GAMS Rev 239 XXX-DEG 23.9.2 Mac x86_64/Darwin 01/13/13 14:10:36 Page 1 Ex1 C o m p i l a t i o n 4 5 OPTION SOLPRINT = ON ; 6 7 SETS 8 m flows / 1*4 / 9 i(m) subset / 2*4 / 10 ; 11 12 PARAMETERS 13 OCT(m) the values of the octane numbers 14 / 1 99 , 15 2 105 , 16 3 95 , 17 4 99 / 18 BENZ(m) the values of benzene content in the flows 19 / 1 0 , 20 2 0 , 21 3 0 , 22 4 0.02 / 23 P(m) the prices of the different flows in dollar per kg 24 / 1 0.1 , 25 2 0.2 , 26 3 0.12, 27 4 0.185 / 28 29 VARIABLES 30 COST 31 X(m) 32 ; 33 34 POSITIVE VARIABLES 35 X(m) flow rate of stream m 36 ; 37 38 EQUATIONS 39 E1,E2,I1,I2,I3 40 ; 41 42 *E1..COST =E= SUM(m, P(m)*X(m)); 43 E1..COST =E= P('1')*(1+X('1'))*X('1') + SUM(m$(ORD(m) NE 1), P(m)*X(m)); 44 *E1..COST =E= P('1')*(1+X('1'))*X('1') + SUM(i, P(i)*X(i)); 45 E2..1 =E= SUM(m, X(m)); 46 I1..98 =L= SUM(m, X(m)*OCT(m)); 47 I2..0.01 =G= SUM(m, X(m)*BENZ(m)); 48 I3..0.4 =G= X('1'); 49 50 51 MODEL JUPITER/ALL/; 52 53 SOLVE JUPITER USING NLP MINIMIZING COST; COMPILATION TIME = 0.003 SECONDS 3 Mb DEX239-239 Aug 29, 2012 GAMS Rev 239 XXX-DEG 23.9.2 Mac x86_64/Darwin 01/13/13 14:10:36 Page 2 Ex1 Equation Listing SOLVE JUPITER Using NLP From line 53 ---- E1 =E= E1.. COST - (0.1)*X(1) - 0.2*X(2) - 0.12*X(3) - 0.185*X(4) =E= 0 ; (LHS = 0) ---- E2 =E= E2.. - X(1) - X(2) - X(3) - X(4) =E= -1 ; (LHS = 0, INFES = 1 ****) ---- I1 =L= I1.. - 99*X(1) - 105*X(2) - 95*X(3) - 99*X(4) =L= -98 ; (LHS = 0, INFES = 98 ****) ---- I2 =G= I2.. - 0.02*X(4) =G= -0.01 ; (LHS = 0) ---- I3 =G= I3.. - X(1) =G= -0.4 ; (LHS = 0) GAMS Rev 239 XXX-DEG 23.9.2 Mac x86_64/Darwin 01/13/13 14:10:36 Page 3 Ex1 Column Listing SOLVE JUPITER Using NLP From line 53 ---- COST COST (.LO, .L, .UP, .M = -INF, 0, +INF, 0) 1 E1 ---- X flow rate of stream m X(1) (.LO, .L, .UP, .M = 0, 0, +INF, 0) (-0.1) E1 -1 E2 -99 I1 -1 I3 X(2) (.LO, .L, .UP, .M = 0, 0, +INF, 0) -0.2 E1 -1 E2 -105 I1 X(3) (.LO, .L, .UP, .M = 0, 0, +INF, 0) -0.12 E1 -1 E2 -95 I1 REMAINING ENTRY SKIPPED GAMS Rev 239 XXX-DEG 23.9.2 Mac x86_64/Darwin 01/13/13 14:10:36 Page 4 Ex1 Model Statistics SOLVE JUPITER Using NLP From line 53 MODEL STATISTICS BLOCKS OF EQUATIONS 5 SINGLE EQUATIONS 5 BLOCKS OF VARIABLES 2 SINGLE VARIABLES 5 NON ZERO ELEMENTS 15 NON LINEAR N-Z 1 DERIVATIVE POOL 10 CONSTANT POOL 16 CODE LENGTH 7 GENERATION TIME = 0.001 SECONDS 4 Mb DEX239-239 Aug 29, 2012 EXECUTION TIME = 0.002 SECONDS 4 Mb DEX239-239 Aug 29, 2012 GAMS Rev 239 XXX-DEG 23.9.2 Mac x86_64/Darwin 01/13/13 14:10:36 Page 5 Ex1 Solution Report SOLVE JUPITER Using NLP From line 53 S O L V E S U M M A R Y MODEL JUPITER OBJECTIVE COST TYPE NLP DIRECTION MINIMIZE SOLVER CONOPT FROM LINE 53 **** SOLVER STATUS 1 Normal Completion **** MODEL STATUS 2 Locally Optimal **** OBJECTIVE VALUE 0.1372 RESOURCE USAGE, LIMIT 0.029 1000.000 ITERATION COUNT, LIMIT 6 2000000000 EVALUATION ERRORS 0 0 CONOPT 3 Jul 4, 2012 23.9.2 DEX 34973.35015 DEG Mac x86_64/Darwin C O N O P T 3 version 3.15F Copyright (C) ARKI Consulting and Development A/S Bagsvaerdvej 246 A DK-2880 Bagsvaerd, Denmark The model has 5 variables and 5 constraints with 15 Jacobian elements, 1 of which are nonlinear. The Hessian of the Lagrangian has 1 elements on the diagonal, 0 elements below the diagonal, and 1 nonlinear variables. ** Optimal solution. Reduced gradient less than tolerance. CONOPT time Total 0.024 seconds of which: Function evaluations 0.000 = 0.0% 1st Derivative evaluations 0.000 = 0.0% LOWER LEVEL UPPER MARGINAL ---- EQU E1 . . . 1.0000 ---- EQU E2 -1.0000 -1.0000 -1.0000 0.6400 ---- EQU I1 -INF -98.0000 -98.0000 -0.0080 ---- EQU I2 -0.0100 . +INF . ---- EQU I3 -0.4000 -0.2600 +INF EPS LOWER LEVEL UPPER MARGINAL ---- VAR COST -INF 0.1372 +INF . GAMS Rev 239 XXX-DEG 23.9.2 Mac x86_64/Darwin 01/13/13 14:10:36 Page 6 Ex1 Solution Report SOLVE JUPITER Using NLP From line 53 ---- VAR X flow rate of stream m LOWER LEVEL UPPER MARGINAL 1 . 0.2600 +INF . 2 . 0.1960 +INF . 3 . 0.5440 +INF . 4 . . +INF 0.0330 **** REPORT SUMMARY : 0 NONOPT 0 INFEASIBLE 0 UNBOUNDED 0 ERRORS EXECUTION TIME = 0.001 SECONDS 2 Mb DEX239-239 Aug 29, 2012 USER: GAMS Development Corporation, Washington, DC G871201/0000CA-ANY Free Demo, 202-342-0180, sales@gams.com, www.gams.com DC0000 **** FILE SUMMARY Input /Users/holene/Documents/NTNU/Project/Gams/ex1_adv_reg/Ex1_adv_reg.gms Output /Users/holene/Documents/NTNU/Project/Gams/ex1_adv_reg/Ex1_adv_reg.lst