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International Journal of Computer Science Engineering and Information Technology Research (IJCSEITR) ISSN 2249-6831 Vol. 3, Issue 3, Aug 2013, 241-250 Š TJPRC Pvt. Ltd.

IMPACT OF G.P ON NETWORKS - A COMPUTATIONAL STUDY ON CASE (II) K. V. L. N. ACHARYULU1 & NAGU VADLANA2 1

Faculty of Mathematics, Department of Mathematics, Bapatla Engineering College, Bapatla, Andhra Pradesh, India 2

Faculty of Computer Science, Department of MCA, Bapatla Engineering College, Bapatla, Andhra Pradesh, India

ABSTRACT The paper concerns with the aim of identifying whether G.P influences a Network in a particular case or not.The maximum possible network is constructed in a systematic way with 124 activities and 94 nodes.G.P applied on Optimistic time estimate among three time estimates namely optimistic, most likely and pessimistic.A computational study has been carried out on the constructed network.Few results are obtained.All float values are calculated.Critical path is traced.Project analysis has been done with standard normal distribution curves which are illustrated where ever feasible.

KEYWORDS: Network, Time Estimates, Float, Critical Path, Normal Distribution AMS Classification: 90-08, 90B10, 90C90

INTRODUCTION Government and private sectors contrive new projects for their exponential development and systematic expansion.The basic feature of any project is to involve non repetition and increase the number of activities.They have big size with most skillful ramification.Past experience can not guide us some times to deal the present complexity which involves huge expenditure, time and management. Then the project needs careful study with effective analysis of entire project to reach the necessary targets.Planning and control on the Project are essential at every endeavor. PERT is an effective method which provides clear picture of relationships between the activities and operations. K.V.L.N.Acharyulu et.al [1-5] obtained some results in game theory and in some special cases of Networks with the impact of various progressions. Wiest and Levy [6] explored new ideas on Networks with management guide to PERT/CPM for the beginners in 1966. Billy E.Gillett [7] discussed various models with PERT in 1979. S.D Sharma [8] explained different applications of PERT&CPM techniques. The paper is aimed to investigate whether G.P supports in a particular case of a Network. The Geometric progression is applied on most likely time estimate among the three time estimations. By the concept of Mathematical induction, some results are obtained. G.P applied on Optimistic time estimate among three time estimates namely optimistic, most likely and pessimistic.A computational study has been acquitted on the constructed network.Few results are obtained. Total Float, Free float and Independent Float are computed.Critical path is ascertainedd.Project analysis has been done with standard normal distribution curves which are illustrated where ever feasible.

BASIC CONSTRUCTION OF NETWORK A network is formed with 124 activities and 94 nodes in a systematic way for analyzing the impact of Geometric Progression.G.P is considered on Optimistic time estimate(a) in Case(II) among three estimates.No error and no dummy activity are involved in the Network.


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Figure 1: Network with 124 Activities and 94 Nodes

PRELIMINARIES AND NOTATIONS 

TE= Earliest excepted completion time of event (TE) Def: For the fixed value of j=TE(j)=Max[TE(i)+ET(i,j)] which ranges over all activities from i-j.

TL= Latest allowable event completion time (TL) Def: For the fixed value of i=TL(i)=Min[TL(j)+ET(i,j)] which ranges over all activities from i-j.

ET= Excepted completion time of activity (I,J)

a = Optimistic time estimate

m = Most likely time estimate

b = Pessimistic time estimate

ES = Earliest start of an activity

EF = Earliest finish of an activity


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LS = Latest start of an activity

LF = Latest finish of an activity

TF = Total Float Def: TF of activity i-j = LFi-j-EFi-j (or) LSi-j-ESi-j

FF = Free Float Def: FF of activity i-j = TF - (TL-TE) of node j

IF = Independent Float Def: IF of activity i-j = FF - (TL-TE) of node i

SE=Slack event time

CPI=Critical Path Indicator

SCT= Scheduled Time

 = Standard deviation of project length

MATERIAL AND METHODS Step 1: Draw the project network completion time Step 2: Compute the excepted duration of each activity by using the formula ET 

From the time estimates a,m and p. Also calculate the excepted variance.

a  4m  b . 6

 2 of each activity

Step 3: Calculate TE, TL Step 4: Find Total Float, Free Float and Independent Float Step 5: Find the critical path and identify the critical activities Step 6: Compute project length which is a square root to sum of variance of all the critical activities. Step 7: From the standard normal variable z 

SCT  ETC

, Where SCT is scheduled Completion time of event,

 =standard deviation of project length.Using the standard normal curve and ETC is expected completion time of the project,we can estimate the probability of completing project within specified time.

RESULTS By employing CPM and PERT algorithm on the Network, the critical path is found from Table-1 which is built with all Activites, Time estimates, ET, Varience.ES, EF, LS, LF and all Float values. The Critical path indicator supplies the critical Activies in the Table-1. Table 1 Activity 1--2 1--3

Time Estimates a m b 1.414 2 1 3.464 4 3

ET

2

1.735 3.744

0.004 0.005

Earliest[E] ES EF 0 1.735 0 3.744

Latest[L] LS LF 124.011 125.746 0 3.744

TF

FF

IF

CPI

124.011 0

0 0

0 0

*


244

2--4 2--5 3--6 3--7 4--8 4--9 5--10 5--11 6--12 6--13 7--14 7--15 8--16 8--17 9--18 9--19 10--20 10--21 11--22 11--23 12--24 12--25 13--26 13--27 14--28 14--29 15--30 15--31 16-32 16-33 17-34 17-35 18-36 18-37 19-38 19-39 20-40 20-41 21-42 21-43 22-44 22-45 23-46 23-47 24-48 24-49 25-50 25-51 26-52 26-53 27-54 27-55 28-56 28-57 29-58 29-59 30-60 30-61 31-62 31-63 32-64 33-64 34-65 35-65 36-66 37-66 38-67 39-67 40-68 41-68 42-69 43-69

K. V. L. N. Acharyulu & Nagu Vadlana

5.477 7.483 9.486 11.489 13.49 15.491 17.492 19.493 21.494 23.494 25.495 27.495 29.495 31.496 33.496 35.496 37.496 39.496 41.496 43.497 45.497 47.497 49.497 51.497 53.497 55.497 57.497 59.497 61.497 63.498 65.498 67.498 69.498 71.498 73.498 75.498 77.498 79.498 81.498 83.498 85.498 87.498 89.498 91.498 93.498 95.498 97.498 99.498 101.498 103.498 105.498 107.498 109.498 111.498 113.498 115.498 117.498 119.498 121.498 123.498 125.499 127.499 129.499 131.499 133.499 135.499 137.499 139.499 141.499 143.499 145.499 147.499

6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148

5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99 101 103 105 107 109 111 113 115 117 119 121 123 125 127 129 131 133 135 137 139 141 143 145 147

5.746 7.747 9.747 11.748 13.748 15.748 17.748 19.748 21.749 23.749 25.749 27.749 29.749 31.749 33.749 35.749 37.749 39.749 41.749 43.749 45.749 47.749 49.749 51.749 53.749 55.749 57.749 59.749 61.749 63.749 65.749 67.749 69.749 71.749 73.749 75.749 77.749 79.749 81.749 83.749 85.749 87.749 89.749 91.749 93.749 95.749 97.749 99.749 101.749 103.749 105.749 107.749 109.749 111.749 113.749 115.749 117.749 119.749 121.749 123.749 125.749 127.749 129.749 131.749 133.749 135.749 137.749 139.749 141.749 143.749 145.749 147.749

0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006

Table 1: Contd., 1.735 7.481 1.735 9.482 3.744 13.491 3.744 15.492 7.481 21.229 7.481 23.229 9.482 27.23 9.482 29.23 13.491 35.24 13.491 37.24 15.492 41.241 15.492 43.241 21.229 50.978 21.229 52.978 23.229 56.978 23.229 58.978 27.23 64.979 27.23 66.979 29.23 70.979 29.23 72.979 35.24 80.989 35.24 82.989 37.24 86.989 37.24 88.989 41.241 94.99 41.241 96.99 43.241 100.99 43.241 102.99 50.978 112.727 50.978 114.727 52.978 118.727 52.978 120.727 56.978 126.727 56.978 128.727 58.978 132.727 58.978 134.727 64.979 142.728 64.979 144.728 66.979 148.728 66.979 150.728 70.979 156.728 70.979 158.728 72.979 162.728 72.979 164.728 80.989 174.738 80.989 176.738 82.989 180.738 82.989 182.738 86.989 188.738 86.989 190.738 88.989 194.738 88.989 196.738 94.99 204.739 94.99 206.739 96.99 210.739 96.99 212.739 100.99 218.739 100.99 220.739 102.99 224.739 102.99 226.739 112.727 238.476 114.727 242.476 118.727 248.476 120.727 252.476 126.727 260.476 128.727 264.476 132.727 270.476 134.727 274.476 142.728 284.477 144.728 288.477 148.728 294.477 150.728 298.477

185.747 125.746 63.745 3.744 219.493 191.493 161.493 133.493 101.492 73.492 43.492 15.492 245.241 233.241 219.241 207.241 191.241 179.241 165.241 153.241 135.241 123.241 109.241 97.241 81.241 69.241 55.241 43.241 278.99 274.99 268.99 264.99 256.99 252.99 246.99 242.99 232.99 228.99 222.99 218.99 210.99 206.99 200.99 196.99 184.99 180.99 174.99 170.99 162.99 158.99 152.99 148.99 138.99 134.99 128.99 124.99 116.99 112.99 106.99 102.99 340.739 338.739 334.739 332.739 326.739 324.739 320.739 318.739 310.739 308.739 304.739 302.739

191.493 133.493 73.492 15.492 233.241 207.241 179.241 153.241 123.241 97.241 69.241 43.241 274.99 264.99 252.99 242.99 228.99 218.99 206.99 196.99 180.99 170.99 158.99 148.99 134.99 124.99 112.99 102.99 340.739 338.739 334.739 332.739 326.739 324.739 320.739 318.739 310.739 308.739 304.739 302.739 296.739 294.739 290.739 288.739 278.739 276.739 272.739 270.739 264.739 262.739 258.739 256.739 248.739 246.739 242.739 240.739 234.739 232.739 228.739 226.739 466.488 466.488 464.488 464.488 460.488 460.488 458.488 458.488 452.488 452.488 450.488 450.488

184.012 124.011 60.001 0 212.012 184.012 152.011 124.011 88.001 60.001 28 0 224.012 212.012 196.012 184.012 164.011 152.011 136.011 124.011 100.001 88.001 72.001 60.001 40 28 12 0 228.012 224.012 216.012 212.012 200.012 196.012 188.012 184.012 168.011 164.011 156.011 152.011 140.011 136.011 128.011 124.011 104.001 100.001 92.001 88.001 76.001 72.001 64.001 60.001 44 40 32 28 16 12 4 0 228.012 224.012 216.012 212.012 200.012 196.012 188.012 184.012 168.011 164.011 156.011 152.011

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 4 0 4 0 4 0 4 0 4 0

-124.011 -124.011 0 0 -184.012 -184.012 -124.011 -124.011 -60.001 -60.001 0 0 -212.012 -212.012 -184.012 -184.012 -152.011 -152.011 -124.011 -124.011 -88.001 -88.001 -60.001 -60.001 -28 -28 0 0 -224.012 -224.012 -212.012 -212.012 -196.012 -196.012 -184.012 -184.012 -164.011 -164.011 -152.011 -152.011 -136.011 -136.011 -124.011 -124.011 -100.001 -100.001 -88.001 -88.001 -72.001 -72.001 -60.001 -60.001 -40 -40 -28 -28 -12 -12 0 0 -224.012 -224.012 -212.012 -212.012 -196.012 -196.012 -184.012 -184.012 -164.011 -164.011 -152.011 -152.011

*

*

*

*


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Impact of G.P on Networks - A Computational Study on Case (II)

44-70 45-70 46-71 47-71 48-72 49-72 50-73 51-73 52-74 53-74 54-75 55-75 56-76 57-76 58-77 59-77 60-78 61-78 62-79 63-79 64-80 65-80 66-81 67-81 68-82 69-82 70-83 71-83 72-84 73-84 74-85 75-85 76-86 77-86 78-87 79-87 80-88 81-88 82-89 83-89 84-90 85-90 86-91 87-91 88-92 89-92 90-93 91-93 92-94 93-94

149.499 151.499 153.499 155.499 157.499 159.499 161.499 163.499 165.499 167.499 169.499 171.499 173.499 175.499 177.499 179.499 181.499 183.499 185.499 187.499 189.499 191.499 193.499 195.499 197.499 199.499 201.499 203.499 205.499 207.499 209.499 211.499 213.499 215.499 217.499 219.499 221.499 223.499 225.499 227.499 229.499 231.499 233.499 235.499 237.499 239.499 241.499 243.499 245.499 247.499

150 152 154 156 158 160 162 164 166 168 170 172 174 176 178 180 182 184 186 188 190 192 194 196 198 200 202 204 206 208 210 212 214 216 218 220 222 224 226 228 230 232 234 236 238 240 242 244 246 248

149 151 153 155 157 159 161 163 165 167 169 171 173 175 177 179 181 183 185 187 189 191 193 195 197 199 201 203 205 207 209 211 213 215 217 219 221 223 225 227 229 231 233 235 237 239 241 243 245 247

149.749 151.749 153.749 155.749 157.749 159.749 161.749 163.749 165.749 167.749 169.749 171.749 173.749 175.749 177.749 179.749 181.749 183.749 185.749 187.749 189.749 191.749 193.749 195.749 197.749 199.749 201.749 203.749 205.749 207.749 209.749 211.749 213.749 215.749 217.749 219.749 221.749 223.749 225.749 227.749 229.749 231.749 233.749 235.749 237.749 239.749 241.749 243.749 245.749 247.749

0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006

Table 1: Contd., 156.728 306.477 158.728 310.477 162.728 316.477 164.728 320.477 174.738 332.487 176.738 336.487 180.738 342.487 182.738 346.487 188.738 354.487 190.738 358.487 194.738 364.487 196.738 368.487 204.739 378.488 206.739 382.488 210.739 388.488 212.739 392.488 218.739 400.488 220.739 404.488 224.739 410.488 226.739 414.488 242.476 432.225 252.476 444.225 264.476 458.225 274.476 470.225 288.477 486.226 298.477 498.226 310.477 512.226 320.477 524.226 336.487 542.236 346.487 554.236 358.487 568.236 368.478 580.227 382.488 596.237 392.488 608.237 404.488 622.237 414.488 634.237 444.225 665.974 470.225 693.974 498.226 723.975 524.226 751.975 554.236 783.985 580.236 811.985 608.237 841.986 634.237 869.986 693.974 931.723 751.976 991.725 811.985 1053.734 869.986 1113.735 991.725 1237.474 1113.735 1361.484

296.739 294.739 290.739 288.739 278.739 276.739 272.739 270.739 264.739 262.739 258.739 256.739 248.739 246.739 242.739 240.739 234.739 232.739 228.739 226.739 466.488 464.488 460.488 458.488 452.488 450.488 446.488 444.488 436.488 434.488 430.488 428.488 422.488 420.488 416.488 414.488 656.237 654.237 650.237 648.237 642.237 640.237 636.237 634.237 877.986 875.986 871.986 869.986 1115.735 1113.735

446.488 446.488 444.488 444.488 436.488 436.488 434.488 434.488 430.488 430.488 428.488 428.488 422.488 422.488 420.488 420.488 416.488 416.488 414.488 414.488 656.237 656.237 654.237 654.237 650.237 650.237 648.237 648.237 642.237 642.237 640.237 640.237 636.237 636.237 634.237 634.237 877.986 877.986 875.986 875.986 871.986 871.986 869.986 869.986 1115.735 1115.735 1113.735 1113.735 1361.484 1361.484

140.011 136.011 128.011 124.011 104.001 100.001 92.001 88.001 76.001 72.001 64.001 60.001 44 40 32 28 16 12 4 0 224.012 212.012 196.012 184.012 164.011 152.011 136.011 124.011 100.001 88.001 72.001 60.01 40 28 12 0 212.012 184.012 152.011 124.011 88.001 60.001 28 0 184.012 124.01 60.001 0 124.01 0

4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 12 0 12 0 12 0 12 0 12 0 12 0 12 0 12 0 28 0 28 0 28 0 28 0 60.002 0 60.001 0 124.01 0

-136.011 -136.011 -124.011 -124.011 -100.001 -100.001 -88.001 -88.001 -72.001 -72.001 -60.001 -60.001 -40 -40 -28 -28 -12 -12 0 0 -212.012 -212.012 -184.012 -184.012 -152.011 -152.011 -124.011 -124.011 -88.001 -88.001 -60.001 -60.01 -28 -28 0 0 -184.012 -184.012 -124.011 -124.011 -60.001 -60.001 0 0 -124.01 -124.01 0 0 0 0

Critical path is identified as below

Project Length is defined as Sum of Variances of each Critical activity i.e Project Length  0.005  0.006  0.006  0.006  0.006  0.006  0.006  0.006  0.006  0.006

=0.2428. The values of TE, TL and SE corresponding to every node are given in Table (2). The slack event time may be positive, negative or zero.

*

*

*

* *


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K. V. L. N. Acharyulu & Nagu Vadlana

It is also observed that the values of slack event time vanish at each critical activity. Slack event time is defined as the amount of time in which the event can be retarded with out involving the scheduled completion time for the project.Any activity on the critical path necessitates time in excess of its expected completion time and detains the project completion consequently. Table 2 Nodes 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54

TE 0 1.735 3.744 7.481 9.482 13.491 15.492 21.229 23.229 27.23 29.23 35.24 37.24 41.241 43.241 50.978 52.978 56.978 58.978 64.979 66.979 70.979 72.979 80.989 82.989 86.989 88.989 94.99 96.99 100.99 102.99 112.727 114.727 118.727 120.727 126.727 128.727 132.727 134.727 142.728 144.728 148.728 150.728 156.728 158.728 162.728 164.728 174.738 176.738 180.738 182.738 188.738 190.738 194.738

TL 0 125.746 3.744 191.493 133.493 73.492 15.492 233.241 207.241 179.241 153.241 123.241 97.241 69.241 43.241 274.99 264.99 252.99 242.99 228.99 218.99 206.99 196.99 180.99 170.99 158.99 148.99 134.99 124.99 112.99 102.99 340.739 338.739 334.739 332.739 326.739 324.739 320.739 318.739 310.739 308.739 304.739 302.739 296.739 294.739 290.739 288.739 278.739 276.739 272.739 270.739 264.739 262.739 258.739

SE 0 124.011 0 184.012 124.011 60.001 0 212.012 184.012 152.011 124.011 88.001 60.001 28 0 224.012 212.012 196.012 184.012 164.011 152.011 136.011 124.011 100.001 88.001 72.001 60.001 40 28 12 0 228.012 224.012 216.012 212.012 200.012 196.012 188.012 184.012 168.011 164.011 156.011 152.011 140.011 136.011 128.011 124.011 104.001 100.001 92.001 88.001 76.001 72.001 64.001


247

Impact of G.P on Networks - A Computational Study on Case (II)

55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94

Table 2: Contd., 196.738 256.739 204.739 248.739 206.739 246.739 210.739 242.739 212.739 240.739 218.739 234.739 220.739 232.739 224.739 228.739 226.739 226.739 242.476 466.488 252.476 464.488 264.476 460.488 274.476 458.488 288.477 452.488 298.477 450.488 310.477 446.488 320.477 444.488 336.487 436.488 346.487 434.488 358.487 430.488 368.478 428.488 382.488 422.488 392.488 420.488 404.488 416.488 414.488 414.488 444.225 656.237 470.225 654.237 498.226 650.237 524.226 648.237 554.236 642.237 580.236 640.237 608.237 636.237 634.237 634.237 693.974 877.986 751.976 875.986 811.985 871.986 869.986 869.986 991.725 1115.735 1113.735 1113.735 1361.484 1361.484

60.001 44 40 32 28 16 12 4 0 224.012 212.012 196.012 184.012 164.011 152.011 136.011 124.011 100.001 88.001 72.001 60.01 40 28 12 0 212.012 184.012 152.011 124.011 88.001 60.001 28 0 184.012 124.01 60.001 0 124.01 0 0

PROJECT ANANLYSIS Project analysis is accomplished with specific schedule times and the standard normal variables are obtained in the entire range of probability from o to 1. The percentage of possibilities of completion of the Project are derived and given in the following Table3.Pictorial representations are also given. Table 3 SCT

ETC

Z

Probability

1360 1361 1362 1363

1361.484 1361.484 1361.484 1361.484

-6.1120 -1.9934 2.1252 6.2438

0 0.0233 0.9830 1

Percentage of Possibility (%) 0 2.3 98.3 100

The Obtained Standard Normal Curves are shown from Figure 2 to Figure 4


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K. V. L. N. Acharyulu & Nagu Vadlana

Figure 2

Figure 3

Figure 4

CONCLUSIONS The conclusions which are obtained from the computational study are listed below. 

It is noticed that G.P influences consistently on Network even though the network has big size.



Constant Variances are identical in any activity of the Network.


Impact of G.P on Networks - A Computational Study on Case (II)

249

In Critical Path o

It is observed that all Total Float values of Critical activities are vanished.

o

The value of Slack event of each node in critical path is null value.

o

TE and TL are identical at each node in critical path.

In the considered data of Net work in which G.P is employed on Optimistic time estimate, the expected completion time of successive activity is raised step by step.

The conditions of the influence of A.P in the Network are given below o

G.P influences positively on Network only when SCT is greater than ETC.

o

G.P does not influence properly when SCT is less than or equal to ETC.

o

Standard Normal Distribution curves provide the percentage of possibilities of the Project.

ACKNOWLEDGEMENTS The authors are thankful to Maddi.N.Murali Krishna for his valuable cooperation.

REFERENCES 1.

K.V.L.N. Acharyulu and Nagu Vadlana, (2013). Influence of G.P on Networks - A Scientific study on Case (I), International Journal of Computer Networking, Wireless and Mobile Communications, Vol. 3, Issue 2, pp. 83-92.

2.

K.V.L.N.Acharyulu and Maddi.N.Murali Krishna,(2013). Impact of A.P on Networks - A Computational study on Case (I), International Journal of Computer Networking, Wireless and Mobile Communications, Vol. 3, Issue 2, pp. 55-793-102.

3.

K.V.L.N.Acharyulu and Maddi.N.Murali Krishna,(2013). Some Remarkable Results in Row and Column both Dominance Game with Brown’s Algorithm, International Journal of Mathematics and Computer Applications Research,Vol. 3, No.1, pp.139-150.

4.

K. V. L. N. Acharyulu, Maddi. N. Murali Krishna, Sateesh Bandikalla & Nagu Vadlana,(2013). A Significant Approach On A Special Case Of Game Theory, International Journal of Computer Science Engineering and Information Technology Research, Vol. 3, Issue 2, pp. 55-78.

5.

K.V.L.N.Acharyulu and Maddi.N.Murali Krishna, (2013). A Scientific Computation On A Peculiar Case of Game Theory in Operations Research, International Journal of Computer Science Engineering and Information Technology Research,Vol. 3 , No.1, pp.175-190.

6.

Wiest, J.D., and F-Levy,(1969).A management Guide to PERT/CPM, Patrick-mall, Inc. Engle Wood Cliffs, N.J.

7.

Billy E. Gillett,(1979).Introduction to operations Research, Tata McGraw-Hill Publishing Company limited, PP.434-453,New York.

8.

S.D.Sharma,(1999). Operations Research, PP.4.300-4.355, Kedar Nath Ram Nath & Co.


27 impact of g p full  

The paper concerns with the aim of identifying whether G.P influences a Network in a particular case or not.The maximum possible network is...

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