Or Assignment - Batch 16

7/31/2019 Or Assignment - Batch 16

1/9

Problem Definition:-

The Power Services Division of JUSCO is responsible for the purchase, sale and

distribution of electricity; augmenting and maintaining the power distributioninfrastructure; as well as for municipal and town management functions in itsservice area.

Tired of 'erratic' and 'highly undependable' JSEB power supply, new and oldindustrial units as well as a large number of domestic users spread over the cityand its suburbs starting from Chandil have started putting in applications with

Jusco for electricity. Several other units are also coming forward to pay up Jusco'sinstallation charges for industrial consumers.

Based upon the projected increase in demand for the current consumers as well asestimated increase in sales through addition of new consumers in the network,

projections for the Financial Year 2009-10 were prepared. The projectedconnected load has been derived based on present connected loads, load underprocess and load expected from fresh applications for each consumer categoryconsidering the present scenario of economic recession and for all othercategories, the load factor has been taken mostly at FY 2008-09 levels.

Table 1-3: Energy Sales Projections for FY 2009-10

Projections for financial year 2010 - 11

Categor

y

Contract demand (KVA)Loadfactor

Consumption

Opening

Load

underprogres

s

Freshapplicatio

n% kWH

Domestic DS I

0 0 235 235 6.67 116800

Domestic DS II

5 59 588 652 7.74 195702

Domestic III

460 118 588 1166 4.43 302785

Domestic DSHT

251 500 500 1251 11.58 879817

Non

domestic NDS I

0 0 176 176 3.33 43800

Nondomestic NDS

II

273 59 1006 1338 10.00 706104

Lowtension LTIS I

743 300 1093 2136 7.69 1050524


2/9

The majority of the growth in FY 2008-09 came from the demand generated by thenewly added consumers. The same pattern will continue in the ensuing year FY2009-10 also as JUSCO is expanding its network across the area.Presently JUSCO is feeding the demand of power from its existing 33/6.4 KV substations located at the following area across the city with a 33/6.6 KV sub stationcoming up at Adityapur area.

Sl. No 33/6.6 KV sub station Location No1 Kadma 1

2 Circuit house 23 L town 14 Manifit 25 Golmuri 2

Cost of feeding to all the consumer area wise from its existing sub stations and thenew one at Adityapur area is tabulated below

Cost of laying feeder lines in Rs/KWh

DS-I DS-II DS-III NDS-I NDS-II LTIS-I

KADMA 5.87 6.32 6.34 5.85 5.65 5.2

ADITYAPUR 6.31 5.65 6.39 4.98 5.96 6.32

CKT HOUSE-1 5.35 5.43 6.45 6.31 5.89 6.67

CKT HOUSE-2 6 5.87 5.15 5.97 6.1 6.34

GOLMURI-1 5.7 6.67 5.65 6.7 6.32 6.4

GOLMURI-2 6.5 6.32 6 7.1 6.12 5.95

L-TOWN 7.2 4.9 5.95 5.55 5.56 6.15

MANIFIT-1 5.34 6.31 6.26 5.95 5.43 7

MANIFIT-2 5.31 6.35 6.1 5.8 5.65 6.9

The cost of feeding has been calculated considering the power loss over thedistance.

The management of JUSCO now lay the feeder lines to the new areas and at thesame time go for maintenance of old feeder lines to meet the supply and demandequilibrium so that the cost of feeding is at a minimum.

It has been estimated that maximum electricity availability at the different substations for the fiscal year 2009-10 will be as tabulated below

S.NO SUB STATION POWER AVAILABILITY IN KWh

1 KADMA 350000

2 ADITYAPUR 411732

3 CKT HOUSE-1 270000

4 CKT HOUSE-2 320000

5 GOLMURI-1 430000

6 GOLMURI-2 310000

7 L-TOWN 390000

8 MANIFIT-1 460000

9 MANIFIT-2 310000


3/9

Problem identification JUSCO wants to minimize the costs of laying the feederlines and distribution of electricity from sub stations to the consumers, while notexceeding the supply available from each sub station and meeting the demand ofeach consumer.

Problem formulation: formulating this problem as a transportation model forfeeding cost minimization

Let us consider Xij be the supply from I sub station to j categorized area. Here i =1 to 9 and j = 1 to 6.

Then,

DS-I DS-II DS-III NDS-I NDS-II LTIS-ISupply

KADMA 5.87 6.32 6.34 5.85 5.65 5.2 350000

ADITYAPUR 6.31 5.65 6.39 4.98 5.96 6.32 411732

CKT HOUSE-1 5.35 5.43 6.45 6.31 5.89 6.67

270000

CKT HOUSE-2 6 5.87 5.15 5.97 6.1 6.34

320000

GOLMURI-1 5.7 6.67 5.65 6.7 6.32 6.4 430000

GOLMURI-2 6.5 6.32 6 7.1 6.12 5.95 310000

L-TOWN 7.2 4.9 5.95 5.55 5.56 6.15 390000

MANIFIT-1 5.34 6.31 6.26 5.95 5.43 7 460000

MANIFIT-2 5.31 6.35 6.1 5.8 5.65 6.9 310000

Demand 116800 195702 302785 879817 706104 1050524 3251732

And

Sl.No

SUBSTATION

DS-I DS-II DS-III NDS-I NDS-II LTIS-IConst-raint

POWERAVAILABILITY IN KWh

1 KADMA X11 X12 X13 X14 X15 X16

350000

2 ADITYAPUR X21 X22 X23 X24 X25 X26

411732

3 CKT HOUSE-1 X31 X32 X33 X34 X35 X36

270000

4 CKT HOUSE-2 X41 X42 X43 X44 X45 X46

320000

5 GOLMURI-1 X51 X52 X53 X54 X55 X56

430000

6 GOLMURI-2 X61 X62 X63 X64 X65 X66

310000

7 L-TOWN X71 X72 X73 X74 X75 X76

390000

8 MANIFIT-1 X81 X82 X83 X84 X85 X86

460000

9 MANIFIT-2 X91 X92 X93 X94 X95 X96

310000

Constraint PROJECTED POWER

DEMAND11680

019570

230278

587981

770610

4 1050524 3251732


4/9

Considering it as a balanced transportation model and solving it using excel solvergenerates following solutionAnswer report:

Microsoft Excel 12.0 Answer Report

Worksheet: [Book1.xls]Sheet3

Report Created: 11/9/2009 11:18:41 AM

Target Cell (Min)

Cell NameOriginalValue Final Value

$L$23 MANIFIT-2 0 17975033

Adjustable Cells

Cell NameOriginalValue Final Value

$E$27 KADMA DS-I 0 0

$F$27 KADMA DS-II 0 0

$G$27 KADMA DS-III 0 0

$H$27 KADMA NDS-I 0 0

$I$27 KADMA NDS-II 0 0

$J$27 KADMA LTIS-I 0 350000

$E$28 ADITYAPUR DS-I 0 0

$F$28 ADITYAPUR DS-II 0 0

$G$28 ADITYAPUR DS-III 0 0

$H$28 ADITYAPUR NDS-I 0 411732

$I$28 ADITYAPUR NDS-II 0 0

$J$28 ADITYAPUR LTIS-I 0 0

$E$29 CKT HOUSE-1 DS-I 0 77324

$F$29 CKT HOUSE-1 DS-II 0 0

$G$29 CKT HOUSE-1 DS-III 0 0

$H$29 CKT HOUSE-1 NDS-I 0 0

$I$29 CKT HOUSE-1 NDS-II 0 192676

$J$29 CKT HOUSE-1 LTIS-I 0 0

$E$30 CKT HOUSE-2 DS-I 0 0

$F$30 CKT HOUSE-2 DS-II 0 0

$G$30 CKT HOUSE-2 DS-III 0 302785

$H$30 CKT HOUSE-2 NDS-I 0 17215

$I$30 CKT HOUSE-2 NDS-II 0 0

$J$30 CKT HOUSE-2 LTIS-I 0 0

$E$31 GOLMURI-1 DS-I 0 39476

$F$31 GOLMURI-1 DS-II 0 0

$G$31 GOLMURI-1 DS-III 0 0

$H$31 GOLMURI-1 NDS-I 0 0

$I$31 GOLMURI-1 NDS-II 0 0

$J$31 GOLMURI-1 LTIS-I 0 390524

$E$32 GOLMURI-2 DS-I 0 0

$F$32 GOLMURI-2 DS-II 0 0


5/9

$G$32 GOLMURI-2 DS-III 0 0

$H$32 GOLMURI-2 NDS-I 0 0

$I$32 GOLMURI-2 NDS-II 0 0

$J$32 GOLMURI-2 LTIS-I 0 310000

$E$33 L-TOWN DS-I 0 0

$F$33 L-TOWN DS-II 0 195702

$G$33 L-TOWN DS-III 0 0

$H$33 L-TOWN NDS-I 0 194298

$I$33 L-TOWN NDS-II 0 0

$J$33 L-TOWN LTIS-I 0 0

$E$34 MANIFIT-1 DS-I 0 0

$F$34 MANIFIT-1 DS-II 0 0

$G$34 MANIFIT-1 DS-III 0 0

$H$34 MANIFIT-1 NDS-I 0 0

$I$34 MANIFIT-1 NDS-II 0 460000

$J$34 MANIFIT-1 LTIS-I 0 0

$E$35 MANIFIT-2 DS-I 0 0

$F$35 MANIFIT-2 DS-II 0 0

$G$35 MANIFIT-2 DS-III 0 0$H$35 MANIFIT-2 NDS-I 0 256572

$I$35 MANIFIT-2 NDS-II 0 53428

$J$35 MANIFIT-2 LTIS-I 0 0

Constraints

Cell Name Cell Value Formula StatusSlac

k

$E$37 DS-I 116800$E$37>=$E$38 Binding 0

$F$37 DS-II 195702 $F$37>=$F$38 Binding 0

$G$37 DS-III 302785$G$37>=$G$38 Binding 0

$H$37 NDS-I 879817$H$37>=$H$38 Binding 0

$I$37 NDS-II 706104 $I$37>=$I$38 Binding 0

$J$37 LTIS-I 1050524 $J$37>=$J$38 Binding 0

$K$27 KADMA 350000$K$27


6/9

Sensitivity report:Microsoft Excel 12.0 Sensitivity Report

Worksheet: [Book1.xls]Sheet3

Report Created: 11/9/2009 11:18:42 AM

Adjustable Cells

Final

Reduced Objective

Allowable

Allowable

Cell Name Value CostCoefficien

t IncreaseDecreas

e

$E$27 KADMA DS-I 0 1.37 5.87 1.00E+30 1.37

$F$27 KADMA DS-II 0 1.78 6.32 1.00E+30 1.78

$G$27 KADMA DS-III 0 1.97 6.34 1.00E+30 1.97

$H$27 KADMA NDS-I 0 0.66 5.85 1.00E+30 0.66

$I$27 KADMA NDS-II 0 0.61 5.65 1.00E+30 0.61

$J$27 KADMA LTIS-I 350000 0 5.2 0.61 1.00E+30

$E$28 ADITYAPUR DS-I 0 2.02 6.31 1.00E+30 2.02

$F$28 ADITYAPUR DS-II 0 1.32 5.65 1.00E+30 1.32

$G$28 ADITYAPUR DS-III 0 2.23 6.39 1.00E+30 2.23

$H$28 ADITYAPUR NDS-I 411732 0 4.98 1.13 1.00E+30

$I$28 ADITYAPUR NDS-II 0 1.13 5.96 1.00E+30 1.13

$J$28 ADITYAPUR LTIS-I 0 1.33 6.32 1.00E+30 1.33$E$29 CKT HOUSE-1 DS-I 77324 0 5.35 0.2 0.08

$F$29 CKT HOUSE-1 DS-II 0 0.04 5.43 1.00E+30 0.04

$G$29 CKT HOUSE-1 DS-III 0 1.23 6.45 1.00E+30 1.23

$H$29 CKT HOUSE-1 NDS-I 0 0.27 6.31 1.00E+30 0.27

$I$29 CKT HOUSE-1 NDS-II 192676 0 5.89 0.04 0.2

$J$29 CKT HOUSE-1 LTIS-I 0 0.62 6.67 1.00E+30 0.62

$E$30 CKT HOUSE-2 DS-I 0 0.72 6 1.00E+30 0.72

$F$30 CKT HOUSE-2 DS-II 0 0.55 5.87 1.00E+30 0.55

$G$30 CKT HOUSE-2 DS-III 302785 0 5.15 0.08 5.57

$H$30 CKT HOUSE-2 NDS-I 17215 0 5.97 0.28 0.08$I$30 CKT HOUSE-2 NDS-II 0 0.28 6.1 1.00E+30 0.28

$J$30 CKT HOUSE-2 LTIS-I 0 0.36 6.34 1.00E+30 0.36

$E$31 GOLMURI-1 DS-I 39476 0 5.7 0.08 0.35

$F$31 GOLMURI-1 DS-II 0 0.93 6.67 1.00E+30 0.93

$G$31 GOLMURI-1 DS-III 0 0.08 5.65 1.00E+30 0.08

$H$31 GOLMURI-1 NDS-I 0 0.31 6.7 1.00E+30 0.31

$I$31 GOLMURI-1 NDS-II 0 0.08 6.32 1.00E+30 0.08

$J$31 GOLMURI-1 LTIS-I 390524 0 6.4 0.36 0.33

$E$32 GOLMURI-2 DS-I 0 1.25 6.5 1.00E+30 1.25


7/9

$F$32 GOLMURI-2 DS-II 0 1.03 6.32 1.00E+30 1.03

$G$32 GOLMURI-2 DS-III 0 0.88 6 1.00E+30 0.88

$H$32 GOLMURI-2 NDS-I 0 1.16 7.1 1.00E+30 1.16

$I$32 GOLMURI-2 NDS-II 0 0.33 6.12 1.00E+30 0.33

$J$32 GOLMURI-2 LTIS-I 310000 0 5.95 0.33 1.00E+30

$E$33 L-TOWN DS-I 0 2.34 7.2 1.00E+30 2.34

$F$33 L-TOWN DS-II 195702 0 4.9 0.04 5.74

$G$33 L-TOWN DS-III 0 1.22 5.95 1.00E+30 1.22

$H$33 L-TOWN NDS-I 194298 0 5.55 0.16 0.04

$I$33 L-TOWN NDS-II 0 0.16 5.56 1.00E+30 0.16

$J$33 L-TOWN LTIS-I 0 0.59 6.15 1.00E+30 0.59

$E$34 MANIFIT-1 DS-I 0 0.45 5.34 1.00E+30 0.45

$F$34 MANIFIT-1 DS-II 0 1.38 6.31 1.00E+30 1.38

$G$34 MANIFIT-1 DS-III 0 1.5 6.26 1.00E+30 1.5

$H$34 MANIFIT-1 NDS-I 0 0.37 5.95 1.00E+30 0.37

$I$34 MANIFIT-1 NDS-II 460000 0 5.43 0.37 1.00E+30

$J$34 MANIFIT-1 LTIS-I 0 1.41 7 1.00E+30 1.41

$E$35 MANIFIT-2 DS-I 0 0.2 5.31 1.00E+30 0.2

$F$35 MANIFIT-2 DS-II 0 1.2 6.35 1.00E+30 1.2$G$35 MANIFIT-2 DS-III 0 1.12 6.1 1.00E+30 1.12

$H$35 MANIFIT-2 NDS-I 256572 0 5.8 0.04 0.16

$I$35 MANIFIT-2 NDS-II 53428 0 5.65 0.16 0.04

$J$35 MANIFIT-2 LTIS-I 0 1.09 6.9 1.00E+30 1.09

Constraints

Final ShadowConstrain

tAllowabl

eAllowabl

e

Cell Name Value Price R.H. Side IncreaseDecreas

e

$E$37 DS-I 116800 5.7 116800 0 39476

$F$37 DS-II 195702 5.74 195702 0 39476

$G$37 DS-III 302785 5.57 302785 0 39476

$H$37 NDS-I 879817 6.39 879817 0 39476

$I$37 NDS-II 706104 6.24 706104 0 39476

$J$37 LTIS-I105052

4 6.4 1050524 0 390524

$K$27 KADMA 350000 -1.2 350000 390524 0

$K$28 ADITYAPUR 411732 -1.41 411732 39476 0

$K$29 CKT HOUSE-1 270000 -0.35 270000 39476 0

$K$30 CKT HOUSE-2 320000 -0.42 320000 39476 0

$K$31 GOLMURI-1 430000 0 430000 1.00E+30 0

$K$32 GOLMURI-2 310000 -0.45 310000 390524 0

$K$33 L-TOWN 390000 -0.84 390000 39476 0

$K$34 MANIFIT-1 460000 -0.81 460000 39476 0

$K$35 MANIFIT-2 310000 -0.59 310000 39476 0


8/9

Analysis :-Q-1:- What is the most profitable plan of demand and supply of electricity for JUSCO? Whatis the total projected cost under this plan?Ans:- according to the existing solution the plan is tabulated below

116800 195702 302785 879817 706104 1050524

DS-I DS-II DS-III NDS-I NDS-II LTIS-I

KADMA 0 0 0 0 0 350000

ADITYAPUR 0 0 0 411732 0 0

CKT HOUSE-1 77324 0 0 0 192676 0

CKT HOUSE-2 0 0 302785 17215 0 0

GOLMURI-1 39476 0 0 0 0 390524

GOLMURI-2 0 0 0 0 0 310000

L-TOWN 0 195702 0 194298 0 0

MANIFIT-1 0 0 0 0 460000 0

MANIFIT-2 0 0 0 256572 53428 0

Total projected cost under this plan is Rs 17975033

Q-2:- How many supply routes are there and how many are suggested by the solution?Ans: - there are a total of 54 routes of power supply and the solution suggests only 14(6+9-1 = 14) routes of power supply from the sub stations.

Q-3:- Suppose JUSCO wants to decrease the cost of supply by Re 0.02 for the Manifit II toNDS I feeder. Is it possible under the current optimal solution?

Ans:- Yes it is possible because the allowable decrease in cost of supply is Re 0.04. thetotal cost of supply, if the rate is decreased by Re. 0.02, the new supply cost will be (oldcost obtained by the solution qty supply * 0.02) = 17975033 256572*0.02 = Rs17969901.56

Q-4 :- For what range of values of the cost of shipping 1 KWh of electricity from substation at L town to DS II will the current basis remain optimal?

Ans :- From the sensitivity report we find that for supplying the electricity from L town to

DS II the objective co efficient can be increased by Rs 0.04 and can be decreased by Rs5.74. So, the range is Rs 4.9-0.04 = Rs 4.86 and 4.9+5.74 = Rs 10.64

Q:-5 :- Suppose JUSCO is planning to use ACSR conductors instead of AAAC conductors thecost of supply from Manifit II sub station to NDS I and NDS II will increase further byby Re 0.02 and decrease by Re 0.03 resp. Can JUSCO implement this under currentoptimal solution?

Ans:- Applying the 100 % rule; if the price is decreased by 0.02 for Manifit II to NDS I,the % is 0.02/0.04*100=50 %. If the price gets increased by 0.1 the % is0.03/0.04*100=75%. The total is 125 % greater than 100 %. So, JUSCO cant go for the useof ACSR conductors instead of AAAC conductors.


9/9

FinalReduce

d ObjectiveAllowabl

eAllowabl

e

Cell Name Value CostCoefficien

t Increase Decrease

$H$35 MANIFIT-2 NDS-I 256572 0 5.8 0.04 0.16

$I$35 MANIFIT-2 NDS-II 53428 0 5.65 0.16 0.04

Or Assignment - Batch 16

Documents

Transcript of Or Assignment - Batch 16