GAMS Rev 232 WIN-VIS 23.2.1 x86/MS Windows 08/18/09 20:37:30 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 3 options limrow = 0, 4 limcol = 0, 5 iterlim = 1e9, 6 reslim = 3600, 7 sysout = off, 8 optcr = 0 ; 9 10 *option minlp = alphaecp; 11 *option minlp = baron; 12 *Option MINLP = CoinBonmin; 13 *option minlp = dicopt; 14 option minlp = sbb; 15 16 sets i products /A, B, C, D, E/ 17 j stages /1*6/ 18 k binary digit /1*2/; 19 20 parameters H horizon timie (h) 21 alpha(j) cost coefficient ($) 22 beta(j) cost coefficient 23 VL(j) lower bound of volume (L) 24 VU(j) upper bound of volume (L) 25 NU(j) maximum number of parallel units ; 26 27 H = 6000; 28 alpha(j) = 250; 29 beta(j) = 0.6; 30 VL(j) = 300; VU(j) = 3000; NU(j) = 4 ; 31 32 parameter Q(i) production rate (kg) / 33 A 250000 34 B 150000 35 C 180000 36 D 160000 37 E 120000 /; 38 39 table S(i,j) size factor for product i in stage j (L per kg) 40 1 2 3 4 5 6 41 A 7.9 2.0 5.2 4.9 6.1 4.2 42 B 0.7 0.8 0.9 3.4 2.1 2.5 43 C 0.7 2.6 1.6 3.6 3.2 2.9 44 D 4.7 2.3 1.6 2.7 1.2 2.5 45 E 1.2 3.6 2.4 4.5 1.6 2.1 46 47 table t(i,j) processing time for product i in stage j (L per kg) 48 1 2 3 4 5 6 49 A 6.4 4.7 8.3 3.9 2.1 1.2 50 B 6.8 6.4 6.5 4.4 2.3 3.2 51 C 1.0 6.3 5.4 11.9 5.7 6.2 52 D 3.2 3.0 3.5 3.3 2.8 3.4 53 E 2.1 2.5 4.2 3.6 3.7 2.2 54 55 56 positive variables N(j), V(j), B(i), TL(i); 57 binary variables y(k,j); 58 variable z; 59 equations obj, c1, c2, c3, c4; 60 61 V.lo(j) = VL(j); V.up(j) = VU(j); 62 N.lo(j) = 1; N.up(j) = NU(j) ; 63 TL.lo(i) = smax(j, t(i,j)/NU(j) ); TL.up(i) = smax(j, t(i,j)); 64 B.lo(i) = Q(i)/ H * smax(j, t(i,j)/NU(j) ); B.up(i) = min( Q(i), smin( j, VU(j)/S(i,j)) ); 65 66 N.l(j) = N.lo(j); V.l(j) = V.lo(j); B.l(i) = B.lo(i); TL.l(i) = TL.lo(i); 67 68 obj.. z =e= sum(j, alpha(j) * N(j) * ( V(j)**beta(j) ) ); 69 70 c1(i,j).. V(j) =g= S(i,j) * B(i); 71 c2(i,j).. N(j) * TL(i) =g= t(i,j); 72 c3.. sum(i, Q(i)*TL(i)/B(i) ) =l= H; 73 c4(j).. N(j) =e= 1 + sum(k, power(2, ord(k)-1) * Y(k,j) ); 74 75 model P1 /all/; 76 P1.workspace = 1024; 77 P1.workfactor = 1; 78 79 solve P1 using minlp minimizing z; COMPILATION TIME = 0.000 SECONDS 3 Mb WIN232-232 Aug 11, 2009 GAMS Rev 232 WIN-VIS 23.2.1 x86/MS Windows 08/18/09 20:37:30 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 Model Statistics SOLVE P1 Using MINLP From line 79 MODEL STATISTICS BLOCKS OF EQUATIONS 5 SINGLE EQUATIONS 68 BLOCKS OF VARIABLES 6 SINGLE VARIABLES 35 NON ZERO ELEMENTS 161 NON LINEAR N-Z 82 DERIVATIVE POOL 18 CONSTANT POOL 23 CODE LENGTH 449 DISCRETE VARIABLES 12 GENERATION TIME = 0.000 SECONDS 4 Mb WIN232-232 Aug 11, 2009 EXECUTION TIME = 0.000 SECONDS 4 Mb WIN232-232 Aug 11, 2009 GAMS Rev 232 WIN-VIS 23.2.1 x86/MS Windows 08/18/09 20:37:30 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 Solution Report SOLVE P1 Using MINLP From line 79 S O L V E S U M M A R Y MODEL P1 OBJECTIVE z TYPE MINLP DIRECTION MINIMIZE SOLVER SBB FROM LINE 79 **** SOLVER STATUS 1 Normal Completion **** MODEL STATUS 8 Integer Solution **** OBJECTIVE VALUE 285506.5082 RESOURCE USAGE, LIMIT 0.438 3600.000 ITERATION COUNT, LIMIT 596 1000000000 EVALUATION ERRORS 0 0 Simple B&B Aug 14, 2009 23.2.1 WIN 12168.12582 VIS x86/MS Windows Integer solution Statistics: B&B nodes : 43 MIP solution : 285506.508244 found in node 42 Best possible : 285506.508244 Absolute gap : 0.000000 optca : 0.000000 Relative gap : 0.000000 optcr : 0.000000 NLP Solver Statistics Total Number of NLP solves : 45 Total Number of NLP failures: 0 Details: conopt # execs 45 # failures 0 LOWER LEVEL UPPER MARGINAL ---- EQU obj . . . 1.000 ---- EQU c1 LOWER LEVEL UPPER MARGINAL A.1 . . +INF 7.009 A.2 . 1132.058 +INF . A.3 . . +INF 21.628 A.4 . 758.311 +INF . A.5 . 11.607 +INF . A.6 . 514.870 +INF . B.1 . 2460.780 +INF . B.2 . 1275.299 +INF . B.3 . 1281.400 +INF . B.4 . . +INF 7.648 B.5 . 710.402 +INF . B.6 . 184.020 +INF . C.1 . 2490.736 +INF . C.2 . . +INF 1.153 C.3 . 810.652 +INF . C.4 . . +INF 5.231 C.5 . . +INF 6.750 C.6 . . +INF 7.021 D.1 . . +INF 8.595 D.2 . 423.466 +INF . D.3 . 953.407 +INF . D.4 . 895.667 +INF . D.5 . 1562.106 +INF . D.6 . 514.062 +INF . E.1 . 2369.483 +INF . E.2 . . +INF 13.515 E.3 . 713.649 +INF . E.4 . 254.632 +INF . E.5 . 1487.374 +INF . E.6 . 1006.402 +INF . ---- EQU c2 LOWER LEVEL UPPER MARGINAL A.1 6.400 6.400 +INF 9958.461 A.2 4.700 6.400 +INF . A.3 8.300 9.600 +INF . A.4 3.900 6.400 +INF . A.5 2.100 3.200 +INF . A.6 1.200 3.200 +INF . B.1 6.800 6.800 +INF 2945.570 B.2 6.400 6.800 +INF . B.3 6.500 10.200 +INF . B.4 4.400 6.800 +INF . B.5 2.300 3.400 +INF . B.6 3.200 3.400 +INF . C.1 1.000 12.400 +INF . C.2 6.300 12.400 +INF . C.3 5.400 18.600 +INF . C.4 11.900 12.400 +INF . C.5 5.700 6.200 +INF . C.6 6.200 6.200 +INF 7485.212 D.1 3.200 6.800 +INF . D.2 3.000 6.800 +INF . D.3 3.500 10.200 +INF . D.4 3.300 6.800 +INF . D.5 2.800 3.400 +INF . D.6 3.400 3.400 +INF 7583.557 E.1 2.100 7.400 +INF . E.2 2.500 7.400 +INF . E.3 4.200 11.100 +INF . E.4 3.600 7.400 +INF . E.5 3.700 3.700 +INF 6909.427 E.6 2.200 3.700 +INF . LOWER LEVEL UPPER MARGINAL ---- EQU c3 -INF 6000.000 6000.000 -30.254 ---- EQU c4 LOWER LEVEL UPPER MARGINAL 1 1.000 1.000 1.000 -1.139E+4 2 1.000 1.000 1.000 23122.291 3 1.000 1.000 1.000 23726.764 4 1.000 1.000 1.000 28107.898 5 1.000 1.000 1.000 625.203 6 1.000 1.000 1.000 -4.750E+4 ---- VAR N LOWER LEVEL UPPER MARGINAL 1 1.000 2.000 4.000 . 2 1.000 2.000 4.000 . 3 1.000 3.000 4.000 . 4 1.000 2.000 4.000 . 5 1.000 1.000 4.000 . 6 1.000 1.000 4.000 . ---- VAR V LOWER LEVEL UPPER MARGINAL 1 300.000 3000.000 3000.000 -3.406 2 300.000 1891.551 3000.000 . 3 300.000 1974.684 3000.000 . 4 300.000 2619.071 3000.000 . 5 300.000 2328.063 3000.000 . 6 300.000 2109.807 3000.000 . ---- VAR B LOWER LEVEL UPPER MARGINAL A 86.458 379.747 379.747 . B 42.500 770.315 882.353 . C 89.250 727.520 833.333 . D 23.333 638.298 638.298 . E 21.000 525.431 666.667 . ---- VAR TL LOWER LEVEL UPPER MARGINAL A 2.075 3.200 8.300 . B 1.700 3.400 6.800 . C 2.975 6.200 11.900 . D 0.875 3.400 3.500 . E 1.050 3.700 4.200 . ---- VAR y LOWER LEVEL UPPER MARGINAL 1.1 . 1.000 1.000 -1.139E+4 1.2 . 1.000 1.000 23122.291 1.3 . . 1.000 23726.764 1.4 . 1.000 1.000 28107.898 1.5 . . 1.000 625.203 1.6 . . 1.000 -4.750E+4 2.1 . . 1.000 -2.278E+4 2.2 . . 1.000 46244.583 2.3 . 1.000 1.000 47453.528 2.4 . . 1.000 56215.795 2.5 . . 1.000 1250.406 2.6 . . 1.000 -9.501E+4 LOWER LEVEL UPPER MARGINAL ---- VAR z -INF 2.8551E+5 +INF . **** REPORT SUMMARY : 0 NONOPT 0 INFEASIBLE 0 UNBOUNDED 0 ERRORS EXECUTION TIME = 0.000 SECONDS 2 Mb WIN232-232 Aug 11, 2009 USER: Ignacio E. Grossmann G090202/0001AP-WIN Carnegie Mellon University, Dept. of Chemical Engineering DC2272 License for teaching and research at degree granting institutions **** FILE SUMMARY Input D:\Optimal Design of multiproduct bach plants\nonconvex1.gms Output D:\Optimal Design of multiproduct bach plants\nonconvex1.lst