Table 2 Comparisons of CPU time (seconds) required to achieve the budget allocation where the competitive equilibrium satisfies power demands between two approaches, error tolerance = 0.01 and average of 10 simulation runs.

2

4

6

8

10

M1

M2

M1

M2

M1

M2

M1

M2

0.033

1.085

0.049

1.228

0.069

1.358

0.088

1.624

0.136

1.882

0.022

1.164

0.080

1.479

0.267

2.255

0.463

3.465

1.011

6.450

0.028

1.270

0.106

2.207

0.312

5.129

0.639

10.545

1.947

19.406

0.025

1.516

0.103

3.788

0.510

10.305

0.875

25.697

2.592

51.210

0.035

1.889

0.130

7.222

0.525

27.027

0.938

44.909

2.455

111.270

0.028

2.482

0.158

12.558

0.603

41.747

1.816

93.028

3.164

190.489

0.028

3.231

0.161

20.454

0.528

66.719

2.464

150.099

2.708

322.979

0.039

4.793

0.184

33.251

0.684

102.846

1.260

263.820

6.006

519.137

0.041

6.529

0.250

46.043

0.627

150.047

2.181

385.401

5.781

773.646

0.042

9.322

0.247

66.839

0.703

215.038

2.645

553.401

4.689

1179.129