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exercise1.lst
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GAMS 40.1.0 93c2a77b Aug 1, 2022 DEX-DEG x86 64bit/Mac OS X - 08/31/22 07:47:35 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
Laboratory 1 - MOS
Exercise 1
Made by:
Juan Andrés Romero C - 202013449
Juan Sebastián Alegría - 202011282
9
10 Sets i 'articles' /a1, a2, a3, a4, a5/;
11
12 Parameter v(i) 'Value of each article' /a1 12, a2 5, a3 9, a4 6, a5 4/;
13 Parameter p(i) 'Weigth of each article' /a1 9, a2 2, a3 2, a4 1, a5 3/;
14
15 Scalar LIMIT 'Maximum weight that the backpack can carry' /10/;
16
17 Variables x(i) 'Indicates if the article is included or not'
18 z 'Target function';
19
20 Binary Variable x;
21
22 Equations targetFunc 'Target function'
23 constraint 'Restriction';
24
25 targetFunc.. z =e= sum((i), v(i)*x(i));
26 constraint.. sum((i), p(i)*x(i)) =l= LIMIT;
27
28 Model exercise1 /all/;
29 option mip=CPLEX;
30 Solve exercise1 using mip maximizing z;
31
32 Display x.l;
33 Display z.l;
COMPILATION TIME = 0.003 SECONDS 3 MB 40.1.0 93c2a77b DEX-DEG
GAMS 40.1.0 93c2a77b Aug 1, 2022 DEX-DEG x86 64bit/Mac OS X - 08/31/22 07:47:35 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 exercise1 Using MIP From line 30
---- targetFunc =E= Target function
targetFunc.. - 12*x(a1) - 5*x(a2) - 9*x(a3) - 6*x(a4) - 4*x(a5) + z =E= 0 ; (LHS = 0)
---- constraint =L= Restriction
constraint.. 9*x(a1) + 2*x(a2) + 2*x(a3) + x(a4) + 3*x(a5) =L= 10 ; (LHS = 0)
GAMS 40.1.0 93c2a77b Aug 1, 2022 DEX-DEG x86 64bit/Mac OS X - 08/31/22 07:47:35 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 exercise1 Using MIP From line 30
---- x Indicates if the article is included or not
x(a1)
(.LO, .L, .UP, .M = 0, 0, 1, 0)
-12 targetFunc
9 constraint
x(a2)
(.LO, .L, .UP, .M = 0, 0, 1, 0)
-5 targetFunc
2 constraint
x(a3)
(.LO, .L, .UP, .M = 0, 0, 1, 0)
-9 targetFunc
2 constraint
REMAINING 2 ENTRIES SKIPPED
---- z Target function
z
(.LO, .L, .UP, .M = -INF, 0, +INF, 0)
1 targetFunc
GAMS 40.1.0 93c2a77b Aug 1, 2022 DEX-DEG x86 64bit/Mac OS X - 08/31/22 07:47:35 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
Range Statistics SOLVE exercise1 Using MIP From line 30
RANGE STATISTICS (ABSOLUTE NON-ZERO FINITE VALUES)
RHS [min, max] : [ 1.000E+01, 1.000E+01] - Zero values observed as well
Bound [min, max] : [ 1.000E+00, 1.000E+00] - Zero values observed as well
Matrix [min, max] : [ 1.000E+00, 1.200E+01]
GAMS 40.1.0 93c2a77b Aug 1, 2022 DEX-DEG x86 64bit/Mac OS X - 08/31/22 07:47:35 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
Model Statistics SOLVE exercise1 Using MIP From line 30
MODEL STATISTICS
BLOCKS OF EQUATIONS 2 SINGLE EQUATIONS 2
BLOCKS OF VARIABLES 2 SINGLE VARIABLES 6
NON ZERO ELEMENTS 11 DISCRETE VARIABLES 5
GENERATION TIME = 0.011 SECONDS 4 MB 40.1.0 93c2a77b DEX-DEG
GAMS 40.1.0 93c2a77b Aug 1, 2022 DEX-DEG x86 64bit/Mac OS X - 08/31/22 07:47:35 Page 6
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 exercise1 Using MIP From line 30
S O L V E S U M M A R Y
MODEL exercise1 OBJECTIVE z
TYPE MIP DIRECTION MAXIMIZE
SOLVER CPLEX FROM LINE 30
**** SOLVER STATUS 1 Normal Completion
**** MODEL STATUS 1 Optimal
**** OBJECTIVE VALUE 24.0000
RESOURCE USAGE, LIMIT 0.052 10000000000.000
ITERATION COUNT, LIMIT 1 2147483647
--- *** This solver runs with a community license. No commercial use.
--- GMO setup time: 0.00s
--- GMO memory 0.50 Mb (peak 0.50 Mb)
--- Dictionary memory 0.00 Mb
--- Cplex 22.1.0.0 link memory 0.00 Mb (peak 0.00 Mb)
--- Starting Cplex
--- MIP status (101): integer optimal solution.
--- Cplex Time: 0.02sec (det. 0.03 ticks)
--- Fixing integer variables and solving final LP...
--- Fixed MIP status (1): optimal.
--- Cplex Time: 0.00sec (det. 0.00 ticks)
Proven optimal solution
MIP Solution: 24.000000 (1 iterations, 0 nodes)
Final Solve: 24.000000 (0 iterations)
Best possible: 24.000000
Absolute gap: 0.000000
Relative gap: 0.000000
LOWER LEVEL UPPER MARGINAL
---- EQU targetFunc . . . 1.0000
---- EQU constraint -INF 8.0000 10.0000 .
targetFunc Target function
constraint Restriction
---- VAR x Indicates if the article is included or not
LOWER LEVEL UPPER MARGINAL
a1 . . 1.0000 12.0000
a2 . 1.0000 1.0000 5.0000
a3 . 1.0000 1.0000 9.0000
a4 . 1.0000 1.0000 6.0000
a5 . 1.0000 1.0000 4.0000
LOWER LEVEL UPPER MARGINAL
---- VAR z -INF 24.0000 +INF .
z Target function
**** REPORT SUMMARY : 0 NONOPT
0 INFEASIBLE
0 UNBOUNDED
GAMS 40.1.0 93c2a77b Aug 1, 2022 DEX-DEG x86 64bit/Mac OS X - 08/31/22 07:47:35 Page 7
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
E x e c u t i o n
---- 32 VARIABLE x.L Indicates if the article is included or not
a2 1.000, a3 1.000, a4 1.000, a5 1.000
---- 33 VARIABLE z.L = 24.000 Target function
EXECUTION TIME = 0.092 SECONDS 4 MB 40.1.0 93c2a77b DEX-DEG
USER: GAMS Community License for Juan Alegria G220811|0002AO-GEN
Universidad de los Andes, CL3634
License for teaching and research at degree granting institutions
**** FILE SUMMARY
Input /Users/zejiran/hack/uniandes/MSO/laboratory-01/exercise1.gms
Output /Users/zejiran/hack/uniandes/MSO/laboratory-01/exercise1.lst