost is calculated only for new facil-ities (Eq. (9).

Total income from the recycling and composting is estimatedusing Eq. (10)

Income Xt

Xm

Xr

Xi

Wirtm ICtm !

Xt

Xm

Xi

Xk

Wiktm IKt !

: 10

ICtm is the unit selling rate of waste material m during time t andIKt is the income from selling of compost during time period t.

3.4. Estimation of environmental risk

Waste management facilities pose environmental risk due topossible release of pollutants (Townsend, Dubey, & Tolaymat,2006). The landll poses the environmental risk by the emissionof landll gases and leachate, whereas the incinerator may causeair pollution problems. Other facilities like composting and recy-cling also pose environmental risk.

Individual risk from the solid waste management facilities canbe calculated as the product of probability of release of contami-nant and its consequences in term of hazard (Rapti, Sdao, & Masi,2006; Valberg, Drivas, McCarthy, & Watson, 1996; Wakeeld &Elliott, 2000).

Individual risk Probability of contaminant release hazard: 11

The hazard to individual population from the solid waste is directlyproportional to the total waste quantity to be treated at the facility.The hazardous consequences to the receptors are considered to beattenuated with distance due to dispersion of pollutant and barriereffect of the pathway. Attenuation of environmental risk to the pop-ulation centers (Melachrinoudis & Cullinane, 1986) is considered tobe in the inverse proportion of distance (i.e. Lij / d1ij ), where Lij isthe attenuation factor from location j to i and dij is the direct radialdistance between locations i and j.

Erkut and Neuman (1993) proposed that the environmental riskdecreases exponentially (i.e., Lij / dajij ) with distance, where expo-nent term aj depends on site conditions such as wind speed, tur-bulence, etc. Giannikos (1998) proposed an asymmetric functionand introduced a term for direction/angle (i.e. Lij / dijfunction/j). Here/j is the angle between directions of plume centerline from the ref-erence axis (e.g. prevailing wind direction at the sites).

Melachrinoudis, Min, and Wu (1995) improvised the asymmet-ric function, by incorporating the exponent term as well as direc-tion of the pollutant plume. The attenuation function can bedescribed as Lij / dajcoshij/iij , where hij is angle between line join-ing to point j and i. This function has been used in the proposedmodel for computing the factor Lij for attenuation of hazardousconsequences. This attenuation function will give a dimensionlessnumber which is called as attenuation factor. Now the individualrisk to the receptor can be written as

Individual risk at the receptor

Probability of contaminant releaseWaste quantity attenuation factor: 12

4662 A.K. Srivastava, A.K. Nema / Expert SysteThe individual risk dened above includes the probability term. Therisk to the receptor from various waste management activities canbe estimated as proposed by Kara, Erkut, and Verter (2003) and gi-ven in Eq. (13)

R Tr1 Tr21 Tr1 Tr31 Tr11 Tr2 Trn1 Tr11 Tr2 1 Trn1; 13

where R = summation of the risk due to various sourcesTr1 = individual risk from source 1Tr2 = individual risk from source 2Tr3 = individual risk from source 3. . .

Trn = iIndividual risk from source n

The above equation (Eq. (13) is nonlinear and hence difcult touse in case of large scale real life problems. The individual risk fromthe waste management facilities normally are of the order of 105

to 104 for per million ton of the waste (Moy, 2005). It is to benoted that the risk further reduces due to the attenuation factor.Erkut and Verter (1998) have suggested that above equation canbe expressed in a simple additive form with a negligible error

R Tr1 Tr2 Tr3 : 14In the present model the individual risk is considered as summationof risk due to landlls and incinerators and the total environmentalrisk is calculated by multiplying with the population exposed.

3.5. Constraints

The problem is subjected to following absolute constraints.

3.5.1. Mass balance of waste at each nodeThis mass balance constraint at waste generation source en-

sures that all the waste quantities generated at various sourcesmust be transported to the transfer stations cum segregation facil-ities which are written as Eq. (15)Xi

Wsit Gst 8s; t: 15

In Eq. (11) Gst and Wsit are the waste quantity generated at sourceduring time t and waste quantity to be transported from sources to transfer station cum segregation facilities s.

Solid waste quantity (Gst) computed in Eq. (15) is assumed asfuzzy and denoted by eGst Gst; ast; bst where Gst, Gst ast andGst + bst are the most possible, most pessimistic and most optimis-tic value of solid waste quantities generated at source s duringtime t. ast and bst dene the extreme deviations of waste quantityat sources during time t on left hand and right hand side respec-tively. The Eq. (15) can be written as Eq. (16) incorporating fuzzynumber and inequalitiesXi

Wsit ~Gst 8s; t: 16

The aspiration level of decision maker (DM) is expressed using thefuzzy number following the memberships function. The fuzzy wastequantities as shown in Fig. 3 can be expressed as Eq. (17), incorpo-rating the aspiration level with respect to uncertain wastequantities

leGst 0;

PiWsit 6 Gst ast;

1 GstP

iWsit

ast; Gst ast 6

PiWsit 6 Gst;

1P

iWsitGst

; Gst 6P

Wsit 6 Gsit bst ;

8>>>>>>>>>>>>> 17

ith Applications 39 (2012) 46574678biti

0; else:

>>>>:

where HVm is caloric value of individual waste component m andRHVl is rated heating value of incinerator.

3.5.3. Capacity constraintsThe operating capacity of a treatment facility depends on sev-

eral factors including availability of equipments, manpower, etc.The waste reaching at a facility must be less than or equal to itscapacity. In addition to this a minimum operating capacities, con-straint is also imposed, which ensures the avoidance of gross re-source underutilization. The capacity constraints are divided intotwo categories, (i) cumulative capacities of the landlls over thetime and (ii) operating capacity of facilities for a unit time, which

ms with Applications 39 (2012) 46574678 4663The aspiration of the DM is completely fullled ifP

iWsit Gst . Italso means that the membership function leGst will be equal to 1.Whereas, if the minimum aspiration level is violated the conditionP

iWsit 6 Gst ast holds. This indicates that even the minimum tar-get of waste management will not be achieved resulting in com-plete dissatisfaction of the decision maker. In case of

PiWsit

varying between Gst ast and Gst + bst the satisfaction level will varybetween 0 and 1. For interpretation of the membership function indecision, the DM will be required to dene possibility level h ofwaste quantity deviation. With the incorporation of possibility levelh in Eq. (17), it can be expressed as Eq. (18)

l~Gitm P h: 18Eq. (16) can be written as Eqs. (19) and (20) and in order to includethe possibility level of deviation in waste quantitiesXi

Wsit P Git ait1 h 8i; t; 19

Xi

Wsit 6 Git bit1 h 8i; t; 20

At the waste segregation facilities, the waste stream is further di-vided into individual waste components and sends to further treat-ment and/or disposal facilitiesXr

Wirtm1;2;4;5 Xl

Wiltm1;2 Xk

Wiktm3 Xj

Wijtm6

Witm 8i; t;m: 21The waste stream reaching at recycling centers will be processed forrecovery of recyclables and the refuse and residue generated atrecycling facilities must be transported to either incinerator orlandlls. Waste reaching at incinerator is burnt and converted intoashXj

Wrjtm Xl

Wrltm xXi

Wirtm 8r; t;m; 22

Xj

Wkjtm Xl

Wkltm nXi

Wiktm 8k; t;m; 23

Xj

Wljt wXi

Xm

Wiltm Xk

Xm

Wkltm Xr

Xm

Wrltm

!8l; t;

24where x and n are the ratio of rejects coming out of recycling andcompost plant respectively. w is the ratio of ash residue generatedat incinerator. Wrjtm and Wrltm are the waste quantity of composi-tion m to be transported from recycling centers to landlls andincinerator respectively during time t. Wkjtm and Wkltm are thewaste quantity of composition m to be transported from compostto landlls and incinerator respectively during time t. Wljt is thequantity of waste residue to be transported for disposal fromincinerators.

3.5.2. Technological constraintsFor the successful operations of incinerator waste of certain

minimum caloric value must only used. The model formulationimposes this condition in the form of a constraint so that the calo-ric value of waste reaching at incinerator will not be less thanrated heating value of incineratorXm

Xi

Wiltm

! HVm

Xr

Wrltm HVm Xk

Wkltm HVm !

A.K. Srivastava, A.K. Nema / Expert SysteP RHVl 8l; t;25is considered as fuzzy constraint. The maximum operating capaci-ties of treatment/disposal facilities (Qu) are also represented byequivalent fuzzy number (fQu) with acceptable tolerance of p. Sim-ilarly minimum operating capacities (Ql) are represented by fuzzynumber, fQl with acceptable tolerance of p. The maximum operat-ing capacity constraints is expressed as fuzzy inequality (Eqs.(26)(28))Xi

Xm

Wijtm Xk

Xm

Wkjtm Xl

Wljt Xr

Xm

Wrjtm

6 eQujt ajet bjnt 8j; t; 26Xi

Xm

Wiltm Xr

Xm

Wrltm Xk

Xm

Wkltm

6 ~Qult alet blet 8l; t; 27X

i

Xm

Wiktm 6 eQukt aket bknt 8k; t: 28The minimum capacity constraints can be expressed as fuzzyinequality as shown in Eqs. (29)(31)Xi

Xm

Wijtm Xk

Xm

Wkjtm Xl

Wljt Xr

Xm

Wrjtm

P eQ ljt 8j; t; 29Xi

Xm

Wiltm Xr

Xm

Wrltm Xk

Xm

Wkltm P eQ llt 8l; t; 30Xi

Xm

Wiktm P eQ lkt 8k; t: 31The fuzzy capacity is assumed to be with a tolerance level that maynot remain available due to uncertainty involved. The membershipfunction (Fig. 4) for capacity (e.g. compost plant) reects the DMslevel of satisfaction as shown in Eq. (32)

iktmW

1

0

kti mktQl ktQukp kp

Fig. 4. Membership function for capacities of waste management facilities.

l~kjt

1; eQ lkt 6Pi

PmWiktm 6 Qukt;

1P

i

PmWiktmQuktpk

; Qlkt 6Pi

PmWiktm 6 Qukt pk;

1 QlktP

i

PmWiktm

pk; Qlkt P

Pi

PmWiktm 6 Qlkt pk

0; else

8>>>>>>>>>>>>>>>>>:32

The membership function for waste management facilities asshown in Fig. 4 is based on the assumption that, if waste quanti-ties reaching to a site are more than the available capacity thensatisfaction level of DM decreases and DM will be totally dissatis-ed if waste ow reaches beyond tolerance point of maximumcapacity (Qukt pk) resulting in infeasible condition. Similarly,the DM will also be totally dissatised if the waste quantity is be-low tolerance point of minimum capacity (Qlkt pk) because thecapacity will remain grossly underutilized. The satisfaction levelof the DM is at its maximum when the waste quantity is betweenthe estimated minimum and maximum operating capacities. For agiven threshold ck, the DMs satisfaction level (l P

i

PmWiktm P ck)

for compost plants capacities can be formulated as Eqs. (33) and(34)Xi

Xm

Wiktm 6 Qukt 1 ckpkt aket bknt

; 33

XX

Xi

Xm

Wiltm Xr

Xm

Wrltm Xk

Xm

Wkltm

6 ~Qult 1 clpl alet blet 8l; t; 36Xi

Xm

Wijtm Xk

Xm

Wkjtm Xl

Wljt Xr

Xm

Wrjtm

P Qljt 1 cjpj 8j; t; 37Xi

Xm

Wiltm Xr

Xm

Wrltm Xk

Xm

Wkltm

P Qllt 1 clpl 8l; t: 38In case of the landlls the available capacity of landll in the entireplanning period is an important consideration, which is restrictedby the site characteristics. Therefore, in case of landlls, one addi-tional constraint for exhaustible capacity is also imposed

yjt P CQj 8j; t; 39where CQj is total cumulative capacity of landll j.

3.5.4. Binary constraintsBinary constraints in the model ensure the inclusion capital of

new facilities if started. Moreover, the facilities will be in operationif it is receiving waste in a particular planning period. An additional

Table 1Planning periods.

Planning periods Years

Ist Planning period 20072009IInd Planning period 20092014IIIrd Planning period 20142019IVth Planning period 20192024

4664 A.K. Srivastava, A.K. Nema / Expert Systems with Applications 39 (2012) 46574678i m

Wiktm P Qlkt 1 ckpkt : 34

Threshold level for other facilities like incinerators and landlls canalso be formulated as shown belowXi

Xm

Wijtm Xk

Xm

Wkjtm Xl

Wljt Xr

Xm

Wrjtm

6 Qujt 1 cjpj ajet bjnt 8j; t; 35Fig. 5. Waste generation source and its treatment/management facilities of Delhi.

binary variable imposes constraint on the landlls, if it is closedonce then cannot be started.

The variable a and b used in above equations are binary in nat-ure for existing and new facilities. These binary variables should be1 if facility is receiving waste and 0 otherwise

e nXi

Xm

Wijtm Xk

Xm

Wkjtm Xl

Wljt Xr

Xm

Wrjtm

6 M ajet bjnt 8j; t; 41Xi

Xm

Wiltm Xr

Xm

Wrltm Xk

Xm

Wkltm

P a b 8l; t; 42

Table 2Projected waste quantities in different zones of Delhi.

Year Yearly waste quantity(Gst) (in 103 tons) in the zone

Shadhara (South) South zone Rohini Central zone Karol Bagh

2007 983 951 1093 749 3692008 1025 991 1139 780 3852009 1068 1033 1187 813 4012010 1114 1077 1237 848 4182011 1161 1122 1290 884 4362012 1210 1170 1344 921 4542013 1261 1220 1401 960 4742014 1315 1271 1461 1001 4942015 1370 1325 1522 1043 5152016 1429 1382 1588 1088 5372017 1489 1440 1654 1133 5592018 1551 1500 1723 1181 5832019 1615 1562 1795 1230 6072020 1682 1626 1869 1280 6322021 1751 1693 1945 1333 6572022 1825 1765 2028 1389 6852023 1902 1839 2113 1448 7142024 1982 1917 2203 1509 745

Table 3Solid waste composition of Delhi (in %).

Waste component

Paper Plastic Organic Metal Glass Others

5.60 6.00 38.60 2.00 1.00 46.80

(Source: Sharholy et al., 2008).

A.K. Srivastava, A.K. Nema / Expert Systems wTable 4The heating value of waste components.

Waste component Heating value (HVm) (kcal/kg)Paper 3440Plastic 6425Food 1810

Table 5Values of parameters used in this case study.

Parameters Value

Average transportation cost (TC) 1 Rs. 5.00 per ton per kmAverage operating cost for landll (OCj)1 Rs. 325.00 per tonAverage operating cost for incinerator (OCl)1 Rs. 1140.00 per tonAverage operating cost for compost (OCk)1 Rs. 35.00 per tonIncome from sell of recyclable2 (ICm) Metal Rs. 430.00 per ton

Glass Rs. 12.00 per tonPlastic Rs. 72.00 per tonPaper Rs. 22.00 per ton

Income from sell of compost3 (IKm) Rs. 9.00 per tonReduction ratio for incinerator3 (w) 0.8Ratio of rejects from compost plants3 (n) 0.1Ratio of rejects from recycling facilities3 (x) 0.1Fixed cost of new landlls3 (FCj) Bhati mines Rs. 30.6 106

Jaitpur Rs. 53.5 106Narela Rs. 76.05 106

1 CPHEEO (2000).2 Agarwal, Singhmar, Kulshrestha, and Mittal (2005).3 Personal Communication, Municipal Corporation of Delhi (2006).Xi

Xm

Wijtm Xk

Xm

Wkjtm Xl

Wljt Xr

Xm

Wrjtm

P aj t bj t 8j; t; 40

City Sadar West Civil lines Shadhara (North) Narela Nagafgarh

261 201 645 657 976 304 552272 209 672 684 1017 317 575283 218 701 713 1060 330 600295 227 730 744 1105 344 625308 237 761 775 1152 359 652321 247 794 808 1200 374 679335 257 827 842 1251 390 708349 268 862 878 1304 406 738364 279 899 915 1359 424 769379 291 937 954 1418 442 802395 304 976 994 1477 460 836412 316 1017 1036 1539 480 871429 329 1059 1079 1602 499 907446 343 1103 1123 1668 520 944465 357 1148 1169 1737 541 983484 372 1197 1219 1810 564 1025505 388 1247 1270 1887 588 1068526 404 1300 1324 1967 613 1113

Table 6Lifetime individual risk from landll for per million ton of solid waste.

Landlls (Rj) Incinerator (Rl)

Air emission Leachate emission Air emission3.9 1005 4.1 1005 3.9 103

ith Applications 39 (2012) 46574678 4665let letXi

Xm

Wiltm Xr

Xm

Wrltm Xk

Xm

Wkltm

6 M alet blet 8l; t: 43Xi

Xm

Wiktm P aket bknt 8k; t; 44

Xi

Xm

Wiktm 6 M aket bknt 8k; t: 45

In the above Eqs. (41), (43), and (45), the coefcient used M is a bignumber, which will be obviously quite larger than capacities. Inaddition two above binary variables, one more binary variable arecomputed for existing and new landlls, to prevent reopening oflandlls after closure (Eqs. (46) and (47)

ajet ajet1 a0jent 8j 2 e; t; 46

bjnt bjnt1 b0jnt 8j 2 n; t: 47

The following Eqs. (46) and (47) prevents reopening of landlls if itis closed

Xt

a0jnt 6 1 8j 2 n; 48

Xt

b0jnt 6 1 8j 2 e: 49

The binary variable b0 also ensures inclusion of x cost in the totalcost at the time of commissioning of new facilities. Therefore, thisvariable must also be computed for compost and incineration facil-ities (Eq. (50) and (51)

blnt blnt1 b0lnt 8l 2 n; t; 50

bknt bknt1 b0knt 8k 2 n; t 51It can be seen that the presented fuzzy model is a non-linear modelin case of unknown waste quantity and value of h and c. The modelis solved as fuzzy parametric programming model using theapproach proposed by Chanas (1983).

4. Example problem

The utility of the model is demonstrated by an example prob-lem, which is inspired from the case of solid waste managementin National Capital City of Delhi, India.

The waste ow network of example problem, consist of existingtwelve zones of MCD as population centres, one incinerator, two

Table 7Projected populations of Delhi. Source: Census of India (2001)

Zone Projected populations (Hst)

Ist Period IInd Period IIIrd Period IVth Period

Shadhra (S) 2,126,234 2,473,452 2,873,121 3,333,623South 2,055,918 2,391,653 2,778,104 3,223,377Rohini 2,362,296 2,748,064 3,192,105 3,703,734Central Zone 1,618,449 1,882,744 2,186,965 2,537,490Karol Bagh 798,593 929,005 1,079,117 1,252,077City Zone 564,205 656,341 762,395 884,591Sadar Bazar 433,617 504,428 585,935 679,849West Zone 1,394,609 1,622,351 1,884,496 2,186,542Civil Lines 1,419,721 1,651,564 1,918,430 2,225,915Shadhra (N) 2,109,325 2,453,781 2,850,272 3,307,112Narela 657,458 764,822 888,405 1,030,798Nagafgarh 1,193,705 1,388,639 1,613,020 1,871,554

Table 8Waste diversion for different values of h under constant c (=1) (waste quantities in 103 tons).

h Planning period Timarpur incinerator Compost Landlls

Ghazipur Bhalswa Okhla Ghazipur Bhalswa Bhatimines Jaitpur Narela

0.0 1 1159 1111 7300 1302 3889 5400 0 0 02 2284 2036 14,534 0 0 0 0 13,300 75633 2809 2504 17,877 0 0 0 0 13,300 12,3614 2755 6745 18,250 0 0 0 5560 13,300 13,300

0.1 1 1172 1205 7300 1316 3992 5400 0 0 02 2309 2058 14,696 0 0 0 0 13,300 77943 2840 2532 18,075 0 0 0 0 13,300 12,6464 2933 7023 18,250 0 0 0 5770 13,300 13,300

0.2 1 1185 1298 7300 1358 4068 5400 0 0 02 2334 2081 14,857 0 0 0 0 13,300 80263 2871 2584 18,250 0 0 0 0 13,300 12,9314 3112 7300 18,250 0 0 0 5980 13,300 13,300

0.3 1 1198 1392 7300 1432 4112 5400 0 0 02 2360 2104 15,018 0 0 0 0 13,300 82583 2903 2810 18,250 0 0 0 0 13,300 13,2164 3290 7578 18,250 0 0 0 6189 13,300 13,300

0.4 1 1211 1485 7300 1505 4156 5400 0 0 02 2385 2126 15,180 0 0 0 1554 12,638 75973 2934 3037 18,250 0 0 0 4158 13,300 9344

4666 A.K. Srivastava, A.K. Nema / Expert Systems with Applications 39 (2012) 465746784 3470 7856 18,250

0.5 1 1224 1579 73002 2411 2149 15,3413 2965 3263 18,2504 3612 8134 18,2500.6 1 1237 1672 73002 2436 2171 15,5033 2996 3490 18,2504 3650 8411 18,250

0.7 1 1249 1766 73002 2461 2194 156643 3027 3716 182504 3688 8689 18250

0.8 1 1262 1859 73002 2487 2217 15,8263 3059 3943 18,2504 3726 8967 18,250

0.9 1 1275 1953 73002 2512 2239 15,9873 3090 4169 18,2504 3764 9245 18,250

1.0 1 1288 2046 73002 2537 2262 16,1493 3121 4395 18,2504 3802 9522 18,2500 0 0 6397 13,300 13,300

1578 4200 5400 0 0 00 0 0 1571 12,773 76780 0 0 4343 13,300 94430 0 0 6643 13,300 13,300

1652 4245 5400 0 0 00 0 0 1587 12,907 77590 0 0 4529 13,300 95430 0 0 6993 13,300 13,300

1725 4289 5400 0 0 00 0 0 1604 13042 78390 0 0 4648 13300 97090 0 0 7343 13300 13300

1799 4333 5400 0 0 00 0 0 1620 13,176 79200 0 0 4696 13,300 99460 0 0 7693 13,300 13,300

1872 4377 5400 0 0 00 0 0 1648 13,300 80010 0 0 4744 13,300 10,1830 0 0 8043 13,300 13,300

1946 4422 5400 0 0 00 0 0 1799 13,300 8082

0 0 0 4791 13,300 10,4210 0 0 8392 13,300 13,300

compost and six landlls (three existing and three candidate sites)of Delhi (Fig. 5). From each of these zones the waste is to be trans-ported to waste management facilities. As per MSW rule the wastebefore transportation to a waste management facilities must besegregated. Therefore, the transfer station is assumed to also actas segregation facilities. These distances are computed from themap of Delhi (http://www.mapmyindia.com) and are based onthe existing road network in Delhi.

The long termmunicipal solid waste management plan involvesactivities associated with transfer and transport, location andcapacity planning of processing, recovery and disposal facilitiesand waste allocation for these facilities. The recommended plan-ning period for long term planning is 1525 years (CPHEEO,2000). However, as a good management practice, the duration ofinitial design period is kept small to take corrective measures ifany (Huang et al., 1997). Taking consideration of above viewsand keeping in view the master plan for Delhi 2021, the planningperiod of present study is considered to be 17 years divided intofour periods (Table 1).

4.1. Waste quantities and composition

Assessment of current and future waste streams is essential andindispensable fundamental in waste management planning (Beiglet al., 2008). In this study, future quantities of waste generation

are estimated based on population forecast and waste generationfactor. Per capita average waste generation in Delhi is estimatedas 0.475 kg/day (Sharholy, Ahmad, Mahmood, & Trivedi, 2008)and also estimated to increase by 1.33% annually (Sharholy et al.,2008). The estimated waste quantities for various zones are shownin Table 2. For the computation of deviation of solid waste quanti-ties generated at source (i.e. ait and bit), the range of 5% is consid-ered in the study.

The composition and characteristics of municipal solid wastesvary from place to place as it depends on number of factors suchas social customs, standard of living, geographical location, cli-mate, etc. MSW is heterogeneous in nature and consists of a num-ber of different materials derived from various types of activities.In absence of projected composition of solid waste for the regionof example problem, the existing average composition of Delhi istaken from literature as input (Table 3).

The caloric value of waste should be controlled to keep incin-erator self sustaining otherwise auxiliary fuels are needed to incin-erate the waste. The total caloric heating values waste iscalculated based on the caloric value of individual waste givenin Table 4 and the rated heating value of solid waste for Timarpurincinerator is 1462.5 kcal/kg (MNES, 2006). The economic dataused for solving the example problem is given in Table 5.

Two types of capacities has been considered in the model (i)operating capacity, which is decided based on the availability of

A.K. Srivastava, A.K. Nema / Expert Systems with Applications 39 (2012) 46574678 4667Fig. 6. Variation of objective values for different value of h(c = 1).

equipment, manpower, other resource like electricity water, and(ii) exhaustive capacity, which is applicable in the case of landllsand decided based on the availability total land area for the landll.Operating capacities of treatment and processing facilities are notconsidered as a constraint. The operating capacity for the landllsis taken as 7200 tons/day and the exhaustible capacity is taken forexisting dumps as 54 105 tons (Personal Communication, Muni-cipal Corporation of Delhi, 2006).

4.2. Environmental risk factor

Risk factor used in model is dened as a quantied value ofharm to environment from unit waste quantities if it is processedor disposed off in a waste management facility. The quanticationof risk involves formal, scientic process to analyze the potentialfor harm following exposure to chemicals or other agents, whichhas been given in literatures (Ministry of Environment, 1999;Defra, 2004, Moy, 2005). The risk factor from waste management

facility is location specic data. For the example problem the riskfactors considered are given in Table 6. The risk factors are as-sumed to be in the similar range as reported by Moy (2005) in ab-sence of risk factor data for Delhi.

The total risk to environment is computed by multiplying therisk factor with receptor population in the region. The data of pro-jected population is taken from the national commission of popu-lation and reproduced in Table 7.

The attenuation of risk has been considered through its path-ways i.e., air and subsurface. The value dispersion angle from itscenterline /i, for the air dispersion is computed as 700 for allthe landll sites as well as incineration sites. This dispersion anglefor air pathway is based on the windrose diagram of annual aver-age wind data, which was collected from Indian MetrologicalDepartment New Delhi. The values of subsurface dispersion angleare computed as 1220, 1240, 2300, 300, 3030 and 2300 for BhattiMines, Jaitpur, Narela, Okhla, Ghazipur, and Bhalswa respectively.These values for subsurface dispersion were calculated based onthe steepest ground slope at the respective landll sites.

Table 9Waste diversion for different values of h under constant c (=1) for scenario I (waste quantities in 000 tons).


Ghazipur Bhalswa Okhla Ghazipur Bhalswa Bhatimines Jaitpur Narela

0.0 1 1159 1111 7300 1302 3889 5400 0 0 02 2284 2036 14,534 0 0 0 0 13,300 75633 2809 2504 17,877 0 0 0 0 13,300 12,3614 2755 6745 18,250 0 0 0 5560 13,300 13,300

0.1 1 1172 1205 7300 1316 3992 5400 0 0 02 2309 2058 14,696 0 0 0 0 13,300 77943 2840 2532 18,075 0 0 0 0 13,300 12,6464 2933 7023 18,250 0 0 0 5770 13,300 13,300

0.2 1 1185 1298 7300 1358 4068 5400 0 0 02 2334 2081 14,857 0 0 0 0 13,300 80263 2871 2584 18,250 0 0 0 0 13,300 12,9314 3112 7300 18,250 0 0 0 5980 13,300 13,300

0.3 1 1198 1392 7300 1432 4112 5400 0 0 02 2360 2104 15,018 0 0 0 0 13,300 82583 2903 2810 18,250 0 0 0 0 13,300 13,2164 3290 7578 18,250 0 0 0 6189 13,300 13,300

0.4 1 1211 1485 7300 1505 4156 5400 0 0 02 2385 2126 15,180 0 0 0 1554 12,638 75973 2934 3037 18,250 0 0 0 4158 13,300 93444 3470 7856 18,250 0 0 0 6397 13,300 13,300

4 3688 8689 18,250

4668 A.K. Srivastava, A.K. Nema / Expert Systems with Applications 39 (2012) 465746780.8 1 1262 1859 73002 2487 2217 15,8263 3059 3943 18,2504 3726 8967 18,250

0.9 1 1275 1953 73002 2512 2239 15,9873 3090 4169 18,2504 3764 9245 18,250

1.0 1 1288 2046 73000.5 1 1224 1579 73002 2411 2149 15,3413 2965 3263 18,2504 3612 8134 18,250

0.6 1 1237 1672 73002 2436 2171 15,5033 2996 3490 18,2504 3650 8411 18,250

0.7 1 1249 1766 73002 2461 2194 15,6643 3027 3716 18,2502 2537 2262 16,1493 3121 4395 18,2504 3802 9522 18,2501578 4200 5400 0 0 00 0 0 1571 12,773 76780 0 0 4343 13,300 94430 0 0 6643 13,300 13,300

1652 4245 5400 0 0 00 0 0 1587 12,907 77590 0 0 4529 13,300 95430 0 0 6993 13,300 13,300

1725 4289 5400 0 0 00 0 0 1604 13,042 78390 0 0 4648 13,300 97090 0 0 7343 13,300 13,300

1799 4333 5400 0 0 00 0 0 1620 13,176 79200 0 0 4696 13,300 99460 0 0 7693 13,300 13,300

1872 4377 5400 0 0 00 0 0 1648 13,300 80010 0 0 4744 13,300 10,1830 0 0 8043 13,300 13,300

1946 4422 5400 0 0 0

0 0 0 1799 13,300 80820 0 0 4791 13,300 104210 0 0 8392 13,300 13,300

5. Results and discussion

The proposed multi-objective, multi-period model was appliedto the example problem to understand the effect of priority to var-ious objectives on waste allocation to various management alter-natives and to study the effect of aspiration level of the decisionmaker to address the uncertainty in waste generation quantitiesand the capacities of the waste management facilities. Waste treat-ment and disposal facilities are simulated in a simplied way in theform of point nodes with only input and output being modeled.The internal process in the facilities is not being modeled in thepresent study.

The example problem was solved for three different cases. Incase I, the model is solved for different values of h, keeping con-stant value of c = 1. The value of c = 1 represent the case of xedcapacities of facilities, i.e. the additional limit of capacity wouldnot be used in case of deviation of waste quantities. In this case,implementation planning is to be carried out with xed planned

capacity. In the case II, model is solved for different value of c withconstant value of h. This case implies the situation when therewould not be deviation in waste quantities but additional capacitywould be available during implementation of planning. Whereas,case III represent the simultaneous changing value h and c. Thiscondition reects the situation, when there is chance of deviationof waste quantities as well as capacities, which were earlier evalu-ated by decision maker as input to the model. The model consistsof two objectives and the model is solved for three different sce-narios in each of the cases explained above. Scenario I represent100% weighting to cost, scenario II represents 5050% weightingto both cost and risk, and scenario III represents 100% weightingto risk.

5.1. Changing value of h with constant c

The example problem has been solved for all three scenarios fordifferent values h between 0 and 1 with an increment of 0.1 and

Table 10Waste diversion for different values of h under constant c (=1) for scenario II (waste quantities in 000 tons).


Okhla Ghazipur Okhla Ghazipur Bhalswa Bhatimines Jaitpur Narela

0.0 1 1159 4061 4350 5400 5189 0 0 0 02 2284 2429 14,140 0 0 0 13,300 0 75633 2809 2989 17,392 0 0 0 13,300 0 12,3614 3445 6745 18,250 0 0 0 13,300 4870 13,300

0.1 1 1172 4106 4399 5400 5307 0 0 0 02 2309 2457 14,297 0 0 0 13,300 0 77943 2840 3022 17,585 0 0 0 13,300 0 12,6464 3483 7023 18,250 0 0 0 13,300 5220 13,300

0.2 1 1185 4151 4447 5400 5400 26 0 0 02 2334 2484 14,454 0 0 0 13,300 0 80263 2871 2584 18,250 0 0 0 13,300 0 129314 3521 7300 18,250 0 0 0 13,300 5570 13,300

0.3 1 1198 4197 4495 5400 5400 144 0 0 02 2360 2511 14,612 0 0 0 13,300 0 82583 2903 2810 18,250 0 0 0 13,300 93 13,2164 3560 7578 18,250 0 0 0 13,300 5919 13,300

0.4 1 1211 4242 4544 5400 5400 261 0 0 02 2385 2538 14,769 0 0 0 13,300 0 84903 2934 3037 18,250 0 0 0 13,300 201 13,3004 3598 7856 18,250 0 0 0 13,300 6269 13,300

0.5 1 1224 4287 4592 5400 5400 379 0 0 0

A.K. Srivastava, A.K. Nema / Expert Systems with Applications 39 (2012) 46574678 46692 2411 0 17,4903 2965 3263 18,2504 3636 8134 18,250

0.6 1 1237 4332 46402 2436 0 17,6743 2996 3490 18,2504 3675 8411 18,250

0.7 1 1249 4377 46892 2461 2619 15,2403 3027 3716 18,2504 3713 8689 18,250

0.8 1 1262 4422 47372 2487 2646 15,3973 3059 6576 15,6174 3751 8967 18,250

0.9 1 1275 4468 47852 2512 2673 15,5543 3090 4169 18,2504 3789 9245 18,250

1.0 1 1288 4513 4833

2 2537 2700 15,7113 3121 4395 18,2504 3828 9522 18,2500 0 0 13,300 0 87210 0 0 13,300 486 13,3000 0 0 13,300 6619 13,300

5400 5400 497 0 0 00 0 0 13,300 0 89530 0 0 13,300 772 13,3000 0 0 13,300 6969 13,300

5400 5400 614 0 0 00 0 0 13,300 0 91850 0 0 13,300 1057 13,3000 0 0 13,300 7318 13,300

5400 5400 732 0 0 00 0 0 13,300 0 94170 0 0 13,300 1342 13,3000 0 0 13,300 7668 13,300

5400 5400 850 0 0 00 0 0 13,300 0 96480 0 0 13,300 1627 13,3000 0 0 13,300 8018 13,300

5400 5400 968 0 0 00 0 0 13,300 0 9880

0 0 0 13,300 1912 13,3000 0 0 13,300 8367 13,300

constant values of c (=1). The variation of the objective values isshown in Fig. 6(a)(c) for scenarios I, II and III, respectively. Thequantities of waste to be diverted towards different facilities areshown in the Tables 811 for scenarios I, II and III respectively.

In case of scenario I (Fig 6(a)) that the total cost of the projectvary linearly except at the values of h between 0.3 and 0.4. Thetotal cost is increasing at a rate of 1.15% until h = 0.3, whereasthe rate increased to 6.73% between h = 0.3 and 0.4. The total costincreases at a rate of 1.04% after h = 0.5. All inert and residue wastegenerated in the planning period I is to be disposed off in the exist-ing landlls (Table 8). However, due to limited cumulative capacityof existing landlls, the waste is to be diverted towards new land-ll sites namely Jaitpur and Narela for planning period II. In thesenew landll sites the, Jaitpur site, being closer to the populationcenters is to receive more waste quantities and only the surpluswaste is to be diverted towards Jaitpur landll site for all the valueof h. The Bhatimines landll site is to start receiving waste in plan-ning period II for value of h more than 0.4 otherwise it will receivewaste only in planning period IV.

Fig. 6(b) shows the increase in the total risk with h in case ofscenario II. The rate of increase of total risk till h = 0.2 is about1.29% whereas after this point risk average increase in risk is about1.40%. This change of rate of increase is due to the start of newlandll site at Jaitpur. Among existing landlls, Bhalswa is closerto the population center, therefore, it starts receiving the wasteonly after the capacities of other existing landlls are exhaustedparticularly after h = 0.2.

In case of scenario III, which considers equal weighting to costas well risk, the decisions of waste diversion and facility locationis observed to be changing more frequently. The rst change in rateof increase of cost is observed at h = 0.2 as soon as the Bhalswalandll starts receiving the waste. Similarly the change in the slopeis observed at h = 0.4 which is due to the start of Jaitpur landll.Comparison of the results of scenario II and III shows the wasteow is similar till h = 0.2 and changes at the start of the Jaitpurlandll for the scenario II at h = 0.3. It can be seen that the startingof Jaitpur landll is deferred till h = 0.4 for scenario III. The Narelalandll has similar waste ow allocation for scenario I and III till

Table 11Waste diversion for different values of h under constant c (=1) for scenario III (waste quantities in 000 tons).

h Planning period Timarpur Incinerator Compost Landlls


0.0 1 1159 4061 4350 5400 5189 0 0 0 02 2284 4780 16,570 0 0 0 13,300 0 75633 2809 5989 17,392 0 0 0 13,300 0 12,3614 3445 6745 18,250 0 0 0 13,300 4870 13,300

0.1 1 1172 4106 4399 5400 5307 0 0 0 02 2309 2457 14,297 0 0 0 13,300 0 77943 2840 3022 17,585 0 0 0 13,300 0 12,6464 3483 7023 18,250 0 0 0 13,300 5220 13,300

0.2 1 1185 4151 4447 5400 5400 26 0 0 02 2334 2484 14,454 0 0 0 13,300 0 80263 2871 3055 17,779 0 0 0 13,300 0 12,9314 3521 7300 18,250 0 0 0 13,300 5570 13,300

0.3 1 1198 4197 4495 5400 5400 144 0 0 02 2360 2511 14,612 0 0 0 13,300 0 82583 2903 3585 17,475 0 0 0 13,300 0 13,2164 3560 7578 18250 0 0 0 13,300 5919 13,300

0.4 1 1211 4242 4544 5400 5400 261 0 0 02 2385 3062 15,306 0 0 0 13,300 0 84903 2934 3037 18,250 0 0 0 13,300 201 13,3004 3598 7856 18,250 0 0 0 13,300 6269 13,300

4670 A.K. Srivastava, A.K. Nema / Expert Systems with Applications 39 (2012) 465746780.5 1 1224 4287 45922 2411 2565 14,9263 2965 3663 17,8514 3636 8134 18,250

0.6 1 1237 4332 46402 2436 5139 12,6743 2996 3490 18,2504 3675 8411 18,250

0.7 1 1249 4377 46892 2461 5620 12,2393 3027 3716 18,2504 3713 8689 18,250

0.8 1 1262 4422 47372 2487 2646 15,3973 3059 4380 17,8124 3751 8967 18,250

0.9 1 1275 4468 47852 2512 2673 15,5543 3090 4169 18,2504 3789 9245 18,250

1.0 1 1288 4513 48332 2537 2700 15,711

3 3121 6710 15,9364 3828 9522 18,2505400 5400 379 0 0 00 0 0 13,300 0 87210 0 0 13,300 486 13,3000 0 0 13,300 6619 13,300

5400 5400 497 0 0 00 0 0 13,300 0 89530 0 0 13,300 772 13,3000 0 0 13,300 6969 13,300

5400 5400 614 0 0 00 0 0 13,300 0 91850 0 0 13,300 1057 13,3000 0 0 13,300 7318 13,300

5400 5400 732 0 0 00 0 0 13,300 0 94170 0 0 13,300 1342 13,3000 0 0 13,300 7668 13,300

5400 5400 850 0 0 00 0 0 13,300 0 96480 0 0 13,300 1627 13,3000 0 0 13,300 8018 13,300

5400 5400 968 0 0 00 0 0 13,300 0 9880

0 0 0 13,300 1912 13,3000 0 0 13,300 8367 13,300

at h = 0.4. For scenario I, Narela landll starts receiving less quan-tity of waste after h = 0.4 due to Bhatimines landll.

It can be observed that the changing priority and weighting todifferent objectives, i.e., minimization of cost and/or risk has signif-icant inuence on the decision of selecting the new landlls as wellas use of the existing landlls. The preference among the new land-lls is Jaitpur, Narela and Bhatimines for minimization of costwhereas, the preference changes to Bhatimines, Narela and Jaitpurfor the minimization of risk. In case of equal weighting to cost andrisk the preference are Bhatimines, Narela and Jaitpur. It was ob-served that, with increasing value of h, the planning period inwhich the new landlls need to be opened gets shortened. Thisindicates the effect of uncertainty of waste forecasting model onthe planning in terms of opening the new landlls.

5.2. Changing value of c with constant h

Effect of changing value of cwith a constant value of h is studiedby solving the example problem for all three scenarios with chang-ing the weighting of cost and risk in the same manner as presentedin above section. The example problem has been solved for differ-ent values c between 0 and 1 in step of 0.1 and constant values of h(=1). Fig. 7(a) shows the variation of total cost with changing valueof c for scenario I. The cost is increasing for all the cases withincreasing value of c. It can be seen that, the total cost varies al-most linearly at the rate of 0.006%, which shows that there is al-most insignicant variation in the total cost with changing

values of c. It can be seen from Table 11, that all the existing land-lls would receive the waste only in rst planning period and allnew landll sites would be started receiving the waste from thesecond planning periods. It is also observed that for all value ofc, none of the new landll is started unexpectedly and the capaci-ties of Jaitpur landll site is exhausted earlier than other landllsites.

The value of total risk increases linearly with changing c(Fig. 7b). The rate of increase of risk is 0.15%. The waste allocationfor different value of c is given in Table 12. It can be seen that,Jaitpur, the closest landll site to population centers, is started inthird planning period for all the values of c. The total cost is con-stant between c = 0.0 and 0.1 for scenario III and a sharp increaseis observed at c = 0.6 (Fig. 7c). The change in the waste allocationfor different value of c is observed only in the planning period,where landll is receiving waste until the full utilization of itsoperating capacity Table 13.

For scenario I, the Jaitpur landll is found to be the most pre-ferred landll and is receives waste till the full utilization of itsoperating capacities for all values of c in planning periods III andIV. However, at the exhaustion of operating capacity of Jaitpurlandll the waste is to be diverted to Bhatimines and Narela land-lls (for cP 0.2). (See Tables 1317).

It has been observed that the preference for changing c amongthe choice of new landlls at Jaitpur, Narela and Bhatimines re-mains same as found in the case of changing h for differentscenarios.

A.K. Srivastava, A.K. Nema / Expert Systems with Applications 39 (2012) 46574678 4671Fig. 7. Variation of objective values for different value of c(h = 1).

5.3. Simultaneous changing value of h and c

The simultaneous changing values of h and c reects the caseswhen uncertain waste quantity deviate positively and part ofworking capacity is not available. The Fig. 8(a)(c) shows the var-iation of objective functions with h and c. For scenario I, the totalcost suddenly increases when value of h as well as c reaches to0.7 (Fig. 8a). The change in rate of increase of cost is observeddue to advancement of starting of Bhatimines landll from plan-ning period III to planning period II. Similar change is observedin Fig. 6(a) at h = 0.4, and c = 1, which show that due to simulta-neous change of c, has resulted in scarcity of the available capacity,therefore an increase in the cost by 3.19%.

An almost linear variation of total risk is obtained in scenario II(Fig. 8b). The sudden change in risk is observed at h as well asc = 0.4. It can be seen that just before this point, the rate of in-crease of total is risk is 1.23%, which becomes 1.67% after thispoint.

The increase in total cost for scenario III is observed non linear(Fig. 8c). The range of variation of total cost is from Rs. 1.02 1011to Rs. 1.15 1011. The Jaitpur landll site would start in the plan-ning period II for h as well as c = 0.6, resulting in sudden change inthe cost.

6. Summary and conclusions

A fuzzy parametric model has been presented in the presentstudy for the long term planning for integrated solid waste man-agement with uncertain parameters. Unlike the existing models,the uncertainties in waste quantities and capacities of waste man-agement facilities have been addressed as inbuilt feature in themodel in terms of the shape of membership function. The outputof model gives a set of alternative solutions for the range of mem-bership function, which reects the aspiration level of the decisionmaker.

Table 12Waste diversion for different values of c under constant h (=1) for scenario I (waste quantities in 000 tons).

c Planning periods Timarpur incinerator Compost Landlls


0.0 1 1288 2046 7300 1856 4422 5490 0 0 02 2537 2262 16,149 0 0 0 1653 13,445 80823 3121 4395 18,250 0 0 0 4702 13,870 99404 3802 9522 18,250 0 0 0 7252 13,870 13,870

0.1 1 1288 2046 7300 1865 4422 5481 0 0 02 2537 2262 16,149 0 0 0 1653 13,445 80823 3121 4395 18,250 0 0 0 4759 13,813 99404 3802 9522 18,250 0 0 0 7366 13,813 13,813

0.2 1 1288 2046 7300 1874 4422 5472 0 0 02 2537 2262 16,149 0 0 0 1653 13,445 80823 3121 4395 18,250 0 0 0 4791 13,756 99654 3802 9522 18,250 0 0 0 7480 13,756 13,756

0.3 1 1288 2046 7300 1883 4422 5463 0 0 02 2537 2262 16,149 0 0 0 1653 13,445 80823 3121 4395 18,250 0 0 0 4791 13,699 10,0224 3802 9522 18,250 0 0 0 7594 13,699 13,699

0.4 1 1288 2046 7300 1892 4422 5454 0 0 02 2537 2262 16,149 0 0 0 1653 13,445 80823 3121 4395 18,250 0 0 0 4791 13,642 10,0794 3802 9522 18,250 0 0 0 7708 13,642 13,642

0.5 1 1288 2046 7300 1901 4422 5445 0 0 0

0 0 0 4791 13,414 10,3070 0 0 8164 13,414 13,414

4672 A.K. Srivastava, A.K. Nema / Expert Systems with Applications 39 (2012) 465746782 2537 2262 16,1493 3121 4395 18,2504 3802 9522 18,250

0.6 1 1288 2046 73002 2537 2262 16,1493 3121 4395 18,2504 3802 9522 18,250

0.7 1 1288 2046 73002 2537 2262 16,1493 3121 4395 18,2504 3802 9522 18,250

0.8 1 1288 2046 73002 2537 2262 16,1493 3121 4395 18,2504 3802 9522 18,250

0.9 1 1288 2046 73002 2537 2262 16,1493 3121 4395 18,2504 3802 9522 18,250

1.0 1 1288 2046 73002 2537 2262 16,149

3 3121 4395 18,2504 3802 9522 18,2501937 4422 5409 0 0 00 0 0 1742 13,357 80820 0 0 4791 13,357 10,3640 0 0 8278 13,357 13,357

1946 4422 5400 0 0 00 0 0 1799 13,300 80820 0 0 1653 13,445 80820 0 0 4791 13,585 10,1360 0 0 7822 13,585 13,585

1910 4422 5436 0 0 00 0 0 1653 13,445 80820 0 0 4791 13,528 10,1930 0 0 7936 13,528 13,528

1919 4422 5427 0 0 00 0 0 1653 13,445 80820 0 0 4791 13,471 10,2500 0 0 8050 13,471 13,471

1928 4422 5418 0 0 00 0 0 1685 13,414 80820 0 0 4791 13,300 104210 0 0 8392 13,300 13,300

Table 13Waste diversion for different values of c under constant h (=1) for scenario II (waste quantities in 000 tons).



0.0 1 1288 4513 4833 5674 5541 553 0 0 02 2537 2700 15711 0 0 0 13,870 0 93103 3121 4395 18,250 0 0 0 13,870 772 13,8704 3828 9522 18,250 0 0 0 13,870 7227 13,870

0.1 1 1288 4513 4833 5646 5527 594 0 0 02 2537 2700 15,711 0 0 0 13,813 0 93673 3121 4395 18,250 0 0 0 13,813 886 13,8134 3828 9522 18,250 0 0 0 13,813 7341 13,813

0.2 1 1288 4513 4833 5619 5513 636 0 0 02 2537 2700 15,711 0 0 0 13,756 0 94243 3121 4395 18,250 0 0 0 13,756 1000 13,7564 3828 9522 18,250 0 0 0 13,756 7455 13,756

0.3 1 1288 4513 4833 5592 5499 677 0 0 02 2537 2700 15,711 0 0 0 13,699 0 94813 3121 4395 18,250 0 0 0 13,699 1114 13,6994 3828 9522 18,250 0 0 0 13,699 7569 13,699

0.4 1 1288 4513 4833 5564 5485 719 0 0 02 2537 2700 15,711 0 0 0 13,642 0 95383 3121 4395 18,250 0 0 0 13,642 1228 13,6424 3828 9522 18,250 0 0 0 13,642 7683 13,642

0.5 1 1288 4513 4833 5537 5471 760 0 0 02 2537 2700 15,711 0 0 0 13,585 0 95953 3121 4395 18,250 0 0 0 13,585 1342 13,5854 3828 9522 18,250 0 0 0 13,585 7797 13,585

0.6 1 1288 4513 4833 5510 5456 802 0 0 02 2537 2700 15,711 0 0 0 13,528 0 96523 3121 4395 18,250 0 0 0 13,528 1456 13,5284 3828 9522 18,250 0 0 0 13,528 7911 13,528

0.7 1 1288 4513 4833 5482 5442 843 0 0 02 2537 2700 15,711 0 0 0 13,471 0 97093 3121 4395 18,250 0 0 0 13,471 1570 13,4714 3828 9522 18,250 0 0 0 13,471 8025 13,471

0.8 1 1288 4513 4833 5455 5428 885 0 0 02 2537 2700 15,711 0 0 0 13,414 0 97663 3121 4395 18,250 0 0 0 13,414 1684 13,4144 3828 9522 18,250 0 0 0 13,414 8139 13,414

0.9 1 1288 4513 4833 5427 5414 926 0 0 02 2537 2700 15,711 0 0 0 13,357 0 98233 3121 4395 18,250 0 0 0 13,357 1798 13,3574 3828 9522 18,250 0 0 0 13,357 8253 13,357

1.0 1 1288 4513 4833 5400 5400 968 0 0 02 2537 2700 15,711 0 0 0 13,300 0 98803 3121 4395 18,250 0 0 0 13,300 1912 13,3004 3828 9522 18,250 0 0 0 13,300 8367 13,300

Table 14Waste diversion for different values of c under constant h (=1) for scenario III (waste quantities in 000 tons).



0.0 1 1159 4061 4350 5674 4916 0 0 0 02 2284 2429 14,140 0 0 0 13,870 0 69933 2809 3189 17,192 0 0 0 13,870 0 11,7914 3445 6745 18,250 0 0 0 13,870 3730 13,870

0.1 1 1172 4106 4399 5646 5061 0 0 0 02 2309 2457 14,297 0 0 0 13,813 0 72813 2840 3022 17,585 0 0 0 13,813 0 12,1334 3483 7023 18,250 0 0 0 13,813 4194 13,813

0.2 1 1185 4151 4447 5619 5206 0 0 0 02 2334 2484 14,454 0 0 0 13,756 0 75703 2871 5702 15,131 0 0 0 13,756 0 12,4754 3521 7300 18,250 0 0 0 13,756 4658 13,756

0.3 1 1198 4197 4495 5592 5351 0 0 0 02 2360 2511 14,612 0 0 0 13,699 0 7859

(continued on next page)

A.K. Srivastava, A.K. Nema / Expert Systems with Applications 39 (2012) 46574678 4673

Table 14 (continued)



3 2903 2810 18,250 0 0 0 13,699 0 12,8174 3560 7578 18,250 0 0 0 13,699 5121 13,699

0.4 1 1211 4242 4544 5564 5485 0 0 0 02 2385 4015 13,291 0 0 0 13,642 0 81483 2934 3037 18,250 0 0 0 13642 0 13,1594 3598 7856 18,250 0 0 0 13,642 5585 13,642

0.5 1 1224 4287 4592 5537 5471 0 0 0 02 2411 2565 14,926 0 0 0 13,585 0 84363 2965 5145 16,368 0 0 0 13,585 0 13,5014 3636 8134 18,250 0 0 0 13,585 6049 13,585

0.6 1 1237 4332 4640 5510 5456 0 0 0 02 2436 0 17,674 0 0 0 13,528 0 87253 2996 3490 18,250 0 0 0 13,528 316 13,5284 3675 8411 18,250 0 0 0 13,528 6513 13,528

0.7 1 1249 4377 4689 5482 5442 0 0 0 02 2461 2619 15,240 0 0 0 13,471 0 90143 3027 3716 18,250 0 0 0 13,471 715 13,4714 3713 8689 18,250 0 0 0 13,471 6976 13,471

0.8 1 1262 4422 4737 5455 5428 0 0 0 02 2487 2646 15,397 0 0 0 13,414 0 93033 3059 6576 15,617 0 0 0 13,414 1114 13,4144 3751 8967 18,250 0 0 0 13,414 7440 13,414

0.9 1 1275 4468 4785 5427 5414 0 0 0 02 2512 2673 15,554 0 0 0 13,357 0 95913 3090 4169 18,250 0 0 0 13,357 1513 13,3574 3789 9245 18,250 0 0 0 13,357 7904 13,357

1.0 1 1288 4513 4833 5400 5400 0 0 0 02 2537 2700 15,711 0 0 0 13,300 0 98803 3121 6710 15,936 0 0 0 13,300 1912 13,3004 3828 9522 18,250 0 0 0 13,300 8367 13,300

Table 15Waste diversion for simultaneous values of h and c for scenario I (waste quantities in 000 tons).

h/c Planning periods Timarpur incinerator Compost Landlls


0.0 1 1159 1111 7300 1302 3799 5490 0 0 02 2284 2036 14,534 0 0 0 0 13,589 72743 2809 2504 17,877 0 0 0 0 13,870 11,7914 2733 6745 18,250 0 0 0 5289 13,870 13,023

0.1 1 1172 1205 7300 1316 3911 5481 0 0 02 2309 2058 14,696 0 0 0 0 13740 73553 2840 2532 18,075 0 0 0 0 13,813 12,1334 2743 7023 18,250 0 0 0 5347 13,813 13,400

0.2 1 1185 1298 7300 1330 4023 5472 0 0 02 2334 2081 14,857 0 0 0 0 13,756 75703 2871 2584 18,250 0 0 0 0 13,756 12,4754 2753 7300 18,250 0 0 0 5426 13,756 13,756

0.3 1 1198 1392 7300 1369 4112 5463 0 0 02 2360 2104 15,018 0 0 0 0 13,699 78593 2903 2810 18,250 0 0 0 0 13,699 12,8174 2891 7578 18,250 0 0 0 5790 13,699 13,699

0.4 1 1211 1485 7300 1451 4156 5454 0 0 02 2385 2126 15,180 0 0 0 0 13,642 81483 2934 3037 18,250 0 0 0 0 13,642 13,1594 3126 7856 18,250 0 0 0 6057 13,642 13,642

0.5 1 1224 1579 7300 1533 4200 5445 0 0 02 2411 2149 15,341 0 0 0 0 13,585 84363 2965 3263 18,250 0 0 0 0 13,585 13,5014 3362 8134 18,250 0 0 0 6323 13,585 13,585

0.6 1 1237 1672 7300 1616 4245 5436 0 0 02 2436 2171 15,503 0 0 0 12,907 77593 2996 3490 18,250 0 0 0 4301 13,528 95434 3607 8411 18,250 0 0 0 6580 13,528 13,528

4674 A.K. Srivastava, A.K. Nema / Expert Systems with Applications 39 (2012) 46574678

Table 16Waste diversion for different simultaneous values of h and c for scenario II (waste quantities in 000 tons).



0.0 1 1159 4061 4350 5674 4916 0 0 0 02 2284 2429 14,140 0 0 0 13,870 0 69933 2809 2989 17,392 0 0 0 13,870 0 11,7914 3445 6745 18,250 0 0 0 13,870 3730 13,870

0.1 1 1172 4106 4399 5646 5061 0 0 0 02 2309 2457 14,297 0 0 0 13,813 0 72813 2840 3022 17,585 0 0 0 13,813 0 12,1334 3483 7023 18,250 0 0 0 13,813 4194 13,813

0.2 1 1185 4151 4447 5619 5206 0 0 0 02 2334 2484 14,454 0 0 0 13,756 0 75703 2871 2584 18,250 0 0 0 13,756 0 12,4754 3521 7300 18,250 0 0 0 13,756 4658 13,756

0.3 1 1198 4197 4495 5592 5351 1 0 0 02 2360 2511 14,612 0 0 0 13,699 0 78593 2903 2810 18,250 0 0 0 13,699 0 12,8174 3560 7578 18,250 0 0 0 13,699 5121 13,699

0.4 1 1211 4242 4544 5564 5485 12 0 0 02 2385 2538 14,769 0 0 0 13,642 0 81483 2934 3624 17,663 0 0 0 13,642 0 13,1594 3598 7856 18,250 0 0 0 13,642 5585 13,642

0.5 1 1224 4287 4592 5537 5471 172 0 0 02 2411 3846 15,645 0 0 0 13,585 0 84363 2965 3263 18,250 0 0 0 13,585 0 13,5014 3636 8134 18,250 0 0 0 13,585 6049 13,585

0.6 1 1237 4332 4640 5510 5456 331 0 0 02 2436 3987 17,674 0 0 0 13,528 0 87253 2996 3490 18,250 0 0 0 13,528 316 13,5284 3675 8411 18,250 0 0 0 13,528 6513 13,528

0.7 1 1249 4377 4689 5482 5442 490 0 0 02 2461 2619 15,240 0 0 0 13,471 0 90143 3027 3716 18,250 0 0 0 13,471 715 13,4714 3713 8689 18,250 0 0 0 13,471 6976 13,471

0.8 1 1262 4422 4737 5455 5428 649 0 0 02 2487 2646 15,397 0 0 0 13,414 0 93033 3059 3943 18,250 0 0 0 13,414 1114 13,4144 3751 8967 18,250 0 0 0 13,414 7440 13,414

0.9 1 1275 4468 4785 5427 5414 808 0 0 02 2512 2673 15,554 0 0 0 13,357 0 95913 3090 4169 18,250 0 0 0 13,357 1513 13,3574 3789 9245 18,250 0 0 0 13,357 7904 13,357

1.0 1 1288 4513 4833 5400 5400 968 0 0 02 2537 2700 15,711 0 0 0 13,300 0 98803 3121 4395 18,250 0 0 0 13,300 1912 13,3004 3828 9522 18,250 0 0 0 13,300 8367 13,300



0.7 1 1249 1766 7300 1698 4289 5427 0 0 02 2461 2194 15,664 0 0 0 1604 13,042 78393 3027 3716 18,250 0 0 0 4544 13,471 96424 3688 8689 18,250 0 0 0 7001 13,471 13,471

0.8 1 1262 1859 7300 1781 4333 5418 0 0 02 2487 2217 15,826 0 0 0 1620 13,176 79203 3059 3943 18,250 0 0 0 4696 13,414 98324 3726 8967 18,250 0 0 0 7465 13,414 13,414

0.9 1 1275 1953 7300 1863 4377 5409 0 0 02 2512 2239 15,987 0 0 0 1637 13,311 80013 3090 4169 18,250 0 0 0 4744 13,357 10,1264 3764 9245 18,250 0 0 0 7929 13,357 13,357

1.0 1 1288 2046 7300 1946 4422 5400 0 0 02 2537 2262 16,149 0 0 0 1799 13,300 80823 3121 4395 18,250 0 0 0 4791 13,300 10,4214 3802 9522 18,250 0 0 0 8392 13,300 13,300

Table 15 (continued)

A.K. Srivastava, A.K. Nema / Expert Systems with Applications 39 (2012) 46574678 4675

ant

ms wTable 17Waste diversion for different simultaneous values of h and c for scenario III (waste qu

h/c Planning periods Timarpur incinerator Compost

Okhla Ghazipur

0.0 1 1159 4061 43502 2284 2429 14,1403 2809 2989 17,3924 3445 6745 18,250

0.1 1 1172 4106 43992 2309 2457 14,2973 2840 2357 18,2504 3483 7023 18,250

0.2 1 1185 4151 44472 2334 2484 14,4543 2871 3055 17,7794 3521 7300 18,250

0.3 1 1198 4197 4495

4676 A.K. Srivastava, A.K. Nema / Expert SysteThe utility of the proposed model is demonstrated by anexample problem. It is observed that the consideration of uncer-tainties in waste quantities and capacities of waste managementfacilities is essential during planning of project, because it wouldinuence the planning decisions to a large extent. The commis-sioning of new facilities is signicantly affected by uncertainparameters mainly waste quantity. The pre-ponement orpostponement of commissioning of new facilities may requiresignicantly additional resources. One of the important observa-tion is that the uncertainties in waste quantity is likely to affectthe planning for waste treatment/disposal facilities more as com-pared with the uncertainty in the capacities of the waste man-agement facilities.

The model simulation can help in understanding the effect ofthe uncertainties in the capacities of the individual treatmentand disposal facilities on the overall plan. The relationship betweenincrease in waste quantity and increase in the total cost/risk in-volved in waste management is found to be nonlinear. Moreover,it was noted that sensitivity of overall plan could be signicantly

2 2360 2511 14,6123 2903 2810 18,2504 3560 7578 18,250

0.4 1 1211 4242 45442 2385 2538 14,7693 2934 3037 18,2504 3598 7856 18,250

0.5 1 1224 4287 45922 2411 2565 14,9263 2965 21513 04 3636 8134 18,250

0.6 1 1237 4332 46402 2436 2592 15,0833 2996 3490 18,2504 3675 8411 18,250

0.7 1 1249 4377 46892 2461 4888 12,9713 3027 3716 18,2504 3713 8689 18,250

0.8 1 1262 4422 47372 2487 2646 15,3973 3059 4380 17,8124 3751 8967 18,250

0.9 1 1275 4468 47852 2512 2673 15,5543 3090 4169 18,2504 3789 9245 18,250

1.0 1 1288 4513 48332 2537 2700 15,7113 3121 6710 15,9364 3828 9522 18,250ities in 000 tons).

Landlls

Okhla Ghazipur Bhalswa Bhatimines Jaitpur Narela

5674 4916 0 0 0 00 0 0 13,870 0 69930 0 0 13,870 0 11,7910 0 0 13,870 3730 13,870

5646 5061 0 0 0 00 0 0 13,813 0 72810 0 0 13,813 0 12,1330 0 0 13,813 4194 13,813

5619 5206 0 0 0 00 0 0 13,756 0 75700 0 0 13,756 0 12,4750 0 0 13,756 4658 13,756

5592 5351 0 0 0 0

ith Applications 39 (2012) 46574678different with respect to the different facilities. It is suggested thatthe planner should identify the sensitivity of the overall plan withrespect to each of the facilities. It has been found that some of thefacilities could be such that a marginal change in their availablecapacities could result in a signicant change in the overallwaste-allocation plan. These sensitive facilities should be plannedwith higher prudence.

The fuzzy multi-period planning for solid waste management isespecially relevant in case of rapidly growing urban centers ofdeveloping countries due to great possibility of uctuating param-eters. As demonstrated using the example problem the multi-period planning model can be a very helpful tool for the decisionmakers especially for addressing locationallocation problem ofwaste disposal facilities with uctuating input parameters. Themodelling results could be suitably interpreted for taking anappropriate decision from the set of close to optimal alternatives.Further, the model simulations can give valuable information foranalysing the existing waste-management practices, the long-termcapacity planning for the citys waste-management system, and

0 0 0 13,699 0 78590 0 0 13,699 0 12,8170 0 0 13,699 5121 13,699

5564 5485 12 0 0 00 0 0 13,642 0 81480 0 0 13,642 0 13,1590 0 0 13,642 5585 13,642

5537 5471 172 0 0 00 0 0 13,585 0 84360 0 0 13,585 0 13,5010 0 0 13,585 6049 13,585

5510 5456 331 0 0 00 0 0 13,528 0 87250 0 0 13,528 316 13,5280 0 0 13,528 6513 13,528

5482 5442 490 0 0 00 0 0 13,471 0 90140 0 0 13,471 715 13,4710 0 0 13,471 6976 13,471

5455 5428 649 0 0 00 0 0 13,414 0 93030 0 0 13,414 1114 13,4140 0 0 13,414 7440 13,414

5427 5414 808 0 0 00 0 0 13,357 0 95910 0 0 13,357 1513 13,3570 0 0 13,357 7904 13,357

5400 5400 968 0 0 00 0 0 13,300 0 98800 0 0 13,300 1912 13,3000 0 0 13,300 8367 13,300

ms wA.K. Srivastava, A.K. Nema / Expert Systethe identication of effective policies regarding waste minimiza-tion and appropriate management options.

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