Fuzzy parametric programming model for multi-objective integrated solid waste management under uncertainty

Fuzzy parametric programming model for multi-objective integrated solid waste management under uncertainty

Expert Systems with Applications 39 (2012) 4657–4678 Contents lists available at SciVerse ScienceDirect Expert Systems with Applications journal hom...

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Expert Systems with Applications 39 (2012) 4657–4678

Contents lists available at SciVerse ScienceDirect

Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa

Fuzzy parametric programming model for multi-objective integrated solid waste management under uncertainty Amitabh Kumar Srivastava a,⇑, Arvind K. Nema b a b

Bundelkhand Institute of Engineering & Technology, Kanpur Road, Jhansi 284128, India Department of Civil Engineering, Indian Institute of Technology Delhi, Huaz Khas, New Delhi 110016, India

a r t i c l e

i n f o

Keywords: Solid waste management Integrated solid waste management system Long term planning Multi-objective and multi-period planning Fuzzy parametric programming

a b s t r a c t Solid waste management is increasingly becoming a challenging task for the municipal authorities due to increasing waste quantities, changing waste composition, decreasing land availability for waste disposal sites and increasing awareness about the environmental risk associated with the waste management facilities. 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 planning for 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 locates the facilities and allocates the waste considering fuzzy waste quantity and capacity of waste management facility. The model addresses uncertainty in waste quantity as well as uncertainties in the operating capacities of waste management facilities simultaneously. It was observed that uncertainty in waste quantity is likely to affect the planning for waste treatment/disposal facilities more as compared with the uncertainty in the capacities of the waste management facilities. The relationship between increase in waste quantity and increase in the total cost/risk involved in waste management is found to be nonlinear. Therefore, it is possible that a marginal change in waste quantity could increase the total cost/risk substantially. The information obtained from the analysis of modeling results can be effectively used for understanding the effect of changing the priorities and objectives of planning decisions on facility selections and waste diversions. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction The regional solid waste management (SWM) system comprises of many interrelated components including transportation, treatment and disposal. These interrelated components must be considered in integration in order to arrive at an optimal waste management plan. Mathematical models can be used to describe the objective, component interactions and available management options. The mathematical models can be subjected to rigorous methods of systems analysis for planning the integrated solid waste management system (ISWM). The mathematical models provide a systematic means by which the decision-maker can explore the various alternatives in order to identify an optimal management strategy. It is to be noted that the planning for an ISWM system for any urban centre is done for a long term, i.e., 20 or 25 years. The basic input for municipal solid waste (MSW) management is the solid waste quantities which changes with respect to time ⇑ Corresponding author. E-mail addresses: [email protected] (A.K. Srivastava), [email protected] ac.in (A.K. Nema). 0957-4174/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2011.09.022

at an increasing rate. Also the land available for the waste disposal facilities is increasingly becoming a scarce resource due to growing awareness about the associated environmental risk in the proximity to these facilities. In order to cope with the uncertainties involved in the solid waste quantities and available capacities of waste management facilities, an efficient and sustainable solid waste management plan is required. 2. Literature review In an optimization model, the uncertainty can be addressed by using interval programming, stochastic modelling and/or fuzzy systems. A number of researchers have applied these techniques to consider the effect of uncertainty in the ISWM models. In interval programming approach the upper and lower bounds of coefficients are determined and then deterministic model is used to address these upper and lower bounds. Interval programming has been widely used by researchers to incorporate uncertainty in 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 noted that, the output of interval programming method is with upper

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Nomenclature Indices T S I Jn Je J Re Rn R Ke Kn K M t s i jn je j re Rn R ke kn k m

OCrt total planning period total number of solid waste source nodes, i.e. population centers total number of transfer stations cum segregation/ sorting facilities total number of new landfills total number of existing landfills total number of landfills total number existing recycling facilities total number new recycling facilities total number recycling facilities total number of existing compost facilities total number of new compost facilities total number of compost facilities total number of waste components index for time (1, . . . , t) index of solid waste source nodes, i.e. population centers index of transfer stations cum segregation/sorting facilities index of new landfills index of existing landfills index of existing landfills (j = je [ jn) index of existing recycling facilities index of new recycling facilities index of recycling facilities (r = re [ rn) index of existing compost facilities index of new compost facilities index of compost facilities index for solid waste composition (m = 1 for paper; m = 2 for plastic; m = 3 for food; m = 4 for metals; m = 5 for glass and m = 6 for others mainly inert)

Input data TCsit unit transportation cost for unit quantity of waste between source/population center and transfer stations (in s  i  t matrix) TCijt unit transportation cost for unit quantity of waste between transfer stations and landfills (in i  j  t matrix) TCilt unit transportation cost for unit quantity of waste between transfer stations and incinerators (in i  l  t matrix) TCikt unit transportation cost for unit quantity of waste between transfer stations and compost plants (in i  k  t matrix) TCirt unit transportation cost for unit quantity of waste between transfer stations and recycling centers (in i  r  t matrix) TCrjt TCrlt

TCkjt TCklt

unit transportation cost for unit quantity of waste between recycling centers and landfills (in r  j  t matrix) unit transportation cost for unit quantity of waste between recycling centers and incinerators (in r  l  t matrix) unit transportation cost for unit quantity of waste between compost plants and landfills. (in k  j  t matrix) unit transportation cost for unit quantity of waste between compost plants and incinerators (in k  l  t matrix)

OCkt OClt OCjt CC jn t CC kn t CC ln t ICtm IKt Gst Ljs air

Ljs sub

Lls Rjair Rjsub Rlair Hst HVm RHVl CQj Qujt Qult Qukt Qljt Qllt Qlkt

x n

w dij

TCljt

unit transportation cost for unit quantity of waste between incinerators and landfills (in l  j  t matrix)

aj

OCit

operating cost of transfer stations cum segregation ‘i’ facilities during time ‘t’ (in i  t matrix)

/j

operating cost of recycling centers ‘r’ during time ‘t’ (in r  t matrix) operating cost of compost plant ‘k’ during time ‘t’ (in k  t matrix) operating cost of incinerators ‘l’ during time ‘t’ (in l  t matrix) operating cost of landfills ‘j’ during time ‘t’ (in j  t matrix) capital cost of new landfills ‘jn’ during time ‘t’ (in jn  t matrix) capital cost of new compost plants ‘kn’ during time ‘t’ (in kn  t matrix) capital cost of new incinerators ‘ln’ during time ‘t’ (in ln  t matrix) unit selling rate of waste material ‘m’ during time ‘t’ (in t  m matrix) unit selling rate of compost during time ‘t’ (in t  1 matrix) quantity of waste generated at population center/source ‘s’ during time period ‘t’ (in s  t matrix) attenuation factor from landfill ‘j’ to source/population center ‘s’ for dispersion of risk through air (in j  s matrix) attenuation factor from landfill ‘j’ to source/population center ‘s’ for dispersion of risk through subsurface medium (in j  s matrix) attenuation factor from incinerator ‘l’ to source/population center ‘s’ for dispersion of risk (in l  s matrix) risk factor from landfill ‘j’ through air medium (in j  1 matrix) risk factor from landfill ‘j’ through air medium (in j  1 matrix) risk factor from landfill ‘l’ through air medium (in l  1 matrix) population at source/population centers ‘s’ during time ‘t’ (in s  t matrix) calorific value of individual waste component ‘m’ (in m  1 matrix) rated heating value of incinerator ‘l’ (in l  1 matrix) cumulative capacity of landfill ‘j’ (in j  1 matrix) maximum operating capacity of landfill ‘j’ during time ‘t’ (in j  t matrix) maximum operating capacity of incinerator ‘l’ during time ‘t’ (in l  t matrix) maximum operating capacity of compost ‘k’ during time ‘t’ (in l  t matrix) minimum operating capacity of landfill ‘j’ during time ‘t’ (in j  t matrix) minimum operating capacity of incinerator ‘l’ during time ‘t’. (in l  t matrix) minimum operating capacity of compost ‘k’ during time ‘t’ (in k  t matrix) ratio of rejects and incoming waste at recycling centers (in single number) ratio of rejects and incoming waste at compost plants (in single number) ratio of residue and incoming waste at incinerators (in single number) direct radial distance between locations i and j (in i  j matrix) exponent term depends on site conditions such as wind speed, turbulence (in j  1 matrix) angle between directions of plume centerline from the reference axis (in j  1 matrix)

A.K. Srivastava, A.K. Nema / Expert Systems with Applications 39 (2012) 4657–4678

#ij R Tr1 Tr2 Trn pj pl pk pj pl pk ast bst

angle between line joining to point j and i (in i  j matrix) summation of the risk due to various sources (single number) individual risk from source 1 (single number) individual risk from source 2 (single number) individual risk from source n (single number) tolerance in maximum capacity of landfill ‘j’ (in j  1 matrix) tolerance in maximum capacity of incinerator ‘l’ (in l  1 matrix) tolerance in maximum capacity of compost ‘k’ (in k  1 matrix) tolerance in minimum capacity of landfill ‘j’ (in j  1 matrix) tolerance in minimum capacity of incinerator ‘l’ (in l  1 matrix) tolerance in minimum capacity of compost ‘k’ (in k  1 matrix) lower extreme deviation in waste quantity at source ‘s’ during time ‘t’ (in s  t matrix) upper extreme deviation in waste quantity at source ‘s’ during time ‘t’ (in s  t matrix)

Decision variables/outputs Wsit quantity of waste to be transported from source ‘s’ to transfer station ‘i’ during time ‘t’ Wijtm quantity of waste material ‘m’ to be transported from transfer station ‘i’ to landfill ‘j’ during time ‘t’ Wkjtm quantity of waste material ‘m’ to be transported from compost plant ‘k’ to landfill ‘j’ during time ‘t’ Wljt quantity of waste to be transported from incinerator ‘l’ to landfill ‘j’ during time ‘t’

and lower bounds, but it does not reflect the distribution of uncertainty within the upper and lower bounds. However, the fuzzy linear programming can effectively reflect uncertainties due to human impreciseness with the distribution represented by an appropriate membership function. The optimization techniques with fuzzy theory have been used for addressing the solid waste management problems by various researchers, e.g. Chang, Chen, and Wang (1997) and Chang and Wang (1997). Minimax regret optimization technique is a technique which can reduce a problem with uncertainty into a number of subproblems with certainty. These sub-problems are subjected to an algorithm where the regret (of not achieving the objective, in case of the prevailing uncertainty) is minimized (Igor, 2000). This technique has been used for addressing the solid waste management problems under uncertainty by researchers including Chang and Davila (2006, 2007) and Li and Huang (2006a). The interval programming technique was improved by Li and Huang (2006b) and Li, Huang, Nie, and Huang (2006) by proposing a two-stage programming technique in which uncertainties can be expressed as discrete values at certain intervals instead of probability distribution functions. The two stage interval programming was further modified using chance-constrained programming by Li, Huang, Nie, and Qin (2007). The chance constraint interval programming can address to the uncertainties represented by a given probability distributions within the given discrete intervals. Nie, Huang, Li, and Liu (2007) used an interval-parameter fuzzyrobust programming, in which the input parameters are represented as interval numbers of fuzzy membership functions. In this technique it is assumed that the complexity of the real world can be effectively handled using the fuzzy boundary intervals.

Wrjtm Wiltm Wrltm Wkltm Wiktm

aje t ale t ake t bjn t bln t bkn t b0jn t b0ln t b0kn t yjt h

c

lG~ it lk~jt

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quantity of waste material ‘m’ to be transported from recycling centers ‘r’ to landfill ‘j’ during time ‘t’ quantity of waste material ‘m’ to be transported from source ‘i’ to incinerator ‘l’ during time ‘t’ quantity of waste material ‘m’ to be transported from recycling centers ‘r’ to incinerator ‘l’ during time ‘t’ quantity of waste material ‘m’ to be transported from compost plant ‘k’ to incinerator ‘l’ during time ‘t’ quantity of waste material ‘m’ to be transported from transfer stations ‘i’ to compost plants ‘k’ during time ‘t’ binary variable if equal to 1 then existing landfill ‘je’ is in operation during time ‘t’ otherwise 0 binary variable if equal to 1 then existing incinerator ‘le’ is in operation during time ‘t’ otherwise 0 binary variable if equal to 1 then existing compost ‘ke’ is in operation during time ‘t’ otherwise 0 binary variable if equal to 1 then new landfill ‘jn’ is in operation during time ‘t’ otherwise 0 binary variable if equal to 1 then new incinerator ‘ln’ is in operation during time ‘t’ otherwise 0 binary variable if equal to 1 then new compost ‘kn’ is in operation during time ‘t’ otherwise 0 binary variable if equal to 1 then new landfill ‘jn’ is started during time ‘t’ otherwise 0 binary variable if equal to 1 then new incinerator ‘ln’ is started during time ‘t’ otherwise 0 binary variable if equal to 1 then new compost ‘kn’ is started during time ‘t’ otherwise 0 cumulative waste quantity reaching landfill ‘j’ till time ‘t’ possibility level of uncertainty in waste quantity threshold level of uncertainty in capacity membership function for waste quantity membership functions for capacity

Inexact semi infinite programming technique (He and Huang, 2004) takes input parameters in given intervals which are represented as the functions of time. This technique is applied to solid waste management problem by He, Huang, Zeng, and Lu (2008), Guo, Huang, He, and Sun (2008) and Guo, Huang, and He (2008). The inexact semi infinite programming is proved more useful than the interval programming approach because it reflected the dynamic feature of the input variables (e.g., changing waste quantities with respect to time) (Guo, Huang, He, & Zhu, 2009). Li, Huang, Yang, and Nie (2008) used two stage linear programming with fuzzy robust optimization. In two stage programming, initially waste allocation is decided based on the definite quantity of waste generation at the source then the deviated waste quantity is allocated to an available facility. The excess cost due to these additional waste quantities is calculated and termed as the penalty costs (Li, Huang, Nie, & Nie, 2008). The techniques based on fuzzy linear programming enables us to consider uncertainties in the values of decision variables in a more natural and direct way (Zimmermann, 1987). The fuzzy linear programming is suitable in the situation where uncertainties in some of the parameters can be consciously assumed by the decision-maker (Liang, 2008; Pramanik & Roy, 2008). Fuzzy linear programming formulations can be solved using the approach suggested by Bellman and Zadeh (1970). In this approach a maximization problem can be reduced to a deterministic (non-fuzzy) linear programming problem enabling the use of the simplex method. A certain disadvantage of this approach is the fact that one obtains only the maximizing alternative losing the information on the fuzzy decision. A fuzzy decision should provide information on other alternatives which are ‘close’ to the optimal solutions.

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Chanas (1983) proposed a method to overcome the limitations of Bellman–Zadeh’s approach by using the fuzzy parametric programming approach. Chanas’s approach identifies a complete fuzzy decision for the fuzzy mathematical programming problem. The efficient application of fuzzy parametric programming over the other fuzzy linear programming techniques has been demonstrated 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 been used for addressing the uncertainty involved in the solid waste management planning. The fuzzy parametric programming is having definite advantage while addressing to the uncertainties involved in the waste quantities and the capacity constraints on treatment and disposal facilities. Also this approach is unique due to the fact that it gives a set of alternatives which are ‘close’ to the optimal solutions rather than suggesting a unique solution as the optimal solution. A brief description of the fuzzy parametric programming approach is given in the subsequent section. 2.1. The fuzzy parametric programming approach Let us consider the following fuzzy linear programming problem:

min ¼ cx; n X

~; aij xj 6 b i

ð1Þ i ¼ 1; 2; . . . ; m;

ð2Þ

j¼1

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

li ðxÞ ¼

8 s > > > 1  qii <

if

> > > :1

if

n P

aij xj ¼ bi þ si

j¼1 n P

ð3Þ aij xj 6 bi

Eq. (2) can be rewritten as n X

aij xj 6 bi þ u  qi ;

i ¼ 1; 2; . . . m

ð4Þ

j¼1

where parameter uð0 6 u 6 1Þ can be interpreted as the degree of constraints violation. Chanas (1983) has demonstrated that the minimum value of objective function of Eq. (1) can be represented as analytically dependent on u and is a continuous, piece-wise linear and concave function in u. Therefore, above fuzzy linear programming is converted into Eq. (1) and Eq. (4) and can be solved by substituting different values of u between 0 and 1. The fuzzy parametric programming approach for the planning of ISWM is shown in Fig. 1. 3. Developing the model 3.1. Definition of the system The proposed model formulation addresses to the waste management problem consisting of a number of waste generation sources with changing waste quantities and characteristics, a set of existing treatment and disposal facilities at given locations, a set of candidate sites for the treatment and disposal facilities and transportation routes (Fig. 2). The aim of the ISWM planning is to ship the solid waste generated in the region to a suitable treatment or disposal site within a certain period of time after its generation. The set of waste generation sources and transfer stations are represented by ‘s’ and ‘i’, respectively. ‘j’ represents the set of landfills in which jn are the new landfills and je are the existing landfills (j = je [ jn). The set of recycling facilities is represented by r, whereas, k and l represent the sets of compost and incinerators respectively. For each of the waste management facilities, the subscript ‘e’ and ‘n’ shows the existing facilities and the new facilities respectively (i.e. r = re [ rn, k = ke [ kn, l = le [ ln). The total planning period T in divided in the steps of t periods (t e T).

j¼1

where qi is the maximum value of the violation si admissible in the ith constraints. The fuzzy linear programming problem given in Eqs. (1)–(3) can be solved by fuzzy parametric programming approach (Chanas, 1983) as explained below.

3.2. Objective function The objectives considered in the model for optimization are (i) total cost and (ii) environmental risk

Fig. 1. Proposed fuzzy parametric programming approach for ISWM planning.

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Fig. 2. The waste flow network for proposed model formulation.

Minimize ðf1 Þ ¼ Total Cost Minimize ðf2 Þ ¼ Environmental Risk

ð5Þ ð6Þ

The details of methodology used to calculate the total cost and environmental risk are summarized below. 3.3. Estimation of cost The total cost is estimated as the sum of the cost of transportation, operating cost of treatment, and the fixed cost for opening of a new facility minus the income from recycling and compost facilities. The transportation cost include cost will be incurred in transportation of waste from population center or source nodes to transfer station cum segregation facilities, then from segregation facilities to treatment or disposal facilities. The cost incurred in the transportation of waste residue from treatment facilities to disposal facilities has also been included. The operating cost of facilities is cost of processing the waste at treatment and disposal facilities. All the cost components have been converted into the same base year by discounting all the costs at their present worth

whereas TCsit is the transfer cost for unit waste quantity from source nodes/population centers to transfer stations cum segregation facilities. Similarly, TCijt is the transportation cost for unit quantity of waste to be transported between source, ‘i’ and landfill ‘j’ and Wijtm is the quantity of ‘m’ type waste to be transported from source ‘i’ and landfill ‘j’ during time period t. Similarly other terms can be defined. Total operating cost and capital cost of the waste management facilities are computed using Eqs. (8) and (9), respectively

Operation cost ¼

s

þ þ

 OC rt þ

s

þ

XXX X i

þ

þ

m

r

t

j

t

l

t

j

t

l

j

t

W ljt

i

!

W rltm

i

! W irtm

m

i

XX XX t

W iktm

m

XX XX t

!

m

W iltm þ

XX

 OC lt ;

ð8Þ

m

  Capital cost ¼ CC jn t  b0jn t þ CC kn t  b0kn t þ CC ln t  b0ln t ;

W iktm  TC ikt ! W irtm  TC irt

μ

!

Gst

W rjtm  TC rjt !

1

W rltm  TC rlt

m

! W kjtm  TC kjt

m

W kltm  TC klt  W ljt  TC ljt ;

W kltm

m

k

!

m

XXX X t k X l X X 

! W iltm  TC ilt

m

XXX X k

þ

t

XXX X r

þ

k

t

W kjtm

m

k

where OC is the operating cost of facility for unit waste quantity, e.g. OCjt is the capital cost needed to start new landfill ‘jn’ during time ‘t’

W ijtm  TC ijt

m

XXX X r

þ

l

t

r

!

m

XXX X i

þ

t

XXX X i

þ

j

XXX X i

þ

i

W sit  TC sit

t

XX

!

XX XX

l

þ

X

XX

l

r

ð6Þ Transportation cost ¼

W rjtm þ

k

 OC kt þ

W ijtm þ

m

i

m

 OC jt þ

 Income from sale of recyclables and compost;

XXX

t

XX r

þ Capital cost for new facilities

W sit  OC it

t

i

XX XX j

Total cost ¼ Transportation cost þ Operating cost

whereas,

XXX

θ

!

0

m

ð7Þ

a st

G st

bst

∑W

sit

i

Fig. 3. Membership function for solid waste quantities.

ð9Þ

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where CC is the capital cost required to start new facility, e.g. CC jn t is the operating cost of landfill ‘j’ during time ‘t’ and b0 is binary variable. It is assumed that some of the facilities already exist before the planning, therefore, the capital cost is calculated only for new facilities (Eq. (9). Total income from the recycling and composting is estimated using Eq. (10)

Income ¼

XX XX t



m

r

i

X XX m

i

! W irtm  IC tm !

þ

X

R ¼ Tr 1 þ Tr2 ð1  Tr1 Þ þ Tr3 ð1  Tr1 Þð1  Tr 2 Þ þ    þ Trn ð1  Tr 1 Þð1  Tr2 Þ    ð1  Trn1 Þ;

ð13Þ

where R = summation of the risk due to various sources Tr1 = individual risk from source 1 Tr2 = individual risk from source 2 Tr3 = individual risk from source 3 ...

t

W iktm  IK t :

ICtm is the unit selling rate of waste material ‘m’ during time ‘t’ and IKt is the income from selling of compost during time period ‘t’. 3.4. Estimation of environmental risk Waste management facilities pose environmental risk due to possible release of pollutants (Townsend, Dubey, & Tolaymat, 2006). The landfill poses the environmental risk by the emission of landfill gases and leachate, whereas the incinerator may cause air pollution problems. Other facilities like composting and recycling also pose environmental risk. Individual risk from the solid waste management facilities can be calculated as the product of probability of release of contaminant and its consequences in term of hazard (Rapti, Sdao, & Masi, 2006; Valberg, Drivas, McCarthy, & Watson, 1996; Wakefield & Elliott, 2000).

Individual risk ¼ Probability of contaminant release  hazard:

Trn = iIndividual risk from source n

ð10Þ

k

ð11Þ

The hazard to individual population from the solid waste is directly proportional to the total waste quantity to be treated at the facility. The hazardous consequences to the receptors are considered to be attenuated with distance due to dispersion of pollutant and barrier effect of the pathway. Attenuation of environmental risk to the population centers (Melachrinoudis & Cullinane, 1986) is considered to 1 be in the inverse proportion of distance (i.e. Lij / dij ), where Lij is the attenuation factor from location j to i and dij is the direct radial distance between locations i and j. Erkut and Neuman (1993) proposed that the environmental risk a decreases exponentially (i.e., Lij / dij j ) with distance, where exponent term ‘aj’ depends on site conditions such as wind speed, turbulence, etc. Giannikos (1998) proposed an asymmetric function dij and introduced a term for direction/angle (i.e. Lij / functionð/ ). Here jÞ /j is the angle between directions of plume centerline from the reference axis (e.g. prevailing wind direction at the sites). Melachrinoudis, Min, and Wu (1995) improvised the asymmetric function, by incorporating the exponent term as well as direction of the pollutant plume. The attenuation function can be a þcosðhij /i Þ described as Lij / dij j , where hij is angle between line joining to point j and i. This function has been used in the proposed model for computing the factor Lij for attenuation of hazardous consequences. This attenuation function will give a dimensionless number which is called as attenuation factor. Now the individual risk to the receptor can be written as

Individual risk at the receptor ¼ Probability of contaminant release  Waste quantity  attenuation factor:

be estimated as proposed by Kara, Erkut, and Verter (2003) and given in Eq. (13)

ð12Þ

The individual risk defined above includes the probability term. The risk to the receptor from various waste management activities can

The above equation (Eq. (13) is nonlinear and hence difficult to use in case of large scale real life problems. The individual risk from the waste management facilities normally are of the order of 105 to 104 for per million ton of the waste (Moy, 2005). It is to be noted that the risk further reduces due to the attenuation factor. Erkut and Verter (1998) have suggested that above equation can be expressed in a simple additive form with a negligible error

R ¼ Tr 1 þ Tr2 þ Tr 3 þ    :

ð14Þ

In the present model the individual risk is considered as summation of risk due to landfills and incinerators and the total environmental risk 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 node This mass balance constraint at waste generation source ensures that all the waste quantities generated at various sources must be transported to the transfer stations cum segregation facilities which are written as Eq. (15)

X

W sit ¼ Gst

8s; t:

ð15Þ

i

In Eq. (11) Gst and Wsit are the waste quantity generated at source during time ‘t’ and waste quantity to be transported from source ‘s’ to transfer station cum segregation facilities ‘s’. Solid waste quantity (Gst) computed in Eq. (15) is assumed as e st ¼ ðGst ; ast ; bst Þ where Gst, Gst  ast and fuzzy and denoted by G Gst + bst are the most possible, most pessimistic and most optimistic value of solid waste quantities generated at source ‘s’ during time ‘t’. ast and bst define the extreme deviations of waste quantity at source‘s’ during time ‘t’ on left hand and right hand side respectively. The Eq. (15) can be written as Eq. (16) incorporating fuzzy number and inequalities

X

~ st W sit ffi G

8s; t:

ð16Þ

i

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

8 0; > > > > > P > > Gst  W > > i sit <1  ; ast leG ¼ P > st > W Gst > i sit > ; > bit >1  > > > : 0;

P

W sit 6 Gst  ast ;

i

Gst  ast 6

P

W sit 6 Gst ;

i

Gst 6

P i

else:

W sit 6 Gsit þ bst ;

ð17Þ

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A.K. Srivastava, A.K. Nema / Expert Systems with Applications 39 (2012) 4657–4678

P

The aspiration of the DM is completely fulfilled if i W sit ¼ Gst . It also means that the membership function le will be equal to 1. G st Whereas, if the minimum aspiration level is violated the condition P i W sit 6 Gst  ast holds. This indicates that even the minimum target of waste management will not be achieved resulting in comP plete dissatisfaction of the decision maker. In case of iWsit varying between Gst  ast and Gst + bst the satisfaction level will vary between 0 and 1. For interpretation of the membership function in decision, the DM will be required to define possibility level h of waste quantity deviation. With the incorporation of possibility level h in Eq. (17), it can be expressed as Eq. (18)

lG~ itm P h:

ð18Þ

Eq. (16) can be written as Eqs. (19) and (20) and in order to include the possibility level of deviation in waste quantities

X

W sit P Git  ait ð1  hÞ 8i; t;

ð19Þ

W sit 6 Git þ bit ð1  hÞ 8i; t;

ð20Þ

i

X

where HVm is calorific value of individual waste component ‘m’ and RHVl is rated heating value of incinerator. 3.5.3. Capacity constraints The operating capacity of a treatment facility depends on several factors including availability of equipments, manpower, etc. The waste reaching at a facility must be less than or equal to its capacity. In addition to this a minimum operating capacities, constraint is also imposed, which ensures the avoidance of gross resource underutilization. The capacity constraints are divided into two categories, (i) cumulative capacities of the landfills over the time and (ii) operating capacity of facilities for a unit time, which is considered as fuzzy constraint. The maximum operating capacities of treatment/disposal facilities (Qu) are also represented by f with acceptable tolerance of p . Simequivalent fuzzy number ( Qu) ilarly minimum operating capacities (Ql) are represented by fuzzy number, f Ql with acceptable tolerance of p. The maximum operating capacity constraints is expressed as fuzzy inequality (Eqs. (26)–(28))

XX

i

At the waste segregation facilities, the waste stream is further divided into individual waste components and sends to further treatment and/or disposal facilities

X

W irtm¼1;2;4;5 þ

X

r

W iltm¼1;2 þ

X

l

W iktm¼3 þ

X

ð21Þ

The waste stream reaching at recycling centers will be processed for recovery of recyclables and the refuse and residue generated at recycling facilities must be transported to either incinerator or landfills. Waste reaching at incinerator is burnt and converted into ash

X

W rjtm þ

X

j

l

X

X

W kjtm þ

j

W rltm ¼ x 

W irtm

8r; t; m;

ð22Þ

W kltm ¼ n 

W ljt ¼ w 

X

W iktm

8k; t; m;

ð23Þ

XX

j

i

W iltm þ

m

XX k

W kltm þ

m

XX r

W rltm

m

ð24Þ where x and n are the ratio of rejects coming out of recycling and compost plant respectively. w is the ratio of ash residue generated at incinerator. Wrjtm and Wrltm are the waste quantity of composition ‘m’ to be transported from recycling centers to landfills and incinerator respectively during time ‘t’. Wkjtm and Wkltm are the waste quantity of composition ‘m’ to be transported from compost to landfills and incinerator respectively during time ‘t’. Wljt is the quantity of waste residue to be transported for disposal from incinerators. 3.5.2. Technological constraints For the successful operations of incinerator waste of certain minimum calorific value must only used. The model formulation imposes this condition in the form of a constraint so that the calorific value of waste reaching at incinerator will not be less than rated heating value of incinerator

X

X

m

i

P RHV l

! W iltm

 HV m þ

X r

W rltm  HV m þ

X

!

r

W rltm þ

m

W ljt þ

XX r

l

W rjtm

m

ð26Þ XX

W kltm

m

k

ð27Þ

e ukt  ðak t þ b Þ 8k; t: W iktm 6 Q kn t e

ð28Þ

m

i

W ijtm þ

k

e ljt PQ

i

W kjtm þ

m

X

W ljt þ

XX r

l

W rjtm

m

8j; t;

W iltm þ

m

XX i

XX

m

XX

8l; t;

XX

X

The minimum capacity constraints can be expressed as fuzzy inequality as shown in Eqs. (29)–(31)

i

!

m

  ~ lt  al t þ b 6 Qu 8l; t; le t e

XX i

W iltm þ

m

XX

i

l

X

X

i

k

W kjtm þ

  e ujt  aj t þ b 6Q 8j; t; jn t e

XX

W ijtm¼6

XX

m

j

k

8i; t; m:

¼ W itm

i

W ijtm þ

ð29Þ

XX r

W rltm þ

m

e lkt W iktm P Q

XX k

e llt W kltm P Q

8l; t;

ð30Þ

m

8k; t:

ð31Þ

m

The fuzzy capacity is assumed to be with a tolerance level that may not remain available due to uncertainty involved. The membership function (Fig. 4) for capacity (e.g. compost plant) reflects the DM’s level of satisfaction as shown in Eq. (32)

μ kt

1

γ

W kltm  HV m

k

0

8l; t; ð25Þ

pk

Ql kt

Qu kt p k

∑∑W i

iktm

m

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

4664

lk~jt

A.K. Srivastava, A.K. Nema / Expert Systems with Applications 39 (2012) 4657–4678

XX

8 e lkt 6 P P W iktm 6 Qu ; > 1; Q kt > > > m i > > PP > > P P iktm Qukt > < 1  i mW k ; ; Qlkt 6 W iktm 6 Qukt þ p k p m i ¼ P P > > PP Qlkt  W > i m iktm > ; Qlkt P W iktm 6 Qlkt  pk > >1  pk > m > i > : 0; else

i

i

i

  kt Þ ake t þ bkn t ; W iktm 6 ðQukt þ ð1  ck Þp

ð33Þ

  W iktm P Qlkt  ð1  ck Þpkt :

ð34Þ

m

XX m

i

m

r

W rltm þ

XX

m

k

W kltm

m

W ijtm þ

XX

m

k

W kjtm þ

X

m

W ljt þ

ð36Þ

XX r

l

W rjtm

m

P ðQljt  ð1  cj Þpj Þ 8j; t; XX i

W iltm þ

XX

m

r

W rltm þ

ð37Þ XX

m

k

W kltm

m

P ðQllt  ð1  cl Þpl Þ 8l; t:

ð38Þ

In case of the landfills the available capacity of landfill in the entire planning period is an important consideration, which is restricted by the site characteristics. Therefore, in case of landfills, one additional constraint for exhaustible capacity is also imposed

yjt P CQ j

8j; t;

ð39Þ

where CQj is total cumulative capacity of landfill j. 3.5.4. Binary constraints Binary constraints in the model ensure the inclusion capital of new facilities if started. Moreover, the facilities will be in operation if it is receiving waste in a particular planning period. An additional

Table 1 Planning periods.

Threshold level for other facilities like incinerators and landfills can also be formulated as shown below

XX

m

XX

The membership function for waste management facilities as shown in Fig. 4 is based on the assumption that, if waste quantities reaching to a site are more than the available capacity then satisfaction level of DM decreases and DM will be totally dissatisfied if waste flow reaches beyond tolerance point of maximum k ) resulting in infeasible condition. Similarly, capacity (Qukt þ p the DM will also be totally dissatisfied if the waste quantity is below tolerance point of minimum capacity (Qlkt  pk ) because the capacity will remain grossly underutilized. The satisfaction level of the DM is at its maximum when the waste quantity is between the estimated minimum and maximum operating capacities. For a given threshold ck, the DM’s satisfaction level (lðP P W iktm Þ P ck ) i m for compost plant’s capacities can be formulated as Eqs. (33) and (34)

i

XX

~ ult þ ð1  c Þpl Þ  ðal t þ b Þ 8l; t; 6 ðQ le t e l

ð32Þ

XX

W iltm þ

W ijtm þ

XX k

m

W kjtm þ

X

W ljt þ

XX r

l

j Þ  ðaje t þ bj t Þ 8j; t; 6 ðQujt þ ð1  cj Þp n

W rjtm

m

ð35Þ

Planning periods

Years

Ist Planning period IInd Planning period IIIrd Planning period IVth Planning period

2007–2009 2009–2014 2014–2019 2019–2024

Fig. 5. Waste generation source and its’ treatment/management facilities of Delhi.

4665

A.K. Srivastava, A.K. Nema / Expert Systems with Applications 39 (2012) 4657–4678 Table 2 Projected waste quantities in different zones of Delhi. Year

2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024

Yearly waste quantity(Gst) (in 103 tons) in the zone Shadhara (South)

South zone

Rohini

Central zone

Karol Bagh

City

Sadar

West

Civil lines

Shadhara (North)

Narela

Nagafgarh

983 1025 1068 1114 1161 1210 1261 1315 1370 1429 1489 1551 1615 1682 1751 1825 1902 1982

951 991 1033 1077 1122 1170 1220 1271 1325 1382 1440 1500 1562 1626 1693 1765 1839 1917

1093 1139 1187 1237 1290 1344 1401 1461 1522 1588 1654 1723 1795 1869 1945 2028 2113 2203

749 780 813 848 884 921 960 1001 1043 1088 1133 1181 1230 1280 1333 1389 1448 1509

369 385 401 418 436 454 474 494 515 537 559 583 607 632 657 685 714 745

261 272 283 295 308 321 335 349 364 379 395 412 429 446 465 484 505 526

201 209 218 227 237 247 257 268 279 291 304 316 329 343 357 372 388 404

645 672 701 730 761 794 827 862 899 937 976 1017 1059 1103 1148 1197 1247 1300

657 684 713 744 775 808 842 878 915 954 994 1036 1079 1123 1169 1219 1270 1324

976 1017 1060 1105 1152 1200 1251 1304 1359 1418 1477 1539 1602 1668 1737 1810 1887 1967

304 317 330 344 359 374 390 406 424 442 460 480 499 520 541 564 588 613

552 575 600 625 652 679 708 738 769 802 836 871 907 944 983 1025 1068 1113

binary variable imposes constraint on the landfills, if it is closed once then cannot be started. The variable a and b used in above equations are binary in nature for existing and new facilities. These binary variables should be 1 if facility is receiving waste and 0 otherwise

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

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

XX

Landfills (Rj)

i

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).

Incinerator (Rl)

Air emission 3.9  1005

W ijtm þ

m

Leachate emission 4.1  1005

XX k

W kjtm þ

m

X

W ljt þ

Air emission 3.9  103

XX r

l

P ðaje t þ bjn t Þ 8j; t; XX i

W ijtm þ

m

XX k

ð40Þ W kjtm þ

m

X

W ljt þ

XX r

l

6 M  ðaje t þ bjn t Þ 8j; t; Table 4 The heating value of waste components.

XX

Waste component

Heating value (HVm) (kcal/kg)

Paper Plastic Food

3440 6425 1810

i

W iltm þ

m

XX r

W rltm þ

m

i

m

W iltm þ

XX r

XX k

W kltm

m

ð42Þ W rltm þ

m

XX k

W kltm

m

6 M  ðale t þ ble t Þ 8l; t: XX

1 2 3

Parameters

Value

Average transportation cost (TC) 1 Average operating cost for landfill (OCj)1 Average operating cost for incinerator (OCl)1 Average operating cost for compost (OCk)1 Income from sell of recyclable2 (ICm) Metal Glass Plastic Paper Income from sell of compost3 (IKm) Reduction ratio for incinerator3 (w) Ratio of rejects from compost plants3 (n) Ratio of rejects from recycling facilities3 (x) Fixed cost of new landfills3 (FCj) Bhati mines Jaitpur Narela

Rs. 5.00 per ton per km Rs. 325.00 per ton Rs. 1140.00 per ton Rs. 35.00 per ton Rs. 430.00 per ton Rs. 12.00 per ton Rs. 72.00 per ton Rs. 22.00 per ton Rs. 9.00 per ton 0.8 0.1 0.1 Rs. 30.6  106 Rs. 53.5  106 Rs. 76.05  106

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

i

ð43Þ

W iktm P ðake t þ bkn t Þ 8k; t;

ð44Þ

W iktm 6 M  ðake t þ bkn t Þ 8k; t:

ð45Þ

m

XX i

W rjtm

m

ð41Þ

P ðale t þ ble t Þ 8l; t; XX

Table 5 Values of parameters used in this case study.

W rjtm

m

m

In the above Eqs. (41), (43), and (45), the coefficient used M is a big number, which will be obviously quite larger than capacities. In addition two above binary variables, one more binary variable are computed for existing and new landfills, to prevent reopening of landfills after closure (Eqs. (46) and (47)

aje t  aje t1 ¼ a0jen t 8j 2 e; t;

ð46Þ

bjn t  bjn t1 ¼ b0jn t

ð47Þ

8j 2 n; t:

The following Eqs. (46) and (47) prevents reopening of landfills if it is closed

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A.K. Srivastava, A.K. Nema / Expert Systems with Applications 39 (2012) 4657–4678

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

Projected populations (Hst)

Shadhra (S) South Rohini Central Zone Karol Bagh City Zone Sadar Bazar West Zone Civil Lines Shadhra (N) Narela Nagafgarh

X t

X t

Ist Period

IInd Period

IIIrd Period

IVth Period

2,126,234 2,055,918 2,362,296 1,618,449 798,593 564,205 433,617 1,394,609 1,419,721 2,109,325 657,458 1,193,705

2,473,452 2,391,653 2,748,064 1,882,744 929,005 656,341 504,428 1,622,351 1,651,564 2,453,781 764,822 1,388,639

2,873,121 2,778,104 3,192,105 2,186,965 1,079,117 762,395 585,935 1,884,496 1,918,430 2,850,272 888,405 1,613,020

3,333,623 3,223,377 3,703,734 2,537,490 1,252,077 884,591 679,849 2,186,542 2,225,915 3,307,112 1,030,798 1,871,554

a0jn t 6 1 8j 2 n;

ð48Þ

b0jn t 6 1 8j 2 e:

ð49Þ

The binary variable b0 also ensures inclusion of fix cost in the total cost at the time of commissioning of new facilities. Therefore, this variable must also be computed for compost and incineration facilities (Eq. (50) and (51)

bln t  bln t1 ¼ b0ln t bkn t  bkn t1 ¼ b0kn t

8l 2 n; t;

ð50Þ

8k 2 n; t

ð51Þ

It can be seen that the presented fuzzy model is a non-linear model in case of unknown waste quantity and value of h and c. The model is solved as fuzzy parametric programming model using the approach proposed by Chanas (1983). 4. Example problem The utility of the model is demonstrated by an example problem, which is inspired from the case of solid waste management in National Capital City of Delhi, India. The waste flow network of example problem, consist of existing twelve zones of MCD as population centres, one incinerator, two

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

Planning period

Timarpur incinerator

Compost

Landfills

Ghazipur

Bhalswa

Okhla

Ghazipur

Bhalswa

Bhatimines

Jaitpur

Narela

0.0

1 2 3 4

1159 2284 2809 2755

1111 2036 2504 6745

7300 14,534 17,877 18,250

1302 0 0 0

3889 0 0 0

5400 0 0 0

0 0 0 5560

0 13,300 13,300 13,300

0 7563 12,361 13,300

0.1

1 2 3 4

1172 2309 2840 2933

1205 2058 2532 7023

7300 14,696 18,075 18,250

1316 0 0 0

3992 0 0 0

5400 0 0 0

0 0 0 5770

0 13,300 13,300 13,300

0 7794 12,646 13,300

0.2

1 2 3 4

1185 2334 2871 3112

1298 2081 2584 7300

7300 14,857 18,250 18,250

1358 0 0 0

4068 0 0 0

5400 0 0 0

0 0 0 5980

0 13,300 13,300 13,300

0 8026 12,931 13,300

0.3

1 2 3 4

1198 2360 2903 3290

1392 2104 2810 7578

7300 15,018 18,250 18,250

1432 0 0 0

4112 0 0 0

5400 0 0 0

0 0 0 6189

0 13,300 13,300 13,300

0 8258 13,216 13,300

0.4

1 2 3 4

1211 2385 2934 3470

1485 2126 3037 7856

7300 15,180 18,250 18,250

1505 0 0 0

4156 0 0 0

5400 0 0 0

0 1554 4158 6397

0 12,638 13,300 13,300

0 7597 9344 13,300

0.5

1 2 3 4

1224 2411 2965 3612

1579 2149 3263 8134

7300 15,341 18,250 18,250

1578 0 0 0

4200 0 0 0

5400 0 0 0

0 1571 4343 6643

0 12,773 13,300 13,300

0 7678 9443 13,300

0.6

1 2 3 4

1237 2436 2996 3650

1672 2171 3490 8411

7300 15,503 18,250 18,250

1652 0 0 0

4245 0 0 0

5400 0 0 0

0 1587 4529 6993

0 12,907 13,300 13,300

0 7759 9543 13,300

0.7

1 2 3 4

1249 2461 3027 3688

1766 2194 3716 8689

7300 15664 18250 18250

1725 0 0 0

4289 0 0 0

5400 0 0 0

0 1604 4648 7343

0 13042 13300 13300

0 7839 9709 13300

0.8

1 2 3 4

1262 2487 3059 3726

1859 2217 3943 8967

7300 15,826 18,250 18,250

1799 0 0 0

4333 0 0 0

5400 0 0 0

0 1620 4696 7693

0 13,176 13,300 13,300

0 7920 9946 13,300

0.9

1 2 3 4

1275 2512 3090 3764

1953 2239 4169 9245

7300 15,987 18,250 18,250

1872 0 0 0

4377 0 0 0

5400 0 0 0

0 1648 4744 8043

0 13,300 13,300 13,300

0 8001 10,183 13,300

1.0

1 2 3 4

1288 2537 3121 3802

2046 2262 4395 9522

7300 16,149 18,250 18,250

1946 0 0 0

4422 0 0 0

5400 0 0 0

0 1799 4791 8392

0 13,300 13,300 13,300

0 8082 10,421 13,300

A.K. Srivastava, A.K. Nema / Expert Systems with Applications 39 (2012) 4657–4678

compost and six landfills (three existing and three candidate sites) of Delhi (Fig. 5). From each of these zones the waste is to be transported to waste management facilities. As per MSW rule the waste before transportation to a waste management facilities must be segregated. Therefore, the transfer station is assumed to also act as segregation facilities. These distances are computed from the map of Delhi (http://www.mapmyindia.com) and are based on the existing road network in Delhi. The long term municipal solid waste management plan involves activities associated with transfer and transport, location and capacity planning of processing, recovery and disposal facilities and waste allocation for these facilities. The recommended planning period for long term planning is 15–25 years (CPHEEO, 2000). However, as a good management practice, the duration of initial design period is kept small to take corrective measures if any (Huang et al., 1997). Taking consideration of above views and keeping in view the master plan for Delhi 2021, the planning period of present study is considered to be 17 years divided into four periods (Table 1). 4.1. Waste quantities and composition Assessment of current and future waste streams is essential and indispensable fundamental in waste management planning (Beigl et al., 2008). In this study, future quantities of waste generation

4667

are estimated based on population forecast and waste generation factor. Per capita average waste generation in Delhi is estimated as 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 shown in Table 2. For the computation of deviation of solid waste quantities generated at source (i.e. ait and bit), the range of ±5% is considered in the study. The composition and characteristics of municipal solid wastes vary from place to place as it depends on number of factors such as social customs, standard of living, geographical location, climate, etc. MSW is heterogeneous in nature and consists of a number of different materials derived from various types of activities. In absence of projected composition of solid waste for the region of example problem, the existing average composition of Delhi is taken from literature as input (Table 3). The calorific value of waste should be controlled to keep incinerator self sustaining otherwise auxiliary fuels are needed to incinerate the waste. The total calorific heating values waste is calculated based on the calorific value of individual waste given in Table 4 and the rated heating value of solid waste for Timarpur incinerator is 1462.5 kcal/kg (MNES, 2006). The economic data used 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

Fig. 6. Variation of objective values for different value of h(c = 1).

4668

A.K. Srivastava, A.K. Nema / Expert Systems with Applications 39 (2012) 4657–4678

equipment, manpower, other resource like electricity water, and (ii) exhaustive capacity, which is applicable in the case of landfills and decided based on the availability total land area for the landfill. Operating capacities of treatment and processing facilities are not considered as a constraint. The operating capacity for the landfills is taken as 7200 tons/day and the exhaustible capacity is taken for existing dumps as 54  105 tons (Personal Communication, Municipal Corporation of Delhi, 2006).

4.2. Environmental risk factor Risk factor used in model is defined as a quantified value of harm to environment from unit waste quantities if it is processed or disposed off in a waste management facility. The quantification of risk involves formal, scientific process to analyze the potential for harm following exposure to chemicals or other agents, which has been given in literatures (Ministry of Environment, 1999; Defra, 2004, Moy, 2005). The risk factor from waste management

facility is location specific data. For the example problem the risk factors considered are given in Table 6. The risk factors are assumed to be in the similar range as reported by Moy (2005) in absence of risk factor data for Delhi. The total risk to environment is computed by multiplying the risk factor with receptor population in the region. The data of projected population is taken from the national commission of population and reproduced in Table 7. The attenuation of risk has been considered through its pathways i.e., air and subsurface. The value dispersion angle from its centerline ð/i Þ, for the air dispersion is computed as 700 for all the landfill sites as well as incineration sites. This dispersion angle for air pathway is based on the windrose diagram of annual average wind data, which was collected from Indian Metrological Department New Delhi. The values of subsurface dispersion angle are computed as 1220, 1240, 2300, 300, 3030 and 2300 for Bhatti Mines, Jaitpur, Narela, Okhla, Ghazipur, and Bhalswa respectively. These values for subsurface dispersion were calculated based on the steepest ground slope at the respective landfill sites.

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

Planning period

Timarpur incinerator

Compost

Landfills

Ghazipur

Bhalswa

Okhla

Ghazipur

Bhalswa

Bhatimines

Jaitpur

Narela

0.0

1 2 3 4

1159 2284 2809 2755

1111 2036 2504 6745

7300 14,534 17,877 18,250

1302 0 0 0

3889 0 0 0

5400 0 0 0

0 0 0 5560

0 13,300 13,300 13,300

0 7563 12,361 13,300

0.1

1 2 3 4

1172 2309 2840 2933

1205 2058 2532 7023

7300 14,696 18,075 18,250

1316 0 0 0

3992 0 0 0

5400 0 0 0

0 0 0 5770

0 13,300 13,300 13,300

0 7794 12,646 13,300

0.2

1 2 3 4

1185 2334 2871 3112

1298 2081 2584 7300

7300 14,857 18,250 18,250

1358 0 0 0

4068 0 0 0

5400 0 0 0

0 0 0 5980

0 13,300 13,300 13,300

0 8026 12,931 13,300

0.3

1 2 3 4

1198 2360 2903 3290

1392 2104 2810 7578

7300 15,018 18,250 18,250

1432 0 0 0

4112 0 0 0

5400 0 0 0

0 0 0 6189

0 13,300 13,300 13,300

0 8258 13,216 13,300

0.4

1 2 3 4

1211 2385 2934 3470

1485 2126 3037 7856

7300 15,180 18,250 18,250

1505 0 0 0

4156 0 0 0

5400 0 0 0

0 1554 4158 6397

0 12,638 13,300 13,300

0 7597 9344 13,300

0.5

1 2 3 4

1224 2411 2965 3612

1579 2149 3263 8134

7300 15,341 18,250 18,250

1578 0 0 0

4200 0 0 0

5400 0 0 0

0 1571 4343 6643

0 12,773 13,300 13,300

0 7678 9443 13,300

0.6

1 2 3 4

1237 2436 2996 3650

1672 2171 3490 8411

7300 15,503 18,250 18,250

1652 0 0 0

4245 0 0 0

5400 0 0 0

0 1587 4529 6993

0 12,907 13,300 13,300

0 7759 9543 13,300

0.7

1 2 3 4

1249 2461 3027 3688

1766 2194 3716 8689

7300 15,664 18,250 18,250

1725 0 0 0

4289 0 0 0

5400 0 0 0

0 1604 4648 7343

0 13,042 13,300 13,300

0 7839 9709 13,300

0.8

1 2 3 4

1262 2487 3059 3726

1859 2217 3943 8967

7300 15,826 18,250 18,250

1799 0 0 0

4333 0 0 0

5400 0 0 0

0 1620 4696 7693

0 13,176 13,300 13,300

0 7920 9946 13,300

0.9

1 2 3 4

1275 2512 3090 3764

1953 2239 4169 9245

7300 15,987 18,250 18,250

1872 0 0 0

4377 0 0 0

5400 0 0 0

0 1648 4744 8043

0 13,300 13,300 13,300

0 8001 10,183 13,300

1.0

1 2 3 4

1288 2537 3121 3802

2046 2262 4395 9522

7300 16,149 18,250 18,250

1946 0 0 0

4422 0 0 0

5400 0 0 0

0 1799 4791 8392

0 13,300 13,300 13,300

0 8082 10421 13,300

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A.K. Srivastava, A.K. Nema / Expert Systems with Applications 39 (2012) 4657–4678

5. Results and discussion The proposed multi-objective, multi-period model was applied to the example problem to understand the effect of priority to various objectives on waste allocation to various management alternatives and to study the effect of aspiration level of the decision maker to address the uncertainty in waste generation quantities and the capacities of the waste management facilities. Waste treatment and disposal facilities are simulated in a simplified way in the form of point nodes with only input and output being modeled. The internal process in the facilities is not being modeled in the present study. The example problem was solved for three different cases. In case I, the model is solved for different values of h, keeping constant value of c = 1. The value of c = 1 represent the case of fixed capacities of facilities, i.e. the additional limit of capacity would not be used in case of deviation of waste quantities. In this case, implementation planning is to be carried out with fixed planned

capacity. In the case II, model is solved for different value of c with constant value of h. This case implies the situation when there would not be deviation in waste quantities but additional capacity would be available during implementation of planning. Whereas, case III represent the simultaneous changing value h and c. This condition reflects the situation, when there is chance of deviation of waste quantities as well as capacities, which were earlier evaluated by decision maker as input to the model. The model consists of two objectives and the model is solved for three different scenarios in each of the cases explained above. Scenario I represent 100% weighting to cost, scenario II represents 50–50% weighting to both cost and risk, and scenario III represents 100% weighting to risk. 5.1. Changing value of h with constant c The example problem has been solved for all three scenarios for different values h between 0 and 1 with an increment of 0.1 and

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

Planning period

Timarpur incinerator

Compost

Landfills

Okhla

Ghazipur

Okhla

Bhatimines

Jaitpur

Narela

0.0

1 2 3 4

1159 2284 2809 3445

4061 2429 2989 6745

4350 14,140 17,392 18,250

5400 0 0 0

5189 0 0 0

Ghazipur

Bhalswa 0 0 0 0

0 13,300 13,300 13,300

0 0 0 4870

0 7563 12,361 13,300

0.1

1 2 3 4

1172 2309 2840 3483

4106 2457 3022 7023

4399 14,297 17,585 18,250

5400 0 0 0

5307 0 0 0

0 0 0 0

0 13,300 13,300 13,300

0 0 0 5220

0 7794 12,646 13,300

0.2

1 2 3 4

1185 2334 2871 3521

4151 2484 2584 7300

4447 14,454 18,250 18,250

5400 0 0 0

5400 0 0 0

26 0 0 0

0 13,300 13,300 13,300

0 0 0 5570

0 8026 12931 13,300

0.3

1 2 3 4

1198 2360 2903 3560

4197 2511 2810 7578

4495 14,612 18,250 18,250

5400 0 0 0

5400 0 0 0

144 0 0 0

0 13,300 13,300 13,300

0 0 93 5919

0 8258 13,216 13,300

0.4

1 2 3 4

1211 2385 2934 3598

4242 2538 3037 7856

4544 14,769 18,250 18,250

5400 0 0 0

5400 0 0 0

261 0 0 0

0 13,300 13,300 13,300

0 0 201 6269

0 8490 13,300 13,300

0.5

1 2 3 4

1224 2411 2965 3636

4287 0 3263 8134

4592 17,490 18,250 18,250

5400 0 0 0

5400 0 0 0

379 0 0 0

0 13,300 13,300 13,300

0 0 486 6619

0 8721 13,300 13,300

0.6

1 2 3 4

1237 2436 2996 3675

4332 0 3490 8411

4640 17,674 18,250 18,250

5400 0 0 0

5400 0 0 0

497 0 0 0

0 13,300 13,300 13,300

0 0 772 6969

0 8953 13,300 13,300

0.7

1 2 3 4

1249 2461 3027 3713

4377 2619 3716 8689

4689 15,240 18,250 18,250

5400 0 0 0

5400 0 0 0

614 0 0 0

0 13,300 13,300 13,300

0 0 1057 7318

0 9185 13,300 13,300

0.8

1 2 3 4

1262 2487 3059 3751

4422 2646 6576 8967

4737 15,397 15,617 18,250

5400 0 0 0

5400 0 0 0

732 0 0 0

0 13,300 13,300 13,300

0 0 1342 7668

0 9417 13,300 13,300

0.9

1 2 3 4

1275 2512 3090 3789

4468 2673 4169 9245

4785 15,554 18,250 18,250

5400 0 0 0

5400 0 0 0

850 0 0 0

0 13,300 13,300 13,300

0 0 1627 8018

0 9648 13,300 13,300

1.0

1 2 3 4

1288 2537 3121 3828

4513 2700 4395 9522

4833 15,711 18,250 18,250

5400 0 0 0

5400 0 0 0

968 0 0 0

0 13,300 13,300 13,300

0 0 1912 8367

0 9880 13,300 13,300

4670

A.K. Srivastava, A.K. Nema / Expert Systems with Applications 39 (2012) 4657–4678

constant values of c (=1). The variation of the objective values is shown in Fig. 6(a)–(c) for scenarios I, II and III, respectively. The quantities of waste to be diverted towards different facilities are shown in the Tables 8–11 for scenarios I, II and III respectively. In case of scenario I (Fig 6(a)) that the total cost of the project vary linearly except at the values of h between 0.3 and 0.4. The total cost is increasing at a rate of 1.15% until h = 0.3, whereas the rate increased to 6.73% between h = 0.3 and 0.4. The total cost increases at a rate of 1.04% after h = 0.5. All inert and residue waste generated in the planning period I is to be disposed off in the existing landfills (Table 8). However, due to limited cumulative capacity of existing landfills, the waste is to be diverted towards new landfill sites namely Jaitpur and Narela for planning period II. In these new landfill sites the, Jaitpur site, being closer to the population centers is to receive more waste quantities and only the surplus waste is to be diverted towards Jaitpur landfill site for all the value of h. The Bhatimines landfill site is to start receiving waste in planning period II for value of h more than 0.4 otherwise it will receive waste only in planning period IV.

Fig. 6(b) shows the increase in the total risk with h in case of scenario II. The rate of increase of total risk till h = 0.2 is about 1.29% whereas after this point risk average increase in risk is about 1.40%. This change of rate of increase is due to the start of new landfill site at Jaitpur. Among existing landfills, Bhalswa is closer to the population center, therefore, it starts receiving the waste only after the capacities of other existing landfills are exhausted particularly after h = 0.2. In case of scenario III, which considers equal weighting to cost as well risk, the decisions of waste diversion and facility location is observed to be changing more frequently. The first change in rate of increase of cost is observed at h = 0.2 as soon as the Bhalswa landfill starts receiving the waste. Similarly the change in the slope is observed at h = 0.4 which is due to the start of Jaitpur landfill. Comparison of the results of scenario II and III shows the waste flow is similar till h = 0.2 and changes at the start of the Jaitpur landfill for the scenario II at h = 0.3. It can be seen that the starting of Jaitpur landfill is deferred till h = 0.4 for scenario III. The Narela landfill has similar waste flow allocation for scenario I and III till

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

Planning period

Timarpur Incinerator

Compost

Landfills

Okhla

Ghazipur

Okhla

Bhatimines

Jaitpur

Narela

0.0

1 2 3 4

1159 2284 2809 3445

4061 4780 5989 6745

4350 16,570 17,392 18,250

5400 0 0 0

Ghazipur 5189 0 0 0

Bhalswa 0 0 0 0

0 13,300 13,300 13,300

0 0 0 4870

0 7563 12,361 13,300

0.1

1 2 3 4

1172 2309 2840 3483

4106 2457 3022 7023

4399 14,297 17,585 18,250

5400 0 0 0

5307 0 0 0

0 0 0 0

0 13,300 13,300 13,300

0 0 0 5220

0 7794 12,646 13,300

0.2

1 2 3 4

1185 2334 2871 3521

4151 2484 3055 7300

4447 14,454 17,779 18,250

5400 0 0 0

5400 0 0 0

26 0 0 0

0 13,300 13,300 13,300

0 0 0 5570

0 8026 12,931 13,300

0.3

1 2 3 4

1198 2360 2903 3560

4197 2511 3585 7578

4495 14,612 17,475 18250

5400 0 0 0

5400 0 0 0

144 0 0 0

0 13,300 13,300 13,300

0 0 0 5919

0 8258 13,216 13,300

0.4

1 2 3 4

1211 2385 2934 3598

4242 3062 3037 7856

4544 15,306 18,250 18,250

5400 0 0 0

5400 0 0 0

261 0 0 0

0 13,300 13,300 13,300

0 0 201 6269

0 8490 13,300 13,300

0.5

1 2 3 4

1224 2411 2965 3636

4287 2565 3663 8134

4592 14,926 17,851 18,250

5400 0 0 0

5400 0 0 0

379 0 0 0

0 13,300 13,300 13,300

0 0 486 6619

0 8721 13,300 13,300

0.6

1 2 3 4

1237 2436 2996 3675

4332 5139 3490 8411

4640 12,674 18,250 18,250

5400 0 0 0

5400 0 0 0

497 0 0 0

0 13,300 13,300 13,300

0 0 772 6969

0 8953 13,300 13,300

0.7

1 2 3 4

1249 2461 3027 3713

4377 5620 3716 8689

4689 12,239 18,250 18,250

5400 0 0 0

5400 0 0 0

614 0 0 0

0 13,300 13,300 13,300

0 0 1057 7318

0 9185 13,300 13,300

0.8

1 2 3 4

1262 2487 3059 3751

4422 2646 4380 8967

4737 15,397 17,812 18,250

5400 0 0 0

5400 0 0 0

732 0 0 0

0 13,300 13,300 13,300

0 0 1342 7668

0 9417 13,300 13,300

0.9

1 2 3 4

1275 2512 3090 3789

4468 2673 4169 9245

4785 15,554 18,250 18,250

5400 0 0 0

5400 0 0 0

850 0 0 0

0 13,300 13,300 13,300

0 0 1627 8018

0 9648 13,300 13,300

1.0

1 2 3 4

1288 2537 3121 3828

4513 2700 6710 9522

4833 15,711 15,936 18,250

5400 0 0 0

5400 0 0 0

968 0 0 0

0 13,300 13,300 13,300

0 0 1912 8367

0 9880 13,300 13,300

A.K. Srivastava, A.K. Nema / Expert Systems with Applications 39 (2012) 4657–4678

at h = 0.4. For scenario I, Narela landfill starts receiving less quantity of waste after h = 0.4 due to Bhatimines landfill. It can be observed that the changing priority and weighting to different objectives, i.e., minimization of cost and/or risk has significant influence on the decision of selecting the new landfills as well as use of the existing landfills. The preference among the new landfills is Jaitpur, Narela and Bhatimines for minimization of cost whereas, the preference changes to Bhatimines, Narela and Jaitpur for the minimization of risk. In case of equal weighting to cost and risk the preference are Bhatimines, Narela and Jaitpur. It was observed that, with increasing value of h, the planning period in which the new landfills need to be opened gets shortened. This indicates the effect of uncertainty of waste forecasting model on the planning in terms of opening the new landfills. 5.2. Changing value of c with constant h Effect of changing value of c with a constant value of h is studied by solving the example problem for all three scenarios with changing the weighting of cost and risk in the same manner as presented in above section. The example problem has been solved for different 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 value of c for scenario I. The cost is increasing for all the cases with increasing value of c. It can be seen that, the total cost varies almost linearly at the rate of 0.006%, which shows that there is almost insignificant variation in the total cost with changing

4671

values of c. It can be seen from Table 11, that all the existing landfills would receive the waste only in first planning period and all new landfill sites would be started receiving the waste from the second planning periods. It is also observed that for all value of c, none of the new landfill is started unexpectedly and the capacities of Jaitpur landfill site is exhausted earlier than other landfill sites. The value of total risk increases linearly with changing c (Fig. 7b). The rate of increase of risk is 0.15%. The waste allocation for different value of c is given in Table 12. It can be seen that, Jaitpur, the closest landfill site to population centers, is started in third planning period for all the values of c. The total cost is constant between c = 0.0 and 0.1 for scenario III and a sharp increase is observed at c = 0.6 (Fig. 7c). The change in the waste allocation for different value of c is observed only in the planning period, where landfill is receiving waste until the full utilization of its operating capacity Table 13. For scenario I, the Jaitpur landfill is found to be the most preferred landfill and is receives waste till the full utilization of its operating capacities for all values of c in planning periods III and IV. However, at the exhaustion of operating capacity of Jaitpur landfill the waste is to be diverted to Bhatimines and Narela landfills (for c P 0.2). (See Tables 13–17). It has been observed that the preference for changing c among the choice of new landfills at Jaitpur, Narela and Bhatimines remains same as found in the case of changing h for different scenarios.

Fig. 7. Variation of objective values for different value of c(h = 1).

4672

A.K. Srivastava, A.K. Nema / Expert Systems with Applications 39 (2012) 4657–4678

5.3. Simultaneous changing value of h and c The simultaneous changing values of h and c reflects the cases when uncertain waste quantity deviate positively and part of working capacity is not available. The Fig. 8(a)–(c) shows the variation of objective functions with h and c. For scenario I, the total cost suddenly increases when value of h as well as c reaches to 0.7 (Fig. 8a). The change in rate of increase of cost is observed due to advancement of starting of Bhatimines landfill from planning period III to planning period II. Similar change is observed in Fig. 6(a) at h = 0.4, and c = 1, which show that due to simultaneous 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 as c = 0.4. It can be seen that just before this point, the rate of increase of total is risk is 1.23%, which becomes 1.67% after this point.

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  1011 to Rs. 1.15  1011. The Jaitpur landfill site would start in the planning period II for h as well as c = 0.6, resulting in sudden change in the cost.

6. Summary and conclusions A fuzzy parametric model has been presented in the present study for the long term planning for integrated solid waste management with uncertain parameters. Unlike the existing models, the uncertainties in waste quantities and capacities of waste management facilities have been addressed as inbuilt feature in the model in terms of the shape of membership function. The output of model gives a set of alternative solutions for the range of membership function, which reflects the aspiration level of the decision maker.

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

c

Planning periods

Timarpur incinerator

Compost

Landfills

Okhla

Ghazipur

Okhla

Ghazipur

Bhalswa

Bhatimines

Jaitpur

Narela

0.0

1 2 3 4

1288 2537 3121 3802

2046 2262 4395 9522

7300 16,149 18,250 18,250

1856 0 0 0

4422 0 0 0

5490 0 0 0

0 1653 4702 7252

0 13,445 13,870 13,870

0 8082 9940 13,870

0.1

1 2 3 4

1288 2537 3121 3802

2046 2262 4395 9522

7300 16,149 18,250 18,250

1865 0 0 0

4422 0 0 0

5481 0 0 0

0 1653 4759 7366

0 13,445 13,813 13,813

0 8082 9940 13,813

0.2

1 2 3 4

1288 2537 3121 3802

2046 2262 4395 9522

7300 16,149 18,250 18,250

1874 0 0 0

4422 0 0 0

5472 0 0 0

0 1653 4791 7480

0 13,445 13,756 13,756

0 8082 9965 13,756

0.3

1 2 3 4

1288 2537 3121 3802

2046 2262 4395 9522

7300 16,149 18,250 18,250

1883 0 0 0

4422 0 0 0

5463 0 0 0

0 1653 4791 7594

0 13,445 13,699 13,699

0 8082 10,022 13,699

0.4

1 2 3 4

1288 2537 3121 3802

2046 2262 4395 9522

7300 16,149 18,250 18,250

1892 0 0 0

4422 0 0 0

5454 0 0 0

0 1653 4791 7708

0 13,445 13,642 13,642

0 8082 10,079 13,642

0.5

1 2 3 4

1288 2537 3121 3802

2046 2262 4395 9522

7300 16,149 18,250 18,250

1901 0 0 0

4422 0 0 0

5445 0 0 0

0 1653 4791 7822

0 13,445 13,585 13,585

0 8082 10,136 13,585

0.6

1 2 3 4

1288 2537 3121 3802

2046 2262 4395 9522

7300 16,149 18,250 18,250

1910 0 0 0

4422 0 0 0

5436 0 0 0

0 1653 4791 7936

0 13,445 13,528 13,528

0 8082 10,193 13,528

0.7

1 2 3 4

1288 2537 3121 3802

2046 2262 4395 9522

7300 16,149 18,250 18,250

1919 0 0 0

4422 0 0 0

5427 0 0 0

0 1653 4791 8050

0 13,445 13,471 13,471

0 8082 10,250 13,471

0.8

1 2 3 4

1288 2537 3121 3802

2046 2262 4395 9522

7300 16,149 18,250 18,250

1928 0 0 0

4422 0 0 0

5418 0 0 0

0 1685 4791 8164

0 13,414 13,414 13,414

0 8082 10,307 13,414

0.9

1 2 3 4

1288 2537 3121 3802

2046 2262 4395 9522

7300 16,149 18,250 18,250

1937 0 0 0

4422 0 0 0

5409 0 0 0

0 1742 4791 8278

0 13,357 13,357 13,357

0 8082 10,364 13,357

1.0

1 2 3 4

1288 2537 3121 3802

2046 2262 4395 9522

7300 16,149 18,250 18,250

1946 0 0 0

4422 0 0 0

5400 0 0 0

0 1799 4791 8392

0 13,300 13,300 13,300

0 8082 10421 13,300

4673

A.K. Srivastava, A.K. Nema / Expert Systems with Applications 39 (2012) 4657–4678 Table 13 Waste diversion for different values of c under constant h (=1) for scenario II (waste quantities in ‘000 tons).

c

Planning periods

Timarpur incinerator

Okhla

Ghazipur

Okhla

Ghazipur

Bhalswa

Bhatimines

Jaitpur

Narela

0.0

1 2 3 4

1288 2537 3121 3828

4513 2700 4395 9522

4833 15711 18,250 18,250

5674 0 0 0

5541 0 0 0

553 0 0 0

0 13,870 13,870 13,870

0 0 772 7227

0 9310 13,870 13,870

0.1

1 2 3 4

1288 2537 3121 3828

4513 2700 4395 9522

4833 15,711 18,250 18,250

5646 0 0 0

5527 0 0 0

594 0 0 0

0 13,813 13,813 13,813

0 0 886 7341

0 9367 13,813 13,813

0.2

1 2 3 4

1288 2537 3121 3828

4513 2700 4395 9522

4833 15,711 18,250 18,250

5619 0 0 0

5513 0 0 0

636 0 0 0

0 13,756 13,756 13,756

0 0 1000 7455

0 9424 13,756 13,756

0.3

1 2 3 4

1288 2537 3121 3828

4513 2700 4395 9522

4833 15,711 18,250 18,250

5592 0 0 0

5499 0 0 0

677 0 0 0

0 13,699 13,699 13,699

0 0 1114 7569

0 9481 13,699 13,699

0.4

1 2 3 4

1288 2537 3121 3828

4513 2700 4395 9522

4833 15,711 18,250 18,250

5564 0 0 0

5485 0 0 0

719 0 0 0

0 13,642 13,642 13,642

0 0 1228 7683

0 9538 13,642 13,642

0.5

1 2 3 4

1288 2537 3121 3828

4513 2700 4395 9522

4833 15,711 18,250 18,250

5537 0 0 0

5471 0 0 0

760 0 0 0

0 13,585 13,585 13,585

0 0 1342 7797

0 9595 13,585 13,585

0.6

1 2 3 4

1288 2537 3121 3828

4513 2700 4395 9522

4833 15,711 18,250 18,250

5510 0 0 0

5456 0 0 0

802 0 0 0

0 13,528 13,528 13,528

0 0 1456 7911

0 9652 13,528 13,528

0.7

1 2 3 4

1288 2537 3121 3828

4513 2700 4395 9522

4833 15,711 18,250 18,250

5482 0 0 0

5442 0 0 0

843 0 0 0

0 13,471 13,471 13,471

0 0 1570 8025

0 9709 13,471 13,471

0.8

1 2 3 4

1288 2537 3121 3828

4513 2700 4395 9522

4833 15,711 18,250 18,250

5455 0 0 0

5428 0 0 0

885 0 0 0

0 13,414 13,414 13,414

0 0 1684 8139

0 9766 13,414 13,414

0.9

1 2 3 4

1288 2537 3121 3828

4513 2700 4395 9522

4833 15,711 18,250 18,250

5427 0 0 0

5414 0 0 0

926 0 0 0

0 13,357 13,357 13,357

0 0 1798 8253

0 9823 13,357 13,357

1.0

1 2 3 4

1288 2537 3121 3828

4513 2700 4395 9522

4833 15,711 18,250 18,250

5400 0 0 0

5400 0 0 0

968 0 0 0

0 13,300 13,300 13,300

0 0 1912 8367

0 9880 13,300 13,300

Compost

Landfills

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

c

Planning periods

Timarpur incinerator

Okhla

Ghazipur

Okhla

Ghazipur

Bhalswa

Bhatimines

Jaitpur

Narela

0.0

1 2 3 4

1159 2284 2809 3445

4061 2429 3189 6745

4350 14,140 17,192 18,250

5674 0 0 0

4916 0 0 0

0 0 0 0

0 13,870 13,870 13,870

0 0 0 3730

0 6993 11,791 13,870

0.1

1 2 3 4

1172 2309 2840 3483

4106 2457 3022 7023

4399 14,297 17,585 18,250

5646 0 0 0

5061 0 0 0

0 0 0 0

0 13,813 13,813 13,813

0 0 0 4194

0 7281 12,133 13,813

0.2

1 2 3 4

1185 2334 2871 3521

4151 2484 5702 7300

4447 14,454 15,131 18,250

5619 0 0 0

5206 0 0 0

0 0 0 0

0 13,756 13,756 13,756

0 0 0 4658

0 7570 12,475 13,756

0.3

1 2

1198 2360

4197 2511

4495 14,612

5592 0

5351 0

0 0

0 13,699

0 0

0 7859

Compost

Landfills

(continued on next page)

4674

A.K. Srivastava, A.K. Nema / Expert Systems with Applications 39 (2012) 4657–4678

Table 14 (continued)

c

Planning periods

Timarpur incinerator

Compost

Landfills

Okhla

Ghazipur

Okhla

Bhalswa

Bhatimines

Jaitpur

Narela

3 4

2903 3560

2810 7578

18,250 18,250

0 0

Ghazipur 0 0

0 0

13,699 13,699

0 5121

12,817 13,699

0.4

1 2 3 4

1211 2385 2934 3598

4242 4015 3037 7856

4544 13,291 18,250 18,250

5564 0 0 0

5485 0 0 0

0 0 0 0

0 13,642 13642 13,642

0 0 0 5585

0 8148 13,159 13,642

0.5

1 2 3 4

1224 2411 2965 3636

4287 2565 5145 8134

4592 14,926 16,368 18,250

5537 0 0 0

5471 0 0 0

0 0 0 0

0 13,585 13,585 13,585

0 0 0 6049

0 8436 13,501 13,585

0.6

1 2 3 4

1237 2436 2996 3675

4332 0 3490 8411

4640 17,674 18,250 18,250

5510 0 0 0

5456 0 0 0

0 0 0 0

0 13,528 13,528 13,528

0 0 316 6513

0 8725 13,528 13,528

0.7

1 2 3 4

1249 2461 3027 3713

4377 2619 3716 8689

4689 15,240 18,250 18,250

5482 0 0 0

5442 0 0 0

0 0 0 0

0 13,471 13,471 13,471

0 0 715 6976

0 9014 13,471 13,471

0.8

1 2 3 4

1262 2487 3059 3751

4422 2646 6576 8967

4737 15,397 15,617 18,250

5455 0 0 0

5428 0 0 0

0 0 0 0

0 13,414 13,414 13,414

0 0 1114 7440

0 9303 13,414 13,414

0.9

1 2 3 4

1275 2512 3090 3789

4468 2673 4169 9245

4785 15,554 18,250 18,250

5427 0 0 0

5414 0 0 0

0 0 0 0

0 13,357 13,357 13,357

0 0 1513 7904

0 9591 13,357 13,357

1.0

1 2 3 4

1288 2537 3121 3828

4513 2700 6710 9522

4833 15,711 15,936 18,250

5400 0 0 0

5400 0 0 0

0 0 0 0

0 13,300 13,300 13,300

0 0 1912 8367

0 9880 13,300 13,300

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

Planning periods

Timarpur incinerator

Compost

Landfills

Okhla

Ghazipur

Okhla

Ghazipur

Bhalswa

Bhatimines

Jaitpur

Narela

0.0

1 2 3 4

1159 2284 2809 2733

1111 2036 2504 6745

7300 14,534 17,877 18,250

1302 0 0 0

3799 0 0 0

5490 0 0 0

0 0 0 5289

0 13,589 13,870 13,870

0 7274 11,791 13,023

0.1

1 2 3 4

1172 2309 2840 2743

1205 2058 2532 7023

7300 14,696 18,075 18,250

1316 0 0 0

3911 0 0 0

5481 0 0 0

0 0 0 5347

0 13740 13,813 13,813

0 7355 12,133 13,400

0.2

1 2 3 4

1185 2334 2871 2753

1298 2081 2584 7300

7300 14,857 18,250 18,250

1330 0 0 0

4023 0 0 0

5472 0 0 0

0 0 0 5426

0 13,756 13,756 13,756

0 7570 12,475 13,756

0.3

1 2 3 4

1198 2360 2903 2891

1392 2104 2810 7578

7300 15,018 18,250 18,250

1369 0 0 0

4112 0 0 0

5463 0 0 0

0 0 0 5790

0 13,699 13,699 13,699

0 7859 12,817 13,699

0.4

1 2 3 4

1211 2385 2934 3126

1485 2126 3037 7856

7300 15,180 18,250 18,250

1451 0 0 0

4156 0 0 0

5454 0 0 0

0 0 0 6057

0 13,642 13,642 13,642

0 8148 13,159 13,642

0.5

1 2 3 4

1224 2411 2965 3362

1579 2149 3263 8134

7300 15,341 18,250 18,250

1533 0 0 0

4200 0 0 0

5445 0 0 0

0 0 0 6323

0 13,585 13,585 13,585

0 8436 13,501 13,585

0.6

1 2 3 4

1237 2436 2996 3607

1672 2171 3490 8411

7300 15,503 18,250 18,250

1616 0 0 0

4245 0 0 0

5436 0 0 0

0

0 12,907 13,528 13,528

0 7759 9543 13,528

4301 6580

4675

A.K. Srivastava, A.K. Nema / Expert Systems with Applications 39 (2012) 4657–4678 Table 15 (continued) h/c

Planning periods

Timarpur incinerator

Compost

Landfills

Okhla

Ghazipur

Okhla

Ghazipur

Bhalswa

Bhatimines

Jaitpur

Narela

0.7

1 2 3 4

1249 2461 3027 3688

1766 2194 3716 8689

7300 15,664 18,250 18,250

1698 0 0 0

4289 0 0 0

5427 0 0 0

0 1604 4544 7001

0 13,042 13,471 13,471

0 7839 9642 13,471

0.8

1 2 3 4

1262 2487 3059 3726

1859 2217 3943 8967

7300 15,826 18,250 18,250

1781 0 0 0

4333 0 0 0

5418 0 0 0

0 1620 4696 7465

0 13,176 13,414 13,414

0 7920 9832 13,414

0.9

1 2 3 4

1275 2512 3090 3764

1953 2239 4169 9245

7300 15,987 18,250 18,250

1863 0 0 0

4377 0 0 0

5409 0 0 0

0 1637 4744 7929

0 13,311 13,357 13,357

0 8001 10,126 13,357

1.0

1 2 3 4

1288 2537 3121 3802

2046 2262 4395 9522

7300 16,149 18,250 18,250

1946 0 0 0

4422 0 0 0

5400 0 0 0

0 1799 4791 8392

0 13,300 13,300 13,300

0 8082 10,421 13,300

Bhalswa

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

Planning periods

Timarpur incinerator

Compost

Landfills

Okhla

Ghazipur

Okhla

Bhatimines

Jaitpur

Narela

0.0

1 2 3 4

1159 2284 2809 3445

4061 2429 2989 6745

4350 14,140 17,392 18,250

5674 0 0 0

4916 0 0 0

Ghazipur

0 0 0 0

0 13,870 13,870 13,870

0 0 0 3730

0 6993 11,791 13,870

0.1

1 2 3 4

1172 2309 2840 3483

4106 2457 3022 7023

4399 14,297 17,585 18,250

5646 0 0 0

5061 0 0 0

0 0 0 0

0 13,813 13,813 13,813

0 0 0 4194

0 7281 12,133 13,813

0.2

1 2 3 4

1185 2334 2871 3521

4151 2484 2584 7300

4447 14,454 18,250 18,250

5619 0 0 0

5206 0 0 0

0 0 0 0

0 13,756 13,756 13,756

0 0 0 4658

0 7570 12,475 13,756

0.3

1 2 3 4

1198 2360 2903 3560

4197 2511 2810 7578

4495 14,612 18,250 18,250

5592 0 0 0

5351 0 0 0

1 0 0 0

0 13,699 13,699 13,699

0 0 0 5121

0 7859 12,817 13,699

0.4

1 2 3 4

1211 2385 2934 3598

4242 2538 3624 7856

4544 14,769 17,663 18,250

5564 0 0 0

5485 0 0 0

12 0 0 0

0 13,642 13,642 13,642

0 0 0 5585

0 8148 13,159 13,642

0.5

1 2 3 4

1224 2411 2965 3636

4287 3846 3263 8134

4592 15,645 18,250 18,250

5537 0 0 0

5471 0 0 0

172 0 0 0

0 13,585 13,585 13,585

0 0 0 6049

0 8436 13,501 13,585

0.6

1 2 3 4

1237 2436 2996 3675

4332 3987 3490 8411

4640 17,674 18,250 18,250

5510 0 0 0

5456 0 0 0

331 0 0 0

0 13,528 13,528 13,528

0 0 316 6513

0 8725 13,528 13,528

0.7

1 2 3 4

1249 2461 3027 3713

4377 2619 3716 8689

4689 15,240 18,250 18,250

5482 0 0 0

5442 0 0 0

490 0 0 0

0 13,471 13,471 13,471

0 0 715 6976

0 9014 13,471 13,471

0.8

1 2 3 4

1262 2487 3059 3751

4422 2646 3943 8967

4737 15,397 18,250 18,250

5455 0 0 0

5428 0 0 0

649 0 0 0

0 13,414 13,414 13,414

0 0 1114 7440

0 9303 13,414 13,414

0.9

1 2 3 4

1275 2512 3090 3789

4468 2673 4169 9245

4785 15,554 18,250 18,250

5427 0 0 0

5414 0 0 0

808 0 0 0

0 13,357 13,357 13,357

0 0 1513 7904

0 9591 13,357 13,357

1.0

1 2 3 4

1288 2537 3121 3828

4513 2700 4395 9522

4833 15,711 18,250 18,250

5400 0 0 0

5400 0 0 0

968 0 0 0

0 13,300 13,300 13,300

0 0 1912 8367

0 9880 13,300 13,300

4676

A.K. Srivastava, A.K. Nema / Expert Systems with Applications 39 (2012) 4657–4678

Table 17 Waste diversion for different simultaneous values of h and c for scenario III (waste quantities in ‘000 tons). h/c

Planning periods

Timarpur incinerator

Ghazipur

Okhla

Ghazipur

Bhatimines

Jaitpur

Narela

0.0

1 2 3 4

1159 2284 2809 3445

4061 2429 2989 6745

4350 14,140 17,392 18,250

5674 0 0 0

4916 0 0 0

0 0 0 0

0 13,870 13,870 13,870

0 0 0 3730

0 6993 11,791 13,870

0.1

1 2 3 4

1172 2309 2840 3483

4106 2457 2357 7023

4399 14,297 18,250 18,250

5646 0 0 0

5061 0 0 0

0 0 0 0

0 13,813 13,813 13,813

0 0 0 4194

0 7281 12,133 13,813

0.2

1 2 3 4

1185 2334 2871 3521

4151 2484 3055 7300

4447 14,454 17,779 18,250

5619 0 0 0

5206 0 0 0

0 0 0 0

0 13,756 13,756 13,756

0 0 0 4658

0 7570 12,475 13,756

0.3

1 2 3 4

1198 2360 2903 3560

4197 2511 2810 7578

4495 14,612 18,250 18,250

5592 0 0 0

5351 0 0 0

0 0 0 0

0 13,699 13,699 13,699

0 0 0 5121

0 7859 12,817 13,699

0.4

1 2 3 4

1211 2385 2934 3598

4242 2538 3037 7856

4544 14,769 18,250 18,250

5564 0 0 0

5485 0 0 0

12 0 0 0

0 13,642 13,642 13,642

0 0 0 5585

0 8148 13,159 13,642

0.5

1 2 3 4

1224 2411 2965 3636

4287 2565 21513 8134

4592 14,926 0 18,250

5537 0 0 0

5471 0 0 0

172 0 0 0

0 13,585 13,585 13,585

0 0 0 6049

0 8436 13,501 13,585

0.6

1 2 3 4

1237 2436 2996 3675

4332 2592 3490 8411

4640 15,083 18,250 18,250

5510 0 0 0

5456 0 0 0

331 0 0 0

0 13,528 13,528 13,528

0 0 316 6513

0 8725 13,528 13,528

0.7

1 2 3 4

1249 2461 3027 3713

4377 4888 3716 8689

4689 12,971 18,250 18,250

5482 0 0 0

5442 0 0 0

490 0 0 0

0 13,471 13,471 13,471

0 0 715 6976

0 9014 13,471 13,471

0.8

1 2 3 4

1262 2487 3059 3751

4422 2646 4380 8967

4737 15,397 17,812 18,250

5455 0 0 0

5428 0 0 0

649 0 0 0

0 13,414 13,414 13,414

0 0 1114 7440

0 9303 13,414 13,414

0.9

1 2 3 4

1275 2512 3090 3789

4468 2673 4169 9245

4785 15,554 18,250 18,250

5427 0 0 0

5414 0 0 0

808 0 0 0

0 13,357 13,357 13,357

0 0 1513 7904

0 9591 13,357 13,357

1.0

1 2 3 4

1288 2537 3121 3828

4513 2700 6710 9522

4833 15,711 15,936 18,250

5400 0 0 0

5400 0 0 0

968 0 0 0

0 13,300 13,300 13,300

0 0 1912 8367

0 9880 13,300 13,300

Compost Okhla

Landfills

The utility of the proposed model is demonstrated by an example problem. It is observed that the consideration of uncertainties in waste quantities and capacities of waste management facilities is essential during planning of project, because it would influence the planning decisions to a large extent. The commissioning of new facilities is significantly affected by uncertain parameters mainly waste quantity. The pre-ponement or postponement of commissioning of new facilities may require significantly additional resources. One of the important observation is that the uncertainties in waste quantity is likely to affect the planning for waste treatment/disposal facilities more as compared with the uncertainty in the capacities of the waste management facilities. The model simulation can help in understanding the effect of the uncertainties in the capacities of the individual treatment and disposal facilities on the overall plan. The relationship between increase in waste quantity and increase in the total cost/risk involved in waste management is found to be nonlinear. Moreover, it was noted that sensitivity of overall plan could be significantly

Bhalswa

different with respect to the different facilities. It is suggested that the planner should identify the sensitivity of the overall plan with respect to each of the facilities. It has been found that some of the facilities could be such that a marginal change in their available capacities could result in a significant change in the overall waste-allocation plan. These sensitive facilities should be planned with higher prudence. The fuzzy multi-period planning for solid waste management is especially relevant in case of rapidly growing urban centers of developing countries due to great possibility of fluctuating parameters. As demonstrated using the example problem the multiperiod planning model can be a very helpful tool for the decision makers especially for addressing location–allocation problem of waste disposal facilities with fluctuating input parameters. The modelling results could be suitably interpreted for taking an appropriate decision from the set of close to optimal alternatives. Further, the model simulations can give valuable information for analysing the existing waste-management practices, the long-term capacity planning for the city’s waste-management system, and

A.K. Srivastava, A.K. Nema / Expert Systems with Applications 39 (2012) 4657–4678

4677

Fig. 8. Variation of objective values for different value of h and c.

the identification of effective policies regarding waste minimization and appropriate management options.

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