Hello to you all,
I am trying to replicate the results of a Nash-Cournot model that appears in Gabriel et al (2012), page 495, but obtain the following result:
**** SOLVER STATUS 1 Normal Completion
**** MODEL STATUS 5 Locally Infeasible
In addition, there are 23 (out of 25) infeasible equations:
**** REPORT SUMMARY : 0 NONOPT
23 INFEASIBLE (INFES)
I am inexperienced in the use of GAMS but have read the tutorial and the PATH solver documentation but still cannot figure out where is the bug in my code, even after having checked it several times. As you will be able to confirm, I have matched all the variables in my model with its corresponding equality and inequality constraints and have avoided using =l=. I use =g= instead (at least, this worked out with a prefectly competitive, smaller version of this same model).
I will be tremendously grateful if anyone is able to spot what is wrong with my code and helps me to determine why I am obtaining the INFES message in addition to the locally infeasible result.
For your complete understanding of the problem, I attach the following:
- The precise mathematical formulation of the MCP just as it appears in the book (PDF attachment)
- The .gms file
- The .lst file
Please note that I am running this model with a GAMS version / machine details as follows:
GAMSIDE build 40679 / 40979
GAMS Release 24.1.2 r40979 WEX-WEI x86_64/MS Windows
Many thanks in advance!
Luis Boscan
PhD Fellow, Copenhagen Business School
I paste the contents of the .lst file:
GAMS 24.1.2 r40979 Released Jun 16, 2013 WEX-WEI x86_64/MS Windows 10/29/13 19:46:13 Page 1
G e n e r a l A l g e b r a i c M o d e l i n g S y s t e m
C o m p i l a t i o n
1 option mcp=path;
2
3 parameters
4 C11 Generation cost of firm 1 in node 1 /15/
5 C22 Generation cost of firm 2 in node 2 /20/
6 T1 Transmission capacity constraint /10000/
7 eta1 Constant in inverse demand function 1 /40/
8 eta2 Constant in inverse demand function 2 /40/
9 eta3 Constant in inverse demand function 3 /32/
10 kappa1 Slope parameter in demand function 1 /-0.08/
11 kappa2 Slope parameter in demand function 2 /-0.08/
12 kappa3 Slope parameter in demand function 3 /-0.0516/
13 PTDF11 PTDF node 1 line k=1 /-0.33333/
14 PTDF21 PTDF node 2 line k=1 /0.33333/
15
16 positive variables
17 x11 Generation by firm 1 in node 1
18 x22 Generation by firm 2 in node 2
19 s11 Sales by firm 1 in node 1
20 s12 Sales by firm 1 in node 2
21 s13 Sales by firm 1 in node 3
22 s21 Sales by firm 2 in node 1
23 s22 Sales by firm 2 in node 2
24 s23 Sales by firm 2 in node 3
25 mu11 Multiplier of generation capacity of firm 1 in node 1
26 mu22 Multiplier of generation capacity of firm 2 in node 2
27 lambda_plus1 Multiplier for upper bound of transmission constraint
28 lambda_minus1 Multiplier for lower bound of transmission constraint
29 ;
30
31 variables
32 phi1 Multiplier for generator 1’s sales balance constraint
33 phi2 Multiplier for generator 2’s sales balance constraint
34 p1 Price in node 1
35 p2 Price in node 2
36 p3 Price in node 3
37 a1 Net sales by TSO to node 1
38 a2 Net sales by TSO to node 2
39 a3 Net sales by TSO to node 3
40 w1 Per MWh transmission fee to node 1
41 w2 Per MWh transmission fee to node 2
42 w3 Per MWh transmission fee to node 2
43 y1 Transmission to node 1
44 y2 Transmission to node 2
45 y3 Transmission to node 3
46 gamma Multiplier of TSO’s net sales balance
47 ;
48
49 equations
50 *****************
51 Producer’s KKT *
52 *****************
53 eq_x11
54 eq_x22
55 eq_s11
56 eq_s12
57 eq_s13
58 eq_s21
59 eq_s22
60 eq_s23
61
62 **************************
63 Producer’s sale balance *
64 **************************
65 eq_SB1
66 eq_SB2
67
68 ******************
69 * TSO’s KKT *
70 ******************
71 eq_TSO_a1
72 eq_TSO_a2
73 eq_TSO_a3
74 eq_TSO_y1
75 eq_TSO_y2
76 eq_TSO_y3
77
78 *****************
79 TSOs net sales *
80 *****************
81 eq_TSO_MC
82
83 **********************
84 TSOs KKT wrt lambda *
85 **********************
86
87 eqTSO_lambda_plus1
88 eqTSO_lambda_minus1
89
90 **********************
91 * Market clearing *
92 **********************
93 eqMC1
94 eqMC2
95 eqMC3
96
97 ***************************
98 Inverse Demand functions *
99 ***************************
100 eq_p1
101 eq_p2
102 eq_p3
103 ;
104
105 eq_x11…
106 0 =g= -C11+w1+phi1;
107 eq_x22…
108 0 =g= -C22+w2+phi2;
109 eq_s11…
110 0 =g= (p1+s11kappa1)-(w1+phi1);
111 eq_s12…
112 0 =g= (p2+s12kappa2)-(w2+phi1);
113 eq_s13…
114 0 =g= (p3+s13kappa3)-(w3+phi1);
115 eq_s21…
116 0 =g= (p1+s21kappa1)-(w1+phi2);
117 eq_s22…
118 0 =g= (p2+s22kappa2)-(w2+phi2);
119 eq_s23…
120 0 =g= (p3+s23kappa3)-(w3+phi2);
121
122
123
124 eq_SB1…
125 s11+s12+s13-x11 =e= 0;
126 eq_SB2…
127 s21+s22+s23-x22 =e= 0;
128
129
130 eq_TSO_a1…
131 p1-gamma-(PTDF11lambda_plus1)+(PTDF11lambda_minus1) =e= 0;
132
133 eq_TSO_a2…
134 p2-gamma-(PTDF21lambda_plus1)+(PTDF21lambda_minus1) =e= 0;
135
136 eq_TSO_a3…
137 p3-gamma =e= 0;
138 eq_TSO_y1…
139 w1-PTDF11lambda_plus1+PTDF11lambda_minus1 =e= 0;
140 eq_TSO_y2…
141 w2-PTDF21lambda_plus1+PTDF21lambda_minus1 =e= 0;
142 eq_TSO_y3…
143 w3 =e= 0;
144
145
146 eq_TSO_MC…
147 a1+a2+a3 =e= 0;
148
149
150 eqTSO_lambda_plus1…
151 0 =g= PTDF11(a1+y1)+PTDF21*(a2+y2)-T1;
152
153 eqTSO_lambda_minus1…
154 0 =g= -PTDF11*(a1+y1)-PTDF21*(a2+y2)-T1;
155
156 eqMC1…
157 y1-(s11+s21)+x11 =e= 0;
158 eqMC2…
159 y2-(s12+s22)+x22 =e= 0;
160 eqMC3…
161 y3-(s13+s23) =e= 0;
162
163 eq_p1…
164 p1 - (eta1-kappa1*(a1+s11+s21)) =e= 0;
165 eq_p2…
166 p2 - (eta2-kappa2*(a2+s12+s22)) =e= 0;
167 eq_p3…
168 p3 - (eta3-kappa3*(a3+s13+s23)) =e= 0;
169
170
171 model perfectC /eq_x11.x11,eq_x22.x22,eq_s11.s11,eq_s12.s12,eq_s13.s13,
172 eq_s21.s21,eq_s22.s22,eq_s23.s23,eq_SB1.phi1,eq_SB2.phi2,eq_TSO_a1.a1,
173 eq_TSO_a2.a2,eq_TSO_a3.a3,eq_TSO_y1.y1,eq_TSO_y2.y2,eq_TSO_y3.y3,eq_TSO_MC
.gamma,
174 eqTSO_lambda_plus1.lambda_plus1,eqTSO_lambda_minus1.lambda_minus1,
175 eqMC1.w1,eqMC2.w2,eqMC3.w3,eq_p1.p1,eq_p2.p2,eq_p3.p3/
176
177 *List all equations
178 *option limrow = 10000, limcol = 10000;
179
180 *display lambda_plus1.l, lambda_minus1.l;
181
182 solve perfectC using mcp;
COMPILATION TIME = 0.000 SECONDS 2 MB 24.1.2 r40979 WEX-WEI
GAMS 24.1.2 r40979 Released Jun 16, 2013 WEX-WEI x86_64/MS Windows 10/29/13 19:46:13 Page 2
G e n e r a l A l g e b r a i c M o d e l i n g S y s t e m
Equation Listing SOLVE perfectC Using MCP From line 182
---- eq_x11 =G=
eq_x11… - phi1 - w1 =G= -15 ; (LHS = 0)
---- eq_x22 =G=
eq_x22… - phi2 - w2 =G= -20 ; (LHS = 0)
---- eq_s11 =G=
eq_s11… 0.08*s11 + phi1 - p1 + w1 =G= 0 ; (LHS = 0)
---- eq_s12 =G=
eq_s12… 0.08*s12 + phi1 - p2 + w2 =G= 0 ; (LHS = 0)
---- eq_s13 =G=
eq_s13… 0.0516*s13 + phi1 - p3 + w3 =G= 0 ; (LHS = 0)
---- eq_s21 =G=
eq_s21… 0.08*s21 + phi2 - p1 + w1 =G= 0 ; (LHS = 0)
---- eq_s22 =G=
eq_s22… 0.08*s22 + phi2 - p2 + w2 =G= 0 ; (LHS = 0)
---- eq_s23 =G=
eq_s23… 0.0516*s23 + phi2 - p3 + w3 =G= 0 ; (LHS = 0)
---- eq_SB1 =E=
eq_SB1… - x11 + s11 + s12 + s13 =E= 0 ; (LHS = 0)
---- eq_SB2 =E=
eq_SB2… - x22 + s21 + s22 + s23 =E= 0 ; (LHS = 0)
---- eq_TSO_a1 =E=
eq_TSO_a1… 0.33333lambda_plus1 - 0.33333lambda_minus1 + p1 - gamma =E= 0 ;
(LHS = 0)
---- eq_TSO_a2 =E=
eq_TSO_a2… - 0.33333lambda_plus1 + 0.33333lambda_minus1 + p2 - gamma =E= 0 ;
(LHS = 0)
---- eq_TSO_a3 =E=
eq_TSO_a3… p3 - gamma =E= 0 ; (LHS = 0)
---- eq_TSO_y1 =E=
eq_TSO_y1… 0.33333lambda_plus1 - 0.33333lambda_minus1 + w1 =E= 0 ; (LHS = 0)
---- eq_TSO_y2 =E=
eq_TSO_y2… - 0.33333lambda_plus1 + 0.33333lambda_minus1 + w2 =E= 0 ;
(LHS = 0)
---- eq_TSO_y3 =E=
eq_TSO_y3… w3 =E= 0 ; (LHS = 0)
---- eq_TSO_MC =E=
eq_TSO_MC… a1 + a2 + a3 =E= 0 ; (LHS = 0)
---- eqTSO_lambda_plus1 =G=
eqTSO_lambda_plus1… 0.33333a1 - 0.33333a2 + 0.33333y1 - 0.33333y2 =G=
-10000 ; (LHS = 0)
---- eqTSO_lambda_minus1 =G=
eqTSO_lambda_minus1… - 0.33333a1 + 0.33333a2 - 0.33333y1 + 0.33333y2 =G=
-10000 ; (LHS = 0)
---- eqMC1 =E=
eqMC1… x11 - s11 - s21 + y1 =E= 0 ; (LHS = 0)
---- eqMC2 =E=
eqMC2… x22 - s12 - s22 + y2 =E= 0 ; (LHS = 0)
---- eqMC3 =E=
eqMC3… - s13 - s23 + y3 =E= 0 ; (LHS = 0)
---- eq_p1 =E=
eq_p1… - 0.08s11 - 0.08s21 + p1 - 0.08*a1 =E= 40 ; (LHS = 0
, INFES = 40 ****)
---- eq_p2 =E=
eq_p2… - 0.08s12 - 0.08s22 + p2 - 0.08*a2 =E= 40 ; (LHS = 0
, INFES = 40 ****)
---- eq_p3 =E=
eq_p3… - 0.0516s13 - 0.0516s23 + p3 - 0.0516*a3 =E= 32 ;
(LHS = 0, INFES = 32 ****)
GAMS 24.1.2 r40979 Released Jun 16, 2013 WEX-WEI x86_64/MS Windows 10/29/13 19:46:13 Page 3
G e n e r a l A l g e b r a i c M o d e l i n g S y s t e m
Column Listing SOLVE perfectC Using MCP From line 182
---- x11 Generation by firm 1 in node 1
x11
(.LO, .L, .UP, .M = 0, 0, +INF, 0)
-1 eq_SB1
1 eqMC1
---- x22 Generation by firm 2 in node 2
x22
(.LO, .L, .UP, .M = 0, 0, +INF, 0)
-1 eq_SB2
1 eqMC2
---- s11 Sales by firm 1 in node 1
s11
(.LO, .L, .UP, .M = 0, 0, +INF, 0)
0.08 eq_s11
1 eq_SB1
-1 eqMC1
-0.08 eq_p1
---- s12 Sales by firm 1 in node 2
s12
(.LO, .L, .UP, .M = 0, 0, +INF, 0)
0.08 eq_s12
1 eq_SB1
-1 eqMC2
-0.08 eq_p2
---- s13 Sales by firm 1 in node 3
s13
(.LO, .L, .UP, .M = 0, 0, +INF, 0)
0.0516 eq_s13
1 eq_SB1
-1 eqMC3
-0.0516 eq_p3
---- s21 Sales by firm 2 in node 1
s21
(.LO, .L, .UP, .M = 0, 0, +INF, 0)
0.08 eq_s21
1 eq_SB2
-1 eqMC1
-0.08 eq_p1
---- s22 Sales by firm 2 in node 2
s22
(.LO, .L, .UP, .M = 0, 0, +INF, 0)
0.08 eq_s22
1 eq_SB2
-1 eqMC2
-0.08 eq_p2
---- s23 Sales by firm 2 in node 3
s23
(.LO, .L, .UP, .M = 0, 0, +INF, 0)
0.0516 eq_s23
1 eq_SB2
-1 eqMC3
-0.0516 eq_p3
---- lambda_plus1 Multiplier for upper bound of transmission constraint
lambda_plus1
(.LO, .L, .UP, .M = 0, 0, +INF, 0)
0.3333 eq_TSO_a1
-0.3333 eq_TSO_a2
0.3333 eq_TSO_y1
-0.3333 eq_TSO_y2
---- lambda_minus1 Multiplier for lower bound of transmission constraint
lambda_minus1
(.LO, .L, .UP, .M = 0, 0, +INF, 0)
-0.3333 eq_TSO_a1
0.3333 eq_TSO_a2
-0.3333 eq_TSO_y1
0.3333 eq_TSO_y2
---- phi1 Multiplier for generator 1’s sales balance constraint
phi1
(.LO, .L, .UP, .M = -INF, 0, +INF, 0)
-1 eq_x11
1 eq_s11
1 eq_s12
1 eq_s13
---- phi2 Multiplier for generator 2’s sales balance constraint
phi2
(.LO, .L, .UP, .M = -INF, 0, +INF, 0)
-1 eq_x22
1 eq_s21
1 eq_s22
1 eq_s23
---- p1 Price in node 1
p1
(.LO, .L, .UP, .M = -INF, 0, +INF, 0)
-1 eq_s11
-1 eq_s21
1 eq_TSO_a1
1 eq_p1
---- p2 Price in node 2
p2
(.LO, .L, .UP, .M = -INF, 0, +INF, 0)
-1 eq_s12
-1 eq_s22
1 eq_TSO_a2
1 eq_p2
---- p3 Price in node 3
p3
(.LO, .L, .UP, .M = -INF, 0, +INF, 0)
-1 eq_s13
-1 eq_s23
1 eq_TSO_a3
1 eq_p3
---- a1 Net sales by TSO to node 1
a1
(.LO, .L, .UP, .M = -INF, 0, +INF, 0)
1 eq_TSO_MC
0.3333 eqTSO_lambda_plus1
-0.3333 eqTSO_lambda_minus1
-0.08 eq_p1
---- a2 Net sales by TSO to node 2
a2
(.LO, .L, .UP, .M = -INF, 0, +INF, 0)
1 eq_TSO_MC
-0.3333 eqTSO_lambda_plus1
0.3333 eqTSO_lambda_minus1
-0.08 eq_p2
---- a3 Net sales by TSO to node 3
a3
(.LO, .L, .UP, .M = -INF, 0, +INF, 0)
1 eq_TSO_MC
-0.0516 eq_p3
---- w1 Per MWh transmission fee to node 1
w1
(.LO, .L, .UP, .M = -INF, 0, +INF, 0)
-1 eq_x11
1 eq_s11
1 eq_s21
1 eq_TSO_y1
---- w2 Per MWh transmission fee to node 2
w2
(.LO, .L, .UP, .M = -INF, 0, +INF, 0)
-1 eq_x22
1 eq_s12
1 eq_s22
1 eq_TSO_y2
---- w3 Per MWh transmission fee to node 2
w3
(.LO, .L, .UP, .M = -INF, 0, +INF, 0)
1 eq_s13
1 eq_s23
1 eq_TSO_y3
---- y1 Transmission to node 1
y1
(.LO, .L, .UP, .M = -INF, 0, +INF, 0)
0.3333 eqTSO_lambda_plus1
-0.3333 eqTSO_lambda_minus1
1 eqMC1
---- y2 Transmission to node 2
y2
(.LO, .L, .UP, .M = -INF, 0, +INF, 0)
-0.3333 eqTSO_lambda_plus1
0.3333 eqTSO_lambda_minus1
1 eqMC2
---- y3 Transmission to node 3
y3
(.LO, .L, .UP, .M = -INF, 0, +INF, 0)
1 eqMC3
---- gamma Multiplier of TSO’s net sales balance
gamma
(.LO, .L, .UP, .M = -INF, 0, +INF, 0)
-1 eq_TSO_a1
-1 eq_TSO_a2
-1 eq_TSO_a3
GAMS 24.1.2 r40979 Released Jun 16, 2013 WEX-WEI x86_64/MS Windows 10/29/13 19:46:13 Page 4
G e n e r a l A l g e b r a i c M o d e l i n g S y s t e m
Model Statistics SOLVE perfectC Using MCP From line 182
MODEL STATISTICS
BLOCKS OF EQUATIONS 25 SINGLE EQUATIONS 25
BLOCKS OF VARIABLES 25 SINGLE VARIABLES 25
NON ZERO ELEMENTS 87 NON LINEAR N-Z 0
DERIVATIVE POOL 10 CONSTANT POOL 16
CODE LENGTH 0
GENERATION TIME = 0.016 SECONDS 3 MB 24.1.2 r40979 WEX-WEI
EXECUTION TIME = 0.016 SECONDS 3 MB 24.1.2 r40979 WEX-WEI
GAMS 24.1.2 r40979 Released Jun 16, 2013 WEX-WEI x86_64/MS Windows 10/29/13 19:46:13 Page 5
G e n e r a l A l g e b r a i c M o d e l i n g S y s t e m
Solution Report SOLVE perfectC Using MCP From line 182
S O L V E S U M M A R Y
MODEL perfectC
TYPE MCP
SOLVER PATH FROM LINE 182
**** SOLVER STATUS 1 Normal Completion
**** MODEL STATUS 5 Locally Infeasible
RESOURCE USAGE, LIMIT 0.109 1000.000
ITERATION COUNT, LIMIT 2359 2000000000
EVALUATION ERRORS 0 0
25 row/cols, 87 non-zeros, 13.92% dense.
Path 4.7.02 (Sun Jun 16 07:32:56 2013)
Written by Todd Munson, Steven Dirkse, and Michael Ferris
INITIAL POINT STATISTICS
Maximum of X. . . . . . . . . . 0.0000e+000 var: (x11)
Maximum of F. . . . . . . . . . 1.0000e+004 eqn: (eqTSO_lambda_plus1)
Maximum of Grad F . . . . . . . 1.0000e+000 eqn: (eq_SB1)
var: (x11)
INITIAL JACOBIAN NORM STATISTICS
Maximum Row Norm. . . . . . . . 4.0000e+000 eqn: (eq_SB1)
Minimum Row Norm. . . . . . . . 1.0000e+000 eqn: (eq_TSO_y3)
Maximum Column Norm . . . . . . 4.0000e+000 var: (phi1)
Minimum Column Norm . . . . . . 1.0000e+000 var: (y3)
FINAL STATISTICS
Inf-Norm of Complementarity . . 1.0105e+003 eqn: (eqTSO_lambda_plus1)
Inf-Norm of Normal Map. . . . . 1.0004e+004 eqn: (eqTSO_lambda_plus1)
Inf-Norm of Minimum Map . . . . 1.1795e+001 eqn: (eq_x11)
Inf-Norm of Fischer Function. . 1.2902e+001 eqn: (eq_x11)
Inf-Norm of Grad Fischer Fcn. . 3.2811e+000 eqn: (eq_p1)
Two-Norm of Grad Fischer Fcn. . 6.8647e+000
FINAL POINT STATISTICS
Maximum of X. . . . . . . . . . 6.2276e+001 var: (x11)
Maximum of F. . . . . . . . . . 1.0004e+004 eqn: (eqTSO_lambda_plus1)
Maximum of Grad F . . . . . . . 1.0000e+000 eqn: (eq_SB1)
var: (x11)
LOWER LEVEL UPPER MARGINAL
---- EQU eq_x11 -15.000 -26.795 +INF 62.276 INFES
---- EQU eq_x22 -20.000 -29.851 +INF 50.760 INFES
---- EQU eq_s11 . -5.446 +INF 40.651 INFES
---- EQU eq_s12 . -4.480 +INF 21.661 INFES
---- EQU eq_s13 . -0.017 +INF 0.016 INFES
---- EQU eq_s21 . -4.771 +INF 34.914 INFES
---- EQU eq_s22 . -3.804 +INF 15.932 INFES
---- EQU eq_s23 . 1.116 +INF .
---- EQU eq_SB1 . 0.052 . 30.508 INFES
---- EQU eq_SB2 . 0.087 . 31.641 INFES
---- EQU eq_TSO_a1 . 0.315 . -14.394 INFES
---- EQU eq_TSO_a2 . -0.315 . -1.061 INFES
---- EQU eq_TSO_a3 . -1.871 . 15.071 INFES
---- EQU eq_TSO_y1 . -3.679 . 13.563 INFES
---- EQU eq_TSO_y2 . -1.824 . -12.998 INFES
---- EQU eq_TSO_y3 . 2.815 . -0.979 INFES
---- EQU eq_TSO_MC . -0.384 . 35.212 INFES
---- EQU eqTSO_lam~ -1.000E+4 4.409 +INF 0.101 INFES
---- EQU eqTSO_lam~ -1.000E+4 -4.409 +INF .
---- EQU eqMC1 . 0.274 . -3.712 INFES
---- EQU eqMC2 . 0.169 . -1.790 INFES
---- EQU eqMC3 . -0.995 . 2.815 INFES
---- EQU eq_p1 40.000 30.600 40.000 35.493 INFES
---- EQU eq_p2 40.000 32.008 40.000 34.930 INFES
---- EQU eq_p3 32.000 32.563 32.000 33.341 INFES
LOWER LEVEL UPPER MARGINAL
---- VAR x11 . 62.276 +INF -11.795
---- VAR x22 . 50.760 +INF -9.851
---- VAR s11 . 40.651 +INF -5.446
---- VAR s12 . 21.661 +INF -4.480
---- VAR s13 . 0.016 +INF -0.017
---- VAR s21 . 34.914 +INF -4.771
---- VAR s22 . 15.932 +INF -3.804
---- VAR s23 . . +INF 1.116
---- VAR lambda_pl~ . 0.101 +INF 10004.409
---- VAR lambda_mi~ . . +INF 9995.591
---- VAR phi1 -INF 30.508 +INF 0.052
---- VAR phi2 -INF 31.641 +INF 0.087
---- VAR p1 -INF 35.493 +INF -9.400
---- VAR p2 -INF 34.930 +INF -7.992
---- VAR p3 -INF 33.341 +INF 0.563
---- VAR a1 -INF -14.394 +INF 0.315
---- VAR a2 -INF -1.061 +INF -0.315
---- VAR a3 -INF 15.071 +INF -1.871
---- VAR w1 -INF -3.712 +INF 0.274
---- VAR w2 -INF -1.790 +INF 0.169
---- VAR w3 -INF 2.815 +INF -0.995
---- VAR y1 -INF 13.563 +INF -3.679
---- VAR y2 -INF -12.998 +INF -1.824
---- VAR y3 -INF -0.979 +INF 2.815
---- VAR gamma -INF 35.212 +INF -0.384
x11 Generation by firm 1 in node 1
x22 Generation by firm 2 in node 2
s11 Sales by firm 1 in node 1
s12 Sales by firm 1 in node 2
s13 Sales by firm 1 in node 3
s21 Sales by firm 2 in node 1
s22 Sales by firm 2 in node 2
s23 Sales by firm 2 in node 3
lambda_plus1 Multiplier for upper bound of transmission constraint
lambda_minus1 Multiplier for lower bound of transmission constraint
phi1 Multiplier for generator 1’s sales balance constraint
phi2 Multiplier for generator 2’s sales balance constraint
p1 Price in node 1
p2 Price in node 2
p3 Price in node 3
a1 Net sales by TSO to node 1
a2 Net sales by TSO to node 2
a3 Net sales by TSO to node 3
w1 Per MWh transmission fee to node 1
w2 Per MWh transmission fee to node 2
w3 Per MWh transmission fee to node 2
y1 Transmission to node 1
y2 Transmission to node 2
y3 Transmission to node 3
gamma Multiplier of TSO’s net sales balance
**** REPORT SUMMARY : 0 NONOPT
23 INFEASIBLE (INFES)
SUM -9933.509
MAX 11.795
MEAN -431.892
0 UNBOUNDED
0 REDEFINED
0 ERRORS
EXECUTION TIME = 0.000 SECONDS 2 MB 24.1.2 r40979 WEX-WEI
USER: Course License - Enertrain S130920:0523AO-GEN
Berlin University of Technology, Workgroup for InfrastructuDC7910
License for teaching and research at degree granting institutions
**** FILE SUMMARY
Input C:\Users\lbo.eco\Documents\gamsdir\Gabriel\hobbs_NashCournot.gms
Output C:\Users\lbo.eco\Documents\gamsdir\Gabriel\hobbs_NashCournot.lst
\
formulation.pdf (96.5 KB)
hobbs_NashCournot.gms (4.56 KB)
hobbs_NashCournot.lst (21.1 KB)