b2 or report

OPTIMIZATION OF WASTE MANAGEMENT COST IN MUMBAI

OPERATIONS RESEARCH PROJECT REPORT

GROUP B2

U112082 U112087 U112090 U112091 U112097

Gyanashree Maharana Juhi Ujjawal Monalisa Guru Nidhi Murarka Prerna Katyal

31 December, 2012 XAVIER INSTITUTE OF MANAGEMENT, BHUBANESWAR


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ACKNOWLEDGEMENT

We express our heart-felt gratitude to all those who have been instrumental in helping us with the

report or have been associated with the report in every way and made the journey a worth-while

experience.

We thank the batch of 2012-2014 and also the batch of 2011-2013 for having shared their

valuable insights and experiences that went a long way in helping us in the successful completion of our

report.

Last but most important, we thank Dr. Sambit Mukherjee, who provided us with the opportunity to

undertake the project and for extending his complete support in choosing the problem and arriving at the

solution.


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TABLE OF CONTENTS

ACKNOWLEDGEMENT .................................................................................................... 1

PROBLEM DESCRIPTION................................................................................................. 3

WASTE MANAGEMENT IN MUMBAI ............................................................................................ 3

LINEAR PROGRAMMING PROBLEM FORMULATION .................................................... 8

DECISION VARIABLES – .................................................................................................................. 8

OBJECTIVE FUNCTION –................................................................................................................. 9

CONSTRAINTS – ............................................................................................................................ 10

SOLUTION USING LINGO ............................................................................................. 11

PROBLEM STATEMENT – .............................................................................................................. 11

PROBLEM SOLUTION USING LINGO – .................................................................................... 13

OPTIMISED SOLUTION ................................................................................................. 19

MINIMUM COST – ......................................................................................................................... 19

VALUES OF DECISION VARIABLES – ......................................................................................... 19

REFERENCES ................................................................................................................. 21


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PROBLEM DESCRIPTION

WASTE MANAGEMENT IN MUMBAI

Mumbai, the largest city in India, with the population of 13 million, covers a coastal stretch of 603 sq.

Km. It can be divided into 3 sections, viz., the island city (or main city), the western suburbs and the

eastern suburbs. Such a huge population obviously generates a huge amount of waste. Managing such

waste becomes a critical and massive task for the local administration. The Municipal Corporation of

Greater Mumbai (MCGM) is in charge of the management of waste in the city. On a daily basis, Mumbai

generates waste amounting to nearly 9000 tons comprising biodegradable and recyclable materials,

debris, and silt. The biodegradable waste is made up of fruit, and vegetable remainders, leaves, spoiled

food, eggshells, cotton, and so on. Newspapers, plastic, battery cells, wires, iron sheets, glass comprises

recyclable waste. Debris includes construction waste, renovation waste, demolition waste and the like.

Earth and clay from drains and road corners make up the silt.

The prevailing approach to waste management has been one of collection and disposal that is, garbage

is collected from communities by the municipal authorities and disposed off at various dumping sites that

are currently servicing the city. Garbage collectors manually collect the waste generated at the

household level and dumps them in the garbage bin at specified street corners. There are about 6000

community bins in the city. This largely manual operation involves 35000 personnel employed by the

MCGM and is collected by a fleet of 800 vehicles, including vehicles hired from private contractors, that

work in shifts every day. For collecting and transporting garbage and debris, municipal and private

vehicles need to make close to 2000 trips every day.

Community participation in waste management is being promoted by MCGM. Under a joint project

started by the Government of India and MCGM in collaboration with United Nations Center for Human

Settlements community participation in waste management is being encouraged. This program is called

“Advanced Locality Management” (ALM). It is a community-based approach for effective management of

civic services. Under ALM, communities with help from NGOs make arrangements for the waste to be

collected by rag pickers and then process biodegradable wastes and sell the recyclable material.

MCGM provides subsidy and technical help to construct composting pits in these localities. NGOs play an

important role in this set-up by organising the rag pickers and providing them the necessary training for

collecting and composting the waste.

MCGM also partners with Excel industries in converting the organic component of solid wastes into

manure through mechanical aerobic composting. Excel Industry Limited is one of the India’s largest

agrochemical companies. They are leaders in the field of solid waste management that help in

sustainable management of urban environment. The Biotech Division of the company looks after the

conversion of the urban solid waste into useful organic manure through controlled aerobic composting.

This process consists of 2 stages:

i. Biological process for decomposition of organic matter,

ii. Mechanical process for screening the decomposed organic matter.


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Waste is collected by MCGM and supplied to the different compost plants of Excel Industries and then

the waste is processed through aerobic composting. Composting provides a sustainable recycling

procedure through which the organic and biodegradable portion of solid waste is converted to produce

fertilizers that can be used for soil enhancement.

Paresh Shinde has been working in MCGM for the past 10 years. Recently he has been assigned the

charge of waste management for wards A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X

of greater Mumbai. Previously, waste generated from these wards was being dumped at landfills. But

now with rising concerns about these open dumps that threat public health and environmental quality, the

focus is shifting towards more environment-friendly options such as composting. Paresh has been assigned

the job of preparing a schedule for transporting the waste generated at these wards to 3 compost plants

located at Deonar, Mulund and Gorai which are operated by Excel Industries. At these plants, the waste

will be converted to compost by aerobic composting. Waste generated from each of the wards and the

distance from the wards to the compost plants are given in Table 1.

Table 1: Waste generated from ward i (Wi) and distance from generation node to dumpsite.

Distance In Km

Wards Wi (ton) Deonar Mulund Gorai

A 223.67 24 32 45

B 134.38 19.75 27.25 40

C 203.3 23 31 44

D 352.46 21.5 29.5 43

E 299.66 19 27 40

F 283.58 14.5 22.5 35

G 204.93 11.5 19.5 33

H 209.5 16.5 24.5 34

I 382.63 14.25 22.25 35

J 150.65 13.75 22.25 35

K 233.66 14.25 24 37

L 331.93 21 19 17.5

M 312.88 20.5 19 17.5

N 229.28 22 19 11.5

O 271.22 24 21 8.5


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Distance (in kms)

Wards Wi (ton) Deonar Mulund Gorai

P 152.44 33 27 5.9

Q 198.24 35 29 3.6

R 165.94 36 30 5

S 250.98 11 19 33.5

T 352.69 5.5 17 39

U 465.19 2 14 41

V 178 7.75 13 30

W 221.05 13 8.75 26

X 165.17 18 4.5 22

Notes: Table gives distance from ward check post to nearest dumping ground check post. It further gives

distance to the next closest dumping ground check post. Rest of the distances is calculated from the Mumbai

city map considering crow fly distance from centre of ward to the dumping ground.

Source: MCGM (2001).

The transportation cost per ton of waste per km is Rs. 10 and the operating costs per ton of waste at the

Deonar, Mulund, and Gorai plants are Rs. 12, Rs. 11.5 and Rs. 7, respectively, as mentioned in Table 2.

The capacity of the Deonar plant is 4000 tons whereas those of Mulund and Gorai plants are 3000 and

6500 tons respectively, as mentioned in Table 3. The Municipal Corporation of Mumbai has zeroed down

on a certain budget amount for transportation from each ward to the dumping Sites. The same has been

mentioned in Table 4.

Table 2: The Operating Costs in Rs. per ton of waste for each Dumping Sites.

DUMPING SITES OPERATING COSTS (in Rs. per ton of

waste)

Deonar 12

Mulund 11.5

Gorai 7


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Table 3: The Capacity in tons at each of the Dumping Sites.

DUMPING SITES CAPACITY (in tons)

Deonar 4000

Mulund 3000

Gorai 6500

Table 4: The Budget amount for transportation from each ward to the Dumping Sites.

WARD BUDGET AMOUNT (in Rs.)

A 250000

B 230000

C 320000

D 80000

E 500000

F 200000

G 300000

H 400000

I 430000

J 530000

K 620000

L 740000

M 500000

N 600000

O 500000

P 510000

Q 710000

R 820000


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S 670000

T 650000

U 450000

V 430000

W 220000

X 410000

Paresh needs to determine how much waste from each ward should be sent to each of the three

compost plants so that the total cost of transporting as well as the operating cost of composting the

waste is minimised.


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LINEAR PROGRAMMING PROBLEM FORMULATION

DECISION VARIABLES –

Let

WA-Deonar = Weight of waste transported from Ward A to Deonar

WA-Mulund = Weight of waste transported from Ward A to Mulund

WA-Gorai = Weight of waste transported from Ward A to Gorai

WB-Deonar = Weight of waste transported from Ward B to Deonar

WB-Mulund = Weight of waste transported from Ward B to Mulund

WB-Gorai = Weight of waste transported from Ward B to Gorai

WC-Deonar = Weight of waste transported from Ward C to Deonar

WC-Mulund = Weight of waste transported from Ward C to Mulund

WC-Gorai = Weight of waste transported from Ward C to Gorai

WD-Deonar = Weight of waste transported from Ward D to Deonar

WD-Mulund = Weight of waste transported from Ward D to Mulund

WD-Gorai = Weight of waste transported from Ward D to Gorai

WE-Deonar = Weight of waste transported from Ward E to Deonar

WE-Mulund = Weight of waste transported from Ward E to Mulund

WE-Gorai = Weight of waste transported from Ward E to Gorai

WF-Deonar = Weight of waste transported from Ward F to Deonar

WF-Mulund = Weight of waste transported from Ward F to Mulund

WF-Gorai = Weight of waste transported from Ward F to Gorai

WG-Deonar = Weight of waste transported from Ward G to Deonar

WG-Mulund = Weight of waste transported from Ward G to Mulund

WG-Gorai = Weight of waste transported from Ward G to Gorai

WH-Deonar = Weight of waste transported from Ward H to Deonar

WH-Mulund = Weight of waste transported from Ward H to Mulund

WH-Gorai = Weight of waste transported from Ward H to Gorai

WI-Deonar = Weight of waste transported from Ward I to Deonar

WI-Mulund = Weight of waste transported from Ward I to Mulund

WI-Gorai = Weight of waste transported from Ward I to Gorai

WJ-Deonar = Weight of waste transported from Ward J to Deonar

WJ-Mulund = Weight of waste transported from Ward J to Mulund

WJ-Gorai = Weight of waste transported from Ward J to Gorai

WK-Deonar = Weight of waste transported from Ward K to Deonar

WK-Mulund = Weight of waste transported from Ward K to Mulund

WK-Gorai = Weight of waste transported from Ward K to Gorai

WL-Deonar = Weight of waste transported from Ward L to Deonar

WL-Mulund = Weight of waste transported from Ward L to Mulund

WL-Gorai = Weight of waste transported from Ward L to Gorai

WM-Deonar = Weight of waste transported from Ward M to Deonar


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WM-Mulund = Weight of waste transported from Ward M to Mulund

WM-Gorai = Weight of waste transported from Ward M to Gorai

WN-Deonar = Weight of waste transported from Ward N to Deonar

WN-Mulund = Weight of waste transported from Ward N to Mulund

WN-Gorai = Weight of waste transported from Ward N to Gorai

WO-Deonar = Weight of waste transported from Ward O to Deonar

WO-Mulund = Weight of waste transported from Ward O to Mulund

WO-Gorai = Weight of waste transported from Ward O to Gorai

WP-Deonar = Weight of waste transported from Ward P to Deonar

WP-Mulund = Weight of waste transported from Ward P to Mulund

WP-Gorai = Weight of waste transported from Ward P to Gorai

WQ-Deonar = Weight of waste transported from Ward Q to Deonar

WQ-Mulund = Weight of waste transported from Ward Q to Mulund

WQ-Gorai = Weight of waste transported from Ward Q to Gorai

WR-Deonar = Weight of waste transported from Ward R to Deonar

WR-Mulund = Weight of waste transported from Ward R to Mulund

WR-Gorai = Weight of waste transported from Ward R to Gorai

WS-Deonar = Weight of waste transported from Ward S to Deonar

WS-Mulund = Weight of waste transported from Ward S to Mulund

WS-Gorai = Weight of waste transported from Ward S to Gorai

WT-Deonar = Weight of waste transported from Ward T to Deonar

WT-Mulund = Weight of waste transported from Ward T to Mulund

WT-Gorai = Weight of waste transported from Ward T to Gorai

WU-Deonar = Weight of waste transported from Ward U to Deonar

WU-Mulund = Weight of waste transported from Ward U to Mulund

WU-Gorai = Weight of waste transported from Ward U to Gorai

WV-Deonar = Weight of waste transported from Ward V to Deonar

WV-Mulund = Weight of waste transported from Ward V to Mulund

WV-Gorai = Weight of waste transported from Ward V to Gorai

WW-Deonar = Weight of waste transported from Ward W to Deonar

WW-Mulund = Weight of waste transported from Ward W to Mulund

WW-Gorai = Weight of waste transported from Ward W to Gorai

WX-Deonar = Weight of waste transported from Ward X to Deonar

WX-Mulund = Weight of waste transported from Ward X to Mulund

WX-Gorai = Weight of waste transported from Ward X to Gorai

OBJECTIVE FUNCTION –

The objective function is to minimize the total cost associated with transporting the wastes from the wards

to each of the three compost plants as well as the total operating cost of composting the waste.

Let

Wx-y = Waste transported from Ward ‘x’ to Compost Site ‘y’ in tons


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Wi = Waste generated at Ward ‘i’ in tons

Dx-y = Distance between Ward ‘x’ and Compost Site ‘y’ in kms

OCi = Operating Cost per ton of waste at Compost Site ‘i’ in Rs.

Bi = Budget allocated to Ward ‘i’ for transporting wastes to different compost sites in Rs.

Maxi = Maximum Operating Capacity of Compost Site ‘i’ in tons

TrC = Cost of transportation = Rs. 10/ton/km

The objective function thus is –

MINIMIZE Z = ∑ x ∑y [ ( TrC * Dx-y * Wx-y ) + ( OCy * Wx-y ) ]

CONSTRAINTS –

Capacity of Dump Site –

The weight of wastes transported and thus processed at each compost site should be less than or equal to

the maximum capacity of the compost site.

∑ x Wx-y ≤ Maxy , for all compost sites ‘y’

Waste Generated at Ward –

All the waste generated at a particular ward needs to be transported to any of the three compost sites.

No waste goes unprocessed.

∑ y Wx-y = Wx , for all wards ‘x’

Budget for each Ward –

The cost of transporting the wastes from the wards to the compost sites should be less than or equal to the

budget allocated for transportation for the ward under consideration.

∑y ( TrC * Dx-y * Wx-y ) ≤ Bx , for all wards ‘x’


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SOLUTION USING LINGO

LINGO FORMULATION –

! ********************************************************************

LINGO Linear Programming Model for

Waste Management Problem in Mumbai

********************************************************************;

! ********************************************************************

Defining the sets

and the associated attributes for the sets

********************************************************************;

SETS:

! Basic Sets;

! Every ward is identified by the amount of waste generated

and the maximum budget for transportation

allocated per ward ;

Ward: WasteGenerated, MaxBudget;

! Every dumping site has a maximum capacity that can not be exceeded

and the operating cost at each dump site is different;

DumpSite: Capacity, OperatingCost;

! Defining the derived set;

! Every Ward-Dump Site combination is identified by

the distance between the ward and the dump site

and the weight of waste transported from the ward to the dump site;

WaDu (Ward, DumpSite): Distance, WardtoDumpWeight;

ENDSETS

! ********************************************************************

Defining the data

associated with all attributes for the sets

********************************************************************;

DATA:

! There are 24 wards in Mumbai, from A through X;

Ward = A B C D E F G H I J K L M N O P Q R S T U V W X;

! Waste Generated from each ward expressed in tons;

WasteGenerated = 223.67 134.38 203.3 352.46 299.66 283.58 204.93 209.5 382.63

150.65 233.66 331.93 312.88 229.28 271.22 152.44 198.24 165.94 250.98 352.69 465.19

178 221.05 165.17;

! The maximum budget allocated per ward expressed in Rs. ;


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MaxBudget = 250000 230000 320000 80000 500000 200000 300000 400000 430000

530000 620000 740000 500000 600000 500000 510000 710000 820000 670000 650000 450000

430000 220000 410000;

! There are 3 dump sites in Mumbai;

DumpSite = Deonar Mulund Gorai;

! The maximum capacity of waste management site in tons;

Capacity = 4000 3000 6500;

! The operating cost per dumping site expressed in Rs./ton;

OperatingCost = 12 11.5 7;

! The distance between ward and the sites;

! Deonar Mulund Gorai;

Distance = 24 32 45 ! From A;

19.75 27.25 40 ! From B;

23 31 44 ! From C;

21.5 29.5 43 ! From D;

19 27 40 ! From E;

14.5 22.5 35 ! From F;

11.5 19.5 33 ! From G;

16.5 24.5 34 ! From H;

14.25 22.25 35 ! From I;

13.75 22.25 35 ! From J;

14.25 24 37 ! From K;

21 19 17.5 ! From L;

20.5 19 17.5 ! From M;

22 19 11.5 ! From N;

24 21 8.5 ! From O;

33 27 5.9 ! From P;

35 29 3.6 ! From Q;

36 30 5 ! From R;

11 19 33.5 ! From S;

5.5 17 39 ! From T;

2 14 41 ! From U;

7.75 13 30 ! From V;

13 8.75 26 ! From W;

18 4.5 22; ! From X;

ENDDATA

! ********************************************************************

OBJECTIVE FUNCTION

------------------

Minimise the total cost of waste disposal and management

by determining the weight of waste transported from each

ward to each dump site, WardtoDumpWeight

********************************************************************

********************************************************************

DECISION VARIABLE

-----------------

WardtoDumpWeight(i,j) = Weight of waste transported from

Ward-i to Dump Site-j

********************************************************************;


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[TotalCost] MIN = @SUM( WaDu(i,j): ( 10 * Distance(i,j) * WardtoDumpWeight(i,j))+

WardtoDumpWeight(i,j) * OperatingCost(j));

! ********************************************************************

CONSTRAINTS

-----------

********************************************************************;

!---------------------------------------------------------------

The total weight of waste transported from the wards to

each dumping site should be less than or equal to the

maximum capacity of the dumping site under consideration

---------------------------------------------------------------;

@FOR( DumpSite(i):

[Capc] @SUM( Ward(j) : WardtoDumpWeight(j,i)) <= Capacity(i);

);

!---------------------------------------------------------------

All the waste generated at a particular ward must be

transported to any of the three dumping sites

---------------------------------------------------------------;

@FOR( Ward(i):

[Generated] @SUM( DumpSite(j) : WardtoDumpWeight(i,j)) =

WasteGenerated(i);

);

!---------------------------------------------------------------

The total cost of transporting waste from the wards must

be less than equal to the allocated budget for

transportation from the wards

---------------------------------------------------------------;

@FOR( Ward(i):

[Budget] @SUM( DumpSite(j) : WardtoDumpWeight(i,j) * Distance(i,j) *

10) <= MaxBudget(i);

);

! ********************************************************************

---------End of Model-------------

LINGO Linear Programming Model for

Waste Management Problem in Mumbai

********************************************************************;

SOLUTION REPORT USING LINGO –

Global optimal solution found.

Objective value: 814231.1

Infeasibilities: 0.000000

Total solver iterations: 24

Model Class: LP


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Total variables: 72

Nonlinear variables: 0

Integer variables: 0

Total constraints: 52

Nonlinear constraints: 0

Total nonzeros: 288

Nonlinear nonzeros: 0

Variable Value Reduced Cost

WASTEGENERATED( A) 223.6700 0.000000

WASTEGENERATED( B) 134.3800 0.000000

WASTEGENERATED( C) 203.3000 0.000000

WASTEGENERATED( D) 352.4600 0.000000

WASTEGENERATED( E) 299.6600 0.000000

WASTEGENERATED( F) 283.5800 0.000000

WASTEGENERATED( G) 204.9300 0.000000

WASTEGENERATED( H) 209.5000 0.000000

WASTEGENERATED( I) 382.6300 0.000000

WASTEGENERATED( J) 150.6500 0.000000

WASTEGENERATED( K) 233.6600 0.000000

WASTEGENERATED( L) 331.9300 0.000000

WASTEGENERATED( M) 312.8800 0.000000

WASTEGENERATED( N) 229.2800 0.000000

WASTEGENERATED( O) 271.2200 0.000000

WASTEGENERATED( P) 152.4400 0.000000

WASTEGENERATED( Q) 198.2400 0.000000

WASTEGENERATED( R) 165.9400 0.000000

WASTEGENERATED( S) 250.9800 0.000000

WASTEGENERATED( T) 352.6900 0.000000

WASTEGENERATED( U) 465.1900 0.000000

WASTEGENERATED( V) 178.0000 0.000000

WASTEGENERATED( W) 221.0500 0.000000

WASTEGENERATED( X) 165.1700 0.000000

MAXBUDGET( A) 250000.0 0.000000

MAXBUDGET( B) 230000.0 0.000000

MAXBUDGET( C) 320000.0 0.000000

MAXBUDGET( D) 80000.00 0.000000

MAXBUDGET( E) 500000.0 0.000000

MAXBUDGET( F) 200000.0 0.000000

MAXBUDGET( G) 300000.0 0.000000

MAXBUDGET( H) 400000.0 0.000000

MAXBUDGET( I) 430000.0 0.000000

MAXBUDGET( J) 530000.0 0.000000

MAXBUDGET( K) 620000.0 0.000000

MAXBUDGET( L) 740000.0 0.000000

MAXBUDGET( M) 500000.0 0.000000

MAXBUDGET( N) 600000.0 0.000000

MAXBUDGET( O) 500000.0 0.000000

MAXBUDGET( P) 510000.0 0.000000

MAXBUDGET( Q) 710000.0 0.000000

MAXBUDGET( R) 820000.0 0.000000

MAXBUDGET( S) 670000.0 0.000000

MAXBUDGET( T) 650000.0 0.000000


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MAXBUDGET( U) 450000.0 0.000000

MAXBUDGET( V) 430000.0 0.000000

MAXBUDGET( W) 220000.0 0.000000

MAXBUDGET( X) 410000.0 0.000000

CAPACITY( DEONAR) 4000.000 0.000000

CAPACITY( MULUND) 3000.000 0.000000

CAPACITY( GORAI) 6500.000 0.000000

OPERATINGCOST( DEONAR) 12.00000 0.000000

OPERATINGCOST( MULUND) 11.50000 0.000000

OPERATINGCOST( GORAI) 7.000000 0.000000

DISTANCE( A, DEONAR) 24.00000 0.000000

DISTANCE( A, MULUND) 32.00000 0.000000

DISTANCE( A, GORAI) 45.00000 0.000000

DISTANCE( B, DEONAR) 19.75000 0.000000

DISTANCE( B, MULUND) 27.25000 0.000000

DISTANCE( B, GORAI) 40.00000 0.000000

DISTANCE( C, DEONAR) 23.00000 0.000000

DISTANCE( C, MULUND) 31.00000 0.000000

DISTANCE( C, GORAI) 44.00000 0.000000

DISTANCE( D, DEONAR) 21.50000 0.000000

DISTANCE( D, MULUND) 29.50000 0.000000

DISTANCE( D, GORAI) 43.00000 0.000000

DISTANCE( E, DEONAR) 19.00000 0.000000

DISTANCE( E, MULUND) 27.00000 0.000000

DISTANCE( E, GORAI) 40.00000 0.000000

DISTANCE( F, DEONAR) 14.50000 0.000000

DISTANCE( F, MULUND) 22.50000 0.000000

DISTANCE( F, GORAI) 35.00000 0.000000

DISTANCE( G, DEONAR) 11.50000 0.000000

DISTANCE( G, MULUND) 19.50000 0.000000

DISTANCE( G, GORAI) 33.00000 0.000000

DISTANCE( H, DEONAR) 16.50000 0.000000

DISTANCE( H, MULUND) 24.50000 0.000000

DISTANCE( H, GORAI) 34.00000 0.000000

DISTANCE( I, DEONAR) 14.25000 0.000000

DISTANCE( I, MULUND) 22.25000 0.000000

DISTANCE( I, GORAI) 35.00000 0.000000

DISTANCE( J, DEONAR) 13.75000 0.000000

DISTANCE( J, MULUND) 22.25000 0.000000

DISTANCE( J, GORAI) 35.00000 0.000000

DISTANCE( K, DEONAR) 14.25000 0.000000

DISTANCE( K, MULUND) 24.00000 0.000000

DISTANCE( K, GORAI) 37.00000 0.000000

DISTANCE( L, DEONAR) 21.00000 0.000000

DISTANCE( L, MULUND) 19.00000 0.000000

DISTANCE( L, GORAI) 17.50000 0.000000

DISTANCE( M, DEONAR) 20.50000 0.000000

DISTANCE( M, MULUND) 19.00000 0.000000

DISTANCE( M, GORAI) 17.50000 0.000000

DISTANCE( N, DEONAR) 22.00000 0.000000

DISTANCE( N, MULUND) 19.00000 0.000000

DISTANCE( N, GORAI) 11.50000 0.000000

DISTANCE( O, DEONAR) 24.00000 0.000000

DISTANCE( O, MULUND) 21.00000 0.000000

DISTANCE( O, GORAI) 8.500000 0.000000

DISTANCE( P, DEONAR) 33.00000 0.000000


Page 16

DISTANCE( P, MULUND) 27.00000 0.000000

DISTANCE( P, GORAI) 5.900000 0.000000

DISTANCE( Q, DEONAR) 35.00000 0.000000

DISTANCE( Q, MULUND) 29.00000 0.000000

DISTANCE( Q, GORAI) 3.600000 0.000000

DISTANCE( R, DEONAR) 36.00000 0.000000

DISTANCE( R, MULUND) 30.00000 0.000000

DISTANCE( R, GORAI) 5.000000 0.000000

DISTANCE( S, DEONAR) 11.00000 0.000000

DISTANCE( S, MULUND) 19.00000 0.000000

DISTANCE( S, GORAI) 33.50000 0.000000

DISTANCE( T, DEONAR) 5.500000 0.000000

DISTANCE( T, MULUND) 17.00000 0.000000

DISTANCE( T, GORAI) 39.00000 0.000000

DISTANCE( U, DEONAR) 2.000000 0.000000

DISTANCE( U, MULUND) 14.00000 0.000000

DISTANCE( U, GORAI) 41.00000 0.000000

DISTANCE( V, DEONAR) 7.750000 0.000000

DISTANCE( V, MULUND) 13.00000 0.000000

DISTANCE( V, GORAI) 30.00000 0.000000

DISTANCE( W, DEONAR) 13.00000 0.000000

DISTANCE( W, MULUND) 8.750000 0.000000

DISTANCE( W, GORAI) 26.00000 0.000000

DISTANCE( X, DEONAR) 18.00000 0.000000

DISTANCE( X, MULUND) 4.500000 0.000000

DISTANCE( X, GORAI) 22.00000 0.000000

WARDTODUMPWEIGHT( A, DEONAR) 223.6700 0.000000

WARDTODUMPWEIGHT( A, MULUND) 0.000000 79.50000

WARDTODUMPWEIGHT( A, GORAI) 0.000000 205.0000

WARDTODUMPWEIGHT( B, DEONAR) 134.3800 0.000000

WARDTODUMPWEIGHT( B, MULUND) 0.000000 74.50000

WARDTODUMPWEIGHT( B, GORAI) 0.000000 197.5000

WARDTODUMPWEIGHT( C, DEONAR) 203.3000 0.000000

WARDTODUMPWEIGHT( C, MULUND) 0.000000 79.50000

WARDTODUMPWEIGHT( C, GORAI) 0.000000 205.0000

WARDTODUMPWEIGHT( D, DEONAR) 352.4600 0.000000

WARDTODUMPWEIGHT( D, MULUND) 0.000000 79.50000

WARDTODUMPWEIGHT( D, GORAI) 0.000000 210.0000

WARDTODUMPWEIGHT( E, DEONAR) 299.6600 0.000000

WARDTODUMPWEIGHT( E, MULUND) 0.000000 79.50000

WARDTODUMPWEIGHT( E, GORAI) 0.000000 205.0000

WARDTODUMPWEIGHT( F, DEONAR) 283.5800 0.000000

WARDTODUMPWEIGHT( F, MULUND) 0.000000 79.50000

WARDTODUMPWEIGHT( F, GORAI) 0.000000 200.0000

WARDTODUMPWEIGHT( G, DEONAR) 204.9300 0.000000

WARDTODUMPWEIGHT( G, MULUND) 0.000000 79.50000

WARDTODUMPWEIGHT( G, GORAI) 0.000000 210.0000

WARDTODUMPWEIGHT( H, DEONAR) 209.5000 0.000000

WARDTODUMPWEIGHT( H, MULUND) 0.000000 79.50000

WARDTODUMPWEIGHT( H, GORAI) 0.000000 170.0000

WARDTODUMPWEIGHT( I, DEONAR) 382.6300 0.000000

WARDTODUMPWEIGHT( I, MULUND) 0.000000 79.50000

WARDTODUMPWEIGHT( I, GORAI) 0.000000 202.5000

WARDTODUMPWEIGHT( J, DEONAR) 150.6500 0.000000

WARDTODUMPWEIGHT( J, MULUND) 0.000000 84.50000

WARDTODUMPWEIGHT( J, GORAI) 0.000000 207.5000


Page 17

WARDTODUMPWEIGHT( K, DEONAR) 233.6600 0.000000

WARDTODUMPWEIGHT( K, MULUND) 0.000000 97.00000

WARDTODUMPWEIGHT( K, GORAI) 0.000000 222.5000

WARDTODUMPWEIGHT( L, DEONAR) 0.000000 40.00000

WARDTODUMPWEIGHT( L, MULUND) 0.000000 19.50000

WARDTODUMPWEIGHT( L, GORAI) 331.9300 0.000000

WARDTODUMPWEIGHT( M, DEONAR) 0.000000 35.00000

WARDTODUMPWEIGHT( M, MULUND) 0.000000 19.50000

WARDTODUMPWEIGHT( M, GORAI) 312.8800 0.000000

WARDTODUMPWEIGHT( N, DEONAR) 0.000000 110.0000

WARDTODUMPWEIGHT( N, MULUND) 0.000000 79.50000

WARDTODUMPWEIGHT( N, GORAI) 229.2800 0.000000

WARDTODUMPWEIGHT( O, DEONAR) 0.000000 160.0000

WARDTODUMPWEIGHT( O, MULUND) 0.000000 129.5000

WARDTODUMPWEIGHT( O, GORAI) 271.2200 0.000000

WARDTODUMPWEIGHT( P, DEONAR) 0.000000 276.0000

WARDTODUMPWEIGHT( P, MULUND) 0.000000 215.5000

WARDTODUMPWEIGHT( P, GORAI) 152.4400 0.000000

WARDTODUMPWEIGHT( Q, DEONAR) 0.000000 319.0000

WARDTODUMPWEIGHT( Q, MULUND) 0.000000 258.5000

WARDTODUMPWEIGHT( Q, GORAI) 198.2400 0.000000

WARDTODUMPWEIGHT( R, DEONAR) 0.000000 315.0000

WARDTODUMPWEIGHT( R, MULUND) 0.000000 254.5000

WARDTODUMPWEIGHT( R, GORAI) 165.9400 0.000000

WARDTODUMPWEIGHT( S, DEONAR) 250.9800 0.000000

WARDTODUMPWEIGHT( S, MULUND) 0.000000 79.50000

WARDTODUMPWEIGHT( S, GORAI) 0.000000 220.0000

WARDTODUMPWEIGHT( T, DEONAR) 352.6900 0.000000

WARDTODUMPWEIGHT( T, MULUND) 0.000000 114.5000

WARDTODUMPWEIGHT( T, GORAI) 0.000000 330.0000

WARDTODUMPWEIGHT( U, DEONAR) 465.1900 0.000000

WARDTODUMPWEIGHT( U, MULUND) 0.000000 119.5000

WARDTODUMPWEIGHT( U, GORAI) 0.000000 385.0000

WARDTODUMPWEIGHT( V, DEONAR) 178.0000 0.000000

WARDTODUMPWEIGHT( V, MULUND) 0.000000 52.00000

WARDTODUMPWEIGHT( V, GORAI) 0.000000 217.5000

WARDTODUMPWEIGHT( W, DEONAR) 0.000000 43.00000

WARDTODUMPWEIGHT( W, MULUND) 221.0500 0.000000

WARDTODUMPWEIGHT( W, GORAI) 0.000000 168.0000

WARDTODUMPWEIGHT( X, DEONAR) 0.000000 135.5000

WARDTODUMPWEIGHT( X, MULUND) 165.1700 0.000000

WARDTODUMPWEIGHT( X, GORAI) 0.000000 170.5000

Row Slack or Surplus Dual Price

TOTALCOST 814231.1 -1.000000

CAPC( DEONAR) 74.72000 0.000000

CAPC( MULUND) 2613.780 0.000000

CAPC( GORAI) 4838.070 0.000000

GENERATED( A) 0.000000 -252.0000

GENERATED( B) 0.000000 -209.5000

GENERATED( C) 0.000000 -242.0000

GENERATED( D) 0.000000 -227.0000

GENERATED( E) 0.000000 -202.0000

GENERATED( F) 0.000000 -157.0000

GENERATED( G) 0.000000 -127.0000

GENERATED( H) 0.000000 -177.0000


Page 18

GENERATED( I) 0.000000 -154.5000

GENERATED( J) 0.000000 -149.5000

GENERATED( K) 0.000000 -154.5000

GENERATED( L) 0.000000 -182.0000

GENERATED( M) 0.000000 -182.0000

GENERATED( N) 0.000000 -122.0000

GENERATED( O) 0.000000 -92.00000

GENERATED( P) 0.000000 -66.00000

GENERATED( Q) 0.000000 -43.00000

GENERATED( R) 0.000000 -57.00000

GENERATED( S) 0.000000 -122.0000

GENERATED( T) 0.000000 -67.00000

GENERATED( U) 0.000000 -32.00000

GENERATED( V) 0.000000 -89.50000

GENERATED( W) 0.000000 -99.00000

GENERATED( X) 0.000000 -56.50000

BUDGET( A) 196319.2 0.000000

BUDGET( B) 203460.0 0.000000

BUDGET( C) 273241.0 0.000000

BUDGET( D) 4221.100 0.000000

BUDGET( E) 443064.6 0.000000

BUDGET( F) 158880.9 0.000000

BUDGET( G) 276433.0 0.000000

BUDGET( H) 365432.5 0.000000

BUDGET( I) 375475.2 0.000000

BUDGET( J) 509285.6 0.000000

BUDGET( K) 586703.4 0.000000

BUDGET( L) 681912.2 0.000000

BUDGET( M) 445246.0 0.000000

BUDGET( N) 573632.8 0.000000

BUDGET( O) 476946.3 0.000000

BUDGET( P) 501006.0 0.000000

BUDGET( Q) 702863.4 0.000000

BUDGET( R) 811703.0 0.000000

BUDGET( S) 642392.2 0.000000

BUDGET( T) 630602.1 0.000000

BUDGET( U) 440696.2 0.000000

BUDGET( V) 416205.0 0.000000

BUDGET( W) 200658.1 0.000000

BUDGET( X) 402567.3 0.000000


Page 19

OPTIMAL SOLUTION

MINIMUM COST –

The minimum total cost of transporting the waste from the wards to the compost sites and the operating

cost of processing the waste at the compost sites is

Rs. 8, 14, 231.10

VALUES OF DECISION VARIABLES –

The values of the decision variables that result in the optimum cost as obtained above are summed up in

the table below –

Weight of wastes transported (tons)

Wards/ Compost Sites Deonar Mulund Gorai

A 223.67 0.00 0.00

B 134.38 0.00 0.00

C 203.30 0.00 0.00

D 352.46 0.00 0.00

E 299.66 0.00 0.00

F 283.58 0.00 0.00

G 204.93 0.00 0.00

H 209.50 0.00 0.00

I 382.63 0.00 0.00

J 150.65 0.00 0.00

K 233.66 0.00 0.00

L 0.00 0.00 331.93


Page 20

Weight of wastes transported (tons)

Wards/ Compost Sites Deonar Mulund Gorai

M 0.00 0.00 312.88

N 0.00 0.00 229.88

O 0.00 0.00 271.22

P 0.00 0.00 152.44

Q 0.00 0.00 198.24

R 0.00 0.00 165.94

S 250.98 0.00 0.00

T 352.69 0.00 0.00

U 465.19 0.00 0.00

V 178.00 0.00 0.00

W 0.00 221.05 0.00

X 0.00 165.17 0.00


Page 21

REFERENCES

1. Sarika Rathi, “Optimization Model for Integrated Municipal Solid Waste Management in

Mumbai”, Environment and Development Economics, 12, 105-121, 2007.

2. Frederick S. Hillier, Gerald J. Lieberman, Introduction to Operations Research – Concepts and

Cases, 9th Edition

b2 or report

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