Path’s Name

Path’s Set

( w 1 , w 2 )

F j ( p , w )

F ¯ j ( p )

ME

MME

E

I

P1

1-4-8-10-13-14

(0.05, 0.95)

(14, 11)

1.1667

1.5714

0.1667

0.5714

0.5714

178

170

P2

1-4-7-11-14

(0.10, 0.90)

(13, 8)

1.0833

1.1429

0.0833

0.1429

0.1429

193

191

P3

1-4-7-11-12-14

(0.15, 0.85)

(12, 7)

1.0000

1.0000

0.0000

0.0000

0.0000

268

265

P4

1-4-7-11-12-14

(0.20, 0.80)

(12, 7)

1.0000

1.0000

0.0000

0.0000

0.0000

212

209

P5

1-4-7-11-12-14

(0.25, 0.75)

(12, 7)

1.0000

1.0000

0.0000

0.0000

0.0000

468

459

P6

1-4-7-11-12-14

(0.30, 0.70)

(12, 7)

1.0000

1.0000

0.0000

0.0000

0.0000

230

217

P7

1-4-7-11-12-14

(0.35, 0.65)

(12, 7)

1.0000

1.0000

0.0000

0.0000

0.0000

190

186

P8

1-4-7-11-14

(0.40, 0.60)

(13, 8)

1.0833

1.1429

0.0833

0.1429

0.1429

351

342

P9

1-4-7-11-12-14

(0.45, 0.55)

(12, 7)

1.0000

1.0000

0.0000

0.0000

0.0000

225

221

P10

1-4-7-11-12-14

(0.50, 0.50)

(12, 7)

1.0000

1.0000

0.0000

0.0000

0.0000

251

247

P11

1-4-7-11-12-14

(0.55, 0.45)

(12, 7)

1.0000

1.0000

0.0000

0.0000

0.0000

252

248

P12

1-4-7-11-12-14

(0.60, 0.40)

(12, 7)

1.0000

1.0000

0.0000

0.0000

0.0000

274

266

P13

1-4-7-11-12-14

(0.65, 0.35)

(12, 7)

1.0000

1.0000

0.0000

0.0000

0.000

160

158

P14

1-4-7-11-12-14

(0.70, 0.30)

(12, 7)

1.0000

1.0000

0.0000

0.0000

0.0000

343

336

P15

1-4-7-11-13-14

(0.75, 0.25)

(12, 10)

1.0000

1.4286

0.0000

0.4286

0.4286

265

260

P16

1-4-7-11-14

(0.80, 0.20)

(13, 8)

1.0833

1.1429

0.0833

0.1429

0.1429

160

157

P17

1-4-7-11-12-14

(0.85, 0.15)

(12, 7)

1.0000

1.0000

0.0000

0.0000

0.0000

435

430

P18

1-2-5-6-12-14

(0.90, 0.10)

(12, 10)

1.0000

1.4286

0.0000

0.4286

0.4286

204

200

P19

1-4-7-11-13-14

(0.95, 0.05)

(12, 10)

1.0000

1.4286

0.0000

0.4286

0.4286

155

150

The utopian distance and utopian social cost are f 1 ( p ) = 12 and f 2 ( p ) = 7 respectively.