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exercise2.lst
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GAMS 40.1.0 93c2a77b Aug 1, 2022 DEX-DEG x86 64bit/Mac OS X - 08/31/22 07:46:25 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 2
Made by:
Juan Andrés Romero C - 202013449
Juan Sebastián Alegría - 202011282
9
10 Sets e 'Employees' /e1, e2, e3, e4/
11 j 'Jobs' /j1, j2, j3, j4/;
12
13 Table t(e, j) 'Required time'
14
15 j1 j2 j3 j4
16 e1 14 5 8 7
17 e2 2 12 6 5
18 e3 7 8 3 9
19 e4 2 4 6 10;
20
21 Variables x(e,j) 'Employee/Job pair selected'
22 z 'Target function';
23
24 Binary Variable x;
25
26 Equations targetFunc 'Target Function'
27 uniqueConstraintE(e) 'Every employee can only do one job'
28 uniqueConstraintJ(j) 'Every job can be done by only one employee';
29
30 targetFunc.. z =e= sum((e,j), t(e,j)*x(e,j));
31 uniqueConstraintE(e).. sum((j), x(e,j)) =e= 1;
32 uniqueConstraintJ(j).. sum((e), x(e,j)) =e= 1;
33
34 Model Exercise2 /all/;
35 option MIP=CPLEX;
36 Solve Exercise2 using mip minimizing z;
37 Display x.l;
38 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 07:46:25 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 Exercise2 Using MIP From line 36
---- targetFunc =E= Target Function
targetFunc.. - 14*x(e1,j1) - 5*x(e1,j2) - 8*x(e1,j3) - 7*x(e1,j4) - 2*x(e2,j1) - 12*x(e2,j2) - 6*x(e2,j3) - 5*x(e2,j4) - 7*x(e3,j1) - 8*x(e3,j2) - 3*x(e3,j3) - 9*x(e3,j4) - 2*x(e4,j1) - 4*x(e4,j2) - 6*x(e4,j3) - 10*x(e4,j4) + z =E= 0 ; (LHS = 0)
---- uniqueConstraintE =E= Every employee can only do one job
uniqueConstraintE(e1).. x(e1,j1) + x(e1,j2) + x(e1,j3) + x(e1,j4) =E= 1 ; (LHS = 0, INFES = 1 ****)
uniqueConstraintE(e2).. x(e2,j1) + x(e2,j2) + x(e2,j3) + x(e2,j4) =E= 1 ; (LHS = 0, INFES = 1 ****)
uniqueConstraintE(e3).. x(e3,j1) + x(e3,j2) + x(e3,j3) + x(e3,j4) =E= 1 ; (LHS = 0, INFES = 1 ****)
REMAINING ENTRY SKIPPED
---- uniqueConstraintJ =E= Every job can be done by only one employee
uniqueConstraintJ(j1).. x(e1,j1) + x(e2,j1) + x(e3,j1) + x(e4,j1) =E= 1 ; (LHS = 0, INFES = 1 ****)
uniqueConstraintJ(j2).. x(e1,j2) + x(e2,j2) + x(e3,j2) + x(e4,j2) =E= 1 ; (LHS = 0, INFES = 1 ****)
uniqueConstraintJ(j3).. x(e1,j3) + x(e2,j3) + x(e3,j3) + x(e4,j3) =E= 1 ; (LHS = 0, INFES = 1 ****)
REMAINING ENTRY SKIPPED
GAMS 40.1.0 93c2a77b Aug 1, 2022 DEX-DEG x86 64bit/Mac OS X - 08/31/22 07:46:25 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 Exercise2 Using MIP From line 36
---- x Employee/Job pair selected
x(e1,j1)
(.LO, .L, .UP, .M = 0, 0, 1, 0)
-14 targetFunc
1 uniqueConstraintE(e1)
1 uniqueConstraintJ(j1)
x(e1,j2)
(.LO, .L, .UP, .M = 0, 0, 1, 0)
-5 targetFunc
1 uniqueConstraintE(e1)
1 uniqueConstraintJ(j2)
x(e1,j3)
(.LO, .L, .UP, .M = 0, 0, 1, 0)
-8 targetFunc
1 uniqueConstraintE(e1)
1 uniqueConstraintJ(j3)
REMAINING 13 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 07:46:25 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 Exercise2 Using MIP From line 36
RANGE STATISTICS (ABSOLUTE NON-ZERO FINITE VALUES)
RHS [min, max] : [ 1.000E+00, 1.000E+00] - 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, 1.400E+01]
GAMS 40.1.0 93c2a77b Aug 1, 2022 DEX-DEG x86 64bit/Mac OS X - 08/31/22 07:46:25 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 Exercise2 Using MIP From line 36
MODEL STATISTICS
BLOCKS OF EQUATIONS 3 SINGLE EQUATIONS 9
BLOCKS OF VARIABLES 2 SINGLE VARIABLES 17
NON ZERO ELEMENTS 49 DISCRETE VARIABLES 16
GENERATION TIME = 0.006 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 07:46:25 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 Exercise2 Using MIP From line 36
S O L V E S U M M A R Y
MODEL Exercise2 OBJECTIVE z
TYPE MIP DIRECTION MINIMIZE
SOLVER CPLEX FROM LINE 36
**** SOLVER STATUS 1 Normal Completion
**** MODEL STATUS 1 Optimal
**** OBJECTIVE VALUE 15.0000
RESOURCE USAGE, LIMIT 0.035 10000000000.000
ITERATION COUNT, LIMIT 3 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. 0.10 ticks)
--- Fixing integer variables and solving final LP...
--- Fixed MIP status (1): optimal.
--- Cplex Time: 0.00sec (det. 0.01 ticks)
Proven optimal solution
MIP Solution: 15.000000 (3 iterations, 0 nodes)
Final Solve: 15.000000 (0 iterations)
Best possible: 15.000000
Absolute gap: 0.000000
Relative gap: 0.000000
LOWER LEVEL UPPER MARGINAL
---- EQU targetFunc . . . 1.0000
targetFunc Target Function
---- EQU uniqueConstraintE Every employee can only do one job
LOWER LEVEL UPPER MARGINAL
e1 1.0000 1.0000 1.0000 .
e2 1.0000 1.0000 1.0000 .
e3 1.0000 1.0000 1.0000 .
e4 1.0000 1.0000 1.0000 .
---- EQU uniqueConstraintJ Every job can be done by only one employee
LOWER LEVEL UPPER MARGINAL
j1 1.0000 1.0000 1.0000 .
j2 1.0000 1.0000 1.0000 .
j3 1.0000 1.0000 1.0000 .
j4 1.0000 1.0000 1.0000 .
---- VAR x Employee/Job pair selected
LOWER LEVEL UPPER MARGINAL
e1.j1 . . 1.0000 14.0000
e1.j2 . 1.0000 1.0000 5.0000
e1.j3 . . 1.0000 8.0000
e1.j4 . . 1.0000 7.0000
e2.j1 . . 1.0000 2.0000
e2.j2 . . 1.0000 12.0000
e2.j3 . . 1.0000 6.0000
e2.j4 . 1.0000 1.0000 5.0000
e3.j1 . . 1.0000 7.0000
e3.j2 . . 1.0000 8.0000
e3.j3 . 1.0000 1.0000 3.0000
e3.j4 . . 1.0000 9.0000
e4.j1 . 1.0000 1.0000 2.0000
e4.j2 . . 1.0000 4.0000
e4.j3 . . 1.0000 6.0000
e4.j4 . . 1.0000 10.0000
LOWER LEVEL UPPER MARGINAL
---- VAR z -INF 15.0000 +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 07:46:25 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
---- 37 VARIABLE x.L Employee/Job pair selected
j1 j2 j3 j4
e1 1.000
e2 1.000
e3 1.000
e4 1.000
---- 38 VARIABLE z.L = 15.000 Target function
EXECUTION TIME = 0.065 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/exercise2.gms
Output /Users/zejiran/hack/uniandes/MSO/laboratory-01/exercise2.lst