### 1. Introduction

_{2}, NO

_{x}, hydrocarbons, dioxins and furans to the lower atmosphere causing air pollution hazards.

### 2. Literature Review

### 3. Model Description

Borough (administrative divisions of municipality) centers have been assumed as the waste generation points.

Proper segregation done at source by providing two bins – one for biodegradable waste and the other for non-biodegradable waste.

Intermediate/Central sorting (ICS) facility to be provided from where recyclable material will be sent for recycling. Revenue can be earned by selling the recyclables from recycling facility.

Garbage enters central/intermediate sorter and subsequently to the different processing plants, while silt/rubbish goes straight to landfill without sorting or processing.

Treatment and disposal of garbage will be done as per its characteristics – like high calorific value of waste may go for incineration and biodegradable organic waste for composting. In all treatment techniques, pre-sorting facilities will be there for further segregating the inert and recyclable from the waste coming from central sorter. Inert, process rejects and residues from treatment plant will go to engineered landfill.

The municipality uses departmental and hired vehicles to transport wastes. Departmental vehicle takes garbage only while hired vehicles transport both garbage and silt/rubbish (silt and garbage are not mixed, but collected separately).

There are different types of departmental vehicles but only one type of hired vehicle.

The city is divided into zones for each dumpsite.

Minimum and maximum number of trips of departmental vehicles as well as for hired vehicles is fixed for each zone.

The departmental vehicles will have to undertake certain minimum number of trips for each zone.

The drivers and helpers of departmental vehicles will be paid incentives if they carry out more than minimum number of trips. Hired vehicles will be paid on the basis of tonnage of waste they transport to the dumpsites.

For running the model, average waste generation data of the boroughs of the concerned municipality needs to be considered.

Based on average waste actually carried by different types of vehicles from different boroughs, borough-wise minimum and maximum garbage carrying range (in fraction) for both departmental and hired vehicles need to be fixed. This makes the model flexible and more realistic.

Environmental costs of the processing plants and landfilling has not been taken into account.

*D*numbers of dumpsites at

*D*locations. Each dumpsite

*d*has one central sorting station, one incinerator, one composting facility, one landfill and one recycling facility. From the central sorting facility, one stream is recycled to recycling facility, while other streams may go to incinerator, composting plant, or landfill as per the material flow chart illustrated in the Fig. 1. The incinerator and composting unit has pre-sorting units attached to them, so as to increase the efficiency of these processes. From these pre-sorting units, a small recyclable fraction may be dispatched to recycling facility while the inert fraction may be taken directly to landfill.

##### (1)

$$\begin{array}{l}Objective\hspace{0.17em}function=\\ CTRANSP+CINCENT+CTCX+CTCS+CTCI+CTCC\\ -CTREVR-CTREVC-CTREVI\end{array}$$*CTCX*,

*CTCS*,

*CTCI*,

*CTCC*are the total land-filling cost, sorting cost, incineration cost and composting cost for all dumpsites

*d*. The interpretations of the different parameters used in the subsequent equations have been elaborated in the Nomenclature section.

##### (3)

$$\begin{array}{l}CTCS-\sum _{d=1}^{D}\left[{sgf}_{d}\times ics\_sort{cost}_{d}\right]\\ -\sum _{d=1}^{D}\left[{sr}_{d}\times ics\_{rc}_{d}+{sad}_{d}\times ics\_{adc}_{d}\right]=0\end{array}$$##### (4)

$$\begin{array}{c}CTCI-\sum _{d=1}^{D}[{sif}_{d}\times ip\_op{cost}_{d}+{ir}_{d}\times ip\_{rc}_{d}\\ +{iar}_{d}\times ip\_{ac}_{d}+{iir}_{d}\times ip\_{irc}_{d}]=0\end{array}$$##### (5)

$$\begin{array}{l}CTCC-\sum _{d=1}^{D}[{scf}_{d}\times cp\_op{cost}_{d}+{cr}_{d}\times cp\_{rc}_{d}\\ +{cir}_{d}\times cp\_{irc}_{d}+{cpr}_{d}\times cp\_{prc}_{d}]=0\end{array}$$##### (6)

$$CTREVR-\sum _{d=1}^{D}[{sr}_{d}\times ics\_{rr}_{d}+{ir}_{d}\times ip\_{rr}_{d}+{cr}_{d}\times cp\_{rr}_{d}]=0$$*hh*as well as the cost of transportation incurred by departmental vehicles

*dd*. Incidentally, hired vehicles collect and transport both garbage and silt, while departmental vehicles transport garbage only. Rates for garbage and silt collections are different. Also, garbage and silt transportation charges by hired vehicles are paid to them on the basis of different municipality zones from which the wastes are being transported. All liabilities of hired vehicles are the responsibility of the respective private agencies.

*dd*type departmental vehicles is the summation of fuel cost, fixed cost of running vehicles and fixed cost of idle vehicles.

*dd*type departmental vehicle from borough centre to dumpsite:

##### (13)

$$\begin{array}{l}c{tcdd}_{dd}-cfu{eldd}_{dd}-cfx{drdd}_{dd}-cfx{didd}_{dd}=0\\ \forall dd=1,2,\dots ,DD\end{array}$$*cfxdrdd*

*and*

_{dd}*cfxdidd*

*) include annualized capital cost of departmental vehicles, maintenance cost and driver/ helper cost. Everyday approximately 50 to 80% of the departmental vehicles run; other remain in idle/standby condition.*

_{dd}*dd*type departmental vehicle:

##### (14)

$$\begin{array}{l}cfu{eldd}_{dd}-\sum _{d=1}^{D}\sum _{bb=1}^{BB}\left[{qg}_{bb,d,\text{dd}}\times bb\_{fc}_{bb,d,dd}\right]=0\\ \forall dd=1,2,\dots ,DD\end{array}$$*dd*type departmental vehicle:

##### (15)

$$\begin{array}{l}cfx{drdd}_{dd}-dd\_{na}_{dd}\times dd\_{fc}_{dd}=0\\ \forall dd=1,2,\dots ,DD\end{array}$$*dd*type departmental vehicle:

##### (16)

$$\begin{array}{l}cfx{didd}_{dd}-(dd\_{no}_{dd}-dd\_{na}_{dd})\times dd\_{ic}_{dd}=0\\ \forall dd=1,2,\dots ,DD\end{array}$$*bb*:

##### (17)

$$\begin{array}{l}\sum _{d=1}^{D}\sum _{dd=1}^{DD}{qg}_{bb,d,dd}+\sum _{d=1}^{D}{qhhg}_{bb,d}=bb\_{wg}_{bb}\\ \forall bb=1,2,\dots ,BB\end{array}$$*bb*:

##### (18)

$$\begin{array}{l}\sum _{d=1}^{D}{qhhs}_{bb,d}=bb\_{ws}_{bb}\\ \forall bb=1,2,\dots ,DD\end{array}$$*bb*centre by

*dd*type vehicle:

##### (19)

$$\begin{array}{l}\sum _{d=1}^{D}{qg}_{bb,d,dd}\le bb\_{wg}_{bb}\times bb\_{fgddmax}_{bb,dd}\\ \forall bb=1,2,\dots ,BB,\forall dd=1,2,\dots ,DD\end{array}$$*bb*by hired vehicles

*hh*:

##### (20)

$$\begin{array}{l}\sum _{d=1}^{D}{qhhg}_{bb,d}\le bb\_{wg}_{bb}\times bb\_{fghhmax}_{bb}\\ \forall bb=1,2,\dots ,BB\end{array}$$*bb*by

*dd*type departmental vehicles:

##### (21)

$$\begin{array}{l}\sum _{d=1}^{D}{qg}_{bb,d,dd}\ge bb\_{wg}_{bb}\times bb\_{fgddmin}_{bb,dd}\\ \forall bb=1,2,\dots ,BB,\mathrm{\hspace{0.17em}\u200a\u200a}\forall dd=1,2,\dots ,DD\end{array}$$*bb*by hired vehicles

*hh*:

##### (22)

$$\begin{array}{l}\sum _{d=1}^{D}{qhhg}_{bb,d}\ge bb\_{wg}_{bb}\times bb\_{fghhmin}_{bb}\\ \forall bb=1,2,\dots ,BB\end{array}$$*d*:

##### (23)

$$\begin{array}{l}{sgf}_{d}-\sum _{bb=1}^{BB}\sum _{dd=1}^{DD}{qg}_{bb,d,dd}-\sum _{bb=1}^{BB}{qhhg}_{bb,d}=0\\ \forall d=1,2,\dots ,D\end{array}$$*d*:

##### (24)

$$\begin{array}{l}{sgf}_{d}-{sr}_{d}-{sdd}_{d}-{sad}_{d}-{sif}_{d}-{scf}_{d}=0\\ \forall d=1,2,\dots ,D\end{array}$$*d*:

##### (25)

$$\begin{array}{l}{sr}_{d}-{sgf}_{d}\times ics\_{ry}_{d}\le 0\\ \forall d=1,2,\dots ,D\end{array}$$*d*:

##### (26)

$$\begin{array}{l}{sdd}_{d}-{sgf}_{d}\times ics\_{ddy}_{d}\le 0\\ \forall d=1,2,\dots ,D\end{array}$$##### (27)

$$\begin{array}{l}{sif}_{d}-{sgf}_{d}\times ics\_{maxinci}_{d}\le 0\\ \forall d=1,2,\dots ,D\end{array}$$##### (28)

$$\begin{array}{l}{scf}_{d}-{sgf}_{d}\times ics\_{maxcomp}_{d}\le 0\\ \forall d=1,2,\dots ,D\end{array}$$*d*:

##### (29)

$$\begin{array}{l}{ir}_{d}-{sif}_{d}\times ip\_{ry}_{d}=0\\ \forall d=1,2,\dots ,D\end{array}$$*d*:

##### (30)

$$\begin{array}{l}{iir}_{d}-{sif}_{d}\times ip\_{iry}_{d}=0\\ \forall d=1,2,\dots ,D\end{array}$$*d*:

##### (31)

$$\begin{array}{l}{iar}_{d}-{sif}_{d}\times ip\_{ay}_{d}=0\\ \forall d=1,2,\dots ,D\end{array}$$*d*:

*d*:

##### (33)

$$\begin{array}{l}{cr}_{d}-{scf}_{d}\times cp\_{ry}_{d}=0\\ \forall d=1,2,\dots ,D\end{array}$$*d*:

##### (34)

$$\begin{array}{l}{cir}_{d}-{scf}_{d}\times cp\_{iry}_{d}=0\\ \forall d=1,2,\dots ,D\end{array}$$*d*:

##### (35)

$$\begin{array}{l}{cpr}_{d}-{scf}_{d}\times cp\_{pry}_{d}=0\\ \forall d=1,2,\dots ,D\end{array}$$*d*:

##### (36)

$$\begin{array}{l}{cpd}_{d}-{scf}_{d}\times cp\_{prdy}_{d}=0\\ \forall d=1,2,\dots ,D\end{array}$$*d*:

##### (37)

$$\begin{array}{l}{xf}_{d}-{xsilt}_{d}-{xfg}_{d}-{xfrj}_{d}=0\\ \forall d=1,2,\dots ,D\end{array}$$*d*:

##### (38)

$$\begin{array}{l}{xsilt}_{d}-\sum _{bb=1}^{BB}{qhhs}_{bb,d}=0\\ \forall d=1,2,\dots ,D\end{array}$$*d*:

*d*:

##### (40)

$$\begin{array}{l}{xfrj}_{d}-{iir}_{d}-{cir}_{d}-{iar}_{d}-{cpr}_{d}=0\\ \forall d=1,2,\dots ,D\end{array}$$*d*:

*d*:

*d*:

*d*:

*z*number of zones for each dumpsite

*d*. The zone divisions are made based on their proximity to the dumpsite

*d*e.g. Zone 1 is nearer to the dumpsite

*d*while Zone 2 is far from

*d*. The municipality has fixed maximum and minimum trip limits for each zone

*z*of a dumpsite

*d*for a

*dd*-type departmental vehicle. The drivers and the helpers are paid incentives if they undertake trips beyond the minimum trip limits stipulated for a particular zone. Similarly, the hired vehicles

*hh*are paid according to the zone

*z*(of a dumpsite

*d*) from where they are transferring waste. Constraints based on the number of trips made by departmental vehicles in a zone

*z*of a dumpsite

*d*:

##### (48)

$$\begin{array}{l}{at}_{dd,d,z}\times dd\_{cap}_{dd}-\sum _{bb=1}^{BB}{qg}_{bb,d,dd}=0\\ \forall dd=1,2,\dots ,DD,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\forall d=1,2,\dots ,D,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\forall z=1,2,\mathrm{..},Z\end{array}$$*qg*

*, only those*

_{bb,d,dd}*bb*boroughs are considered which belong to the zone

*z*of the dumpsite

*d*.

*hh*in a zone

*z*of a dumpsite

*d*for collection of garbage:

##### (49)

$$\begin{array}{l}{athhg}_{d,z}\times hhg\_cap-\sum _{bb=1}^{BB}{qhhg}_{bb,d}=0\\ \forall d=1,2,\dots ,D,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\forall z=1,2,\dots ,Z\end{array}$$*qhhg*

*, only those*

_{bb,d}*bb*boroughs are considered which belong to the zone

*z*of the dumpsite

*d*.

*hh*in a zone

*z*of a dumpsite

*d*for collection of silt:

##### (50)

$$\begin{array}{l}{athhs}_{d,z}\times hhs\_cap-\sum _{bb=1}^{BB}{qhhs}_{bb,d}=0\\ \forall d=1,2,\dots ,D,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\forall z=1,2,\dots ,Z\end{array}$$*qhhs*

*, only those*

_{bb,d}*bb*boroughs are considered which belong to the zone

*z*of the dumpsite

*d*.

*dd*type departmental vehicle in zone

*z*of

*d*:

##### (51)

$$\begin{array}{l}{at}_{dd,d,z}\le dd\_{na}_{dd}\times zz\_{maxtrip}_{dd,d,z}\\ \forall d=1,2,\dots ,D,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\forall dd=1,2,\dots DD,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\forall z=1,2,\dots ,Z\end{array}$$*dd*type vehicle in all dumpsite

*d*, all zone

*z*:

##### (52)

$$\begin{array}{l}\sum _{d=1}^{D}\sum _{z=1}^{Z}{at}_{dd,d,z}\le dd\_{na}_{dd}\times maxzz\_{maxtrip}_{dd}\\ \forall dd=1,2,\dots ,DD\end{array}$$*dd*type vehicle in all dumpsite

*d*, all zone

*z*:

##### (53)

$$\begin{array}{l}\sum _{d=1}^{D}\sum _{z=1}^{Z}{at}_{dd,d,z}\ge dd\_{na}_{dd}\times minzz\_{mintrip}_{dd}\\ \forall dd=1,2,\dots ,DD\end{array}$$*dd*type departmental vehicle to dumpsite

*d*from zone

*z*of

*d*:

##### (54)

$$\begin{array}{l}{Dg}_{dd,d,z}-\sum _{bb=1}^{BB}{qg}_{bb,d,dd}=0\\ \forall z=1,2,\dots ,Z,\forall d=1,2,\dots ,D,\forall dd=1,2,\dots ,DD\end{array}$$*qg*

*is the total amount of garbage taken by*

_{bb,d,dd}*dd*type vehicle to dumpsite

*d*from all those

*bb*boroughs which belong to zone

*z*of

*d*.

*hh*to dumpsite

*d*from zone

*z*of

*d*:

##### (55)

$$\begin{array}{l}{Dghh}_{d,z}-\sum _{bb=1}^{BB}{qhhg}_{bb,d}=0\\ \forall z=1,2,\dots ,Z,\forall d=1,2,\dots ,D\end{array}$$*qhhg*

*is the total amount of garbage taken by hired vehicle*

_{bb,d}*hh*to dumpsite

*d*from all those

*bb*boroughs which belong to zone

*z*of

*d*.

*hh*to dumpsite

*d*from zone

*z*of

*d*:

##### (56)

$$\begin{array}{l}{Dshh}_{d,z}-\sum _{bb=1}^{BB}{qhhs}_{bb,d}=0\\ \forall z=1,2,\dots ,Z,\forall d=1,2,\dots ,D\end{array}$$*qhhs*

*is the total amount of silt taken by hired vehicle*

_{bb,d}*hh*to dumpsite

*d*from all those

*bb*boroughs which belong to zone

*z*of

*d*.

*dd*-type departmental vehicle drivers and helpers can be approximated by:

### 4. Applying the Model for Kolkata City: A Case Study

Container carrying vehicles (Dumper-Placers): One Dumper-Placer (DP) can hoist and transport only one skip/container at a time to the disposal ground. KMC currently uses two types on skips – 4.5 m

^{3}size (1.75 MT haulage capacity DP) and 7 m^{3}size (2 MT haulage capacity DP). DD1 and DD2 refer to 1.75 MT and 2 MT Dumper Placer, respectively.Payloader loaded Tipper Trucks (11 m

^{3}), DD3: These trucks haul around 7.0 MT of MSW in one single trip to Dhapa.Stationary compactor-cum-hook loader combination (10.5 m

^{3}/9 MT), DD4: KMC is purchasing 198 stationary compactors to be placed at 85 compactor stations. These compactors reduce 30% waste volume by applying 140 bar pressure. KMC is also acquiring 54 hook loaders, to haul these stationary compactors to Dhapa. Each hook loader can haul one stationary compactor at a time.Movable compactors (14 m

^{3}/10 MT), DD5: KMC is purchasing 64 numbers of 14 m^{3}capacity movable compactors. It takes waste from six 4.5 m^{3}skips (or from handcarts), compact it at 140 bar pressure, and hauls waste to the landfill site.Movable compactors (8 m

^{3}/7 MT), DD6: KMC is purchasing 4 numbers of 8 m^{3}capacity movable compactors. These smaller sized compactors can manoeuvre narrow streets and lanes.

### 5. Model Validation

Borough-wise garbage and silt generations were modified to that of 2007 waste generation data.

Departmental vehicles were of 4 types at that time – DD1, DD2, DD3 and DD4. DD1, DD2, DD3 are the same as exists now. However DD4 were the manually loaded 8 m

^{3}tipper trucks, which has been abolished now. Fixed and idle costs, incentive rate, fuel costs, minimum and maximum number of trips of all these vehicle were calculated as per 2007 values.The East dumpsite has been taken as the existing dumpsite at Dhapa and per ton fuel cost for departmental vehicle waste transportation from borough centers to Dhapa were calculated using 2007 diesel rate. The North and South dumpsites were not taken into consideration by fixing the sorter capacity and landfill capacity at these two sites to zero – thus effectively blocking any waste transportation to these sites. Similarly per ton waste transportation costs from borough-centers to East (Dhapa) dumpsite for hired vehicles were re-calculated using 2007 diesel rates.

Incinerator capacities for all sites was kept zero; composting plant capacity for East (Dhapa), North and South dumpsites was fixed at 150 MT/d and 0 MT/d and 0 MT/d, respectively. The 150 MT/d composting plant attaching to Dhapa was running on PPP model – we assumed that KMC received Rs. 87.5 / MT of waste processed as royalty.

Cost of open dumping (without liner, leachate/gas collection mechanism) at Dhapa was taken as Rs. 95/MT.

### 6. Solving the Model for a Futuristic Scenario

### Case 1

### Case 2

Revenue earned by selling power from RDF-based Waste-to-Energy incinerators: Rs. 6.50/kWh (considering a levelized unit cost of electricity (LUCE) generation of Rs. 7.55/kWh unit).

kWh units of electricity generated from unit MT of solid waste undergoing incineration in RDF plant: 200.

Operational cost of RDF plant (including annualized capital cost, transportation cost from sorter to composting plant): Rs. 1,435/MT.