Variable Value Reduced Cost
MIN = @SUM(PARTS(I): OUTCOST(I)*BUY(I)+INCOST(I)*PRODUCE(I));
!Minimizing costs=sum of buying costs and production costs;
@FOR(PARTS(I):BUY(I)+PRODUCE(I)=6100);
!Sum of amount bought+amount produced of each part has to equal 6100;
@SUM(PARTS(I):CUTTIME(I)*PRODUCE(I))<=820;
@SUM(PARTS(I):SHAPETIME(I)*PRODUCE(I))<=820;
@SUM(PARTS(I):FABTIME(I)*PRODUCE(I))<=820;
!Sum of times has to be less than the total hour capacity of the department
that does that job.;
@FOR(PARTS(I):@GIN(BUY(I)));
FOR(PARTS(I):@GIN(PRODUCE(I)));
END
Global optimal solution found.
Objective value: 29256.40
Objective bound: 29256.40
Infeasibilities: 0.000000
Extended solver steps: 0
Total solver iterations: 3
Variable Value Reduced Cost
OUTCOST( SHAFT) 1.210000 0.000000
OUTCOST( BASE) 2.500000 0.000000
OUTCOST( CAGE) 1.950000 0.000000
INCOST( SHAFT) 0.8100000 0.000000
INCOST( BASE) 2.300000 0.000000
INCOST( CAGE) 1.450000 0.000000
BUY( SHAFT) 0.000000 1.210000
BUY( BASE) 2642.000 2.500000
BUY( CAGE) 1824.000 1.950000
PRODUCE( SHAFT) 6100.000 0.8100000
PRODUCE( BASE) 3458.000 2.300000
PRODUCE( CAGE) 4276.000 1.450000
CUTTIME( SHAFT) 0.4000000E-01 0.000000
CUTTIME( BASE) 0.8000000E-01 0.000000
CUTTIME( CAGE) 0.7000000E-01 0.000000
SHAPETIME( SHAFT) 0.6000000E-01 0.000000
SHAPETIME( BASE) 0.2000000E-01 0.000000
SHAPETIME( CAGE) 0.9000000E-01 0.000000
FABTIME( SHAFT) 0.4000000E-01 0.000000
FABTIME( BASE) 0.5000000E-01 0.000000
FABTIME( CAGE) 0.6000000E-01 0.000000
CAPACITY( CUTTING) 820.0000 0.000000
CAPACITY( SHAPING) 820.0000 0.000000
CAPACITY( FABRICATION) 820.0000 0.000000
Row Slack or Surplus Dual Price
1 29256.40 -1.000000
2 0.000000 0.000000
3 0.000000 0.000000
4 0.000000 0.000000
5 0.4000000E-01 0.000000
6 0.000000 0.000000
7 146.5400 0.000000
3. The following math model can be converted to LINGO:
LINGO Model:
Model:
SETS:
PROFS: TOTTEACH, FTEACH, STEACH, SATEACH, SBTEACH, FATEACH, FBTEACH, ABID,
BBID, MAXS, MAXF;
!TOTTEACH=The total number of courses that must be taught by the professor.
FTEACH=The # of courses the prof teaches in the fall.
STEACH=The # of courses the prof teaches in the spring.
SATEACH=The # of course A the prof teaches in the spring.
SBTEACH=The # of course B the prof teaches in the spring.
FATEACH, F_B_TEACH=Similar to above, but in the fall.
ABID, BBID= The bids for courses A and B the prof has given.
MAXS=The max number of courses the professor wishes to teach in the spring.
MAXF=The max number of courses the prof wishes to teach in the fall.;
COURSES: MINI, MAXI, TOTAL;
!MINI=The minimum # of sections of the course required.
MAXI=The maximum # of sections of the course required.
TOTAL=The total # of sections of the course offered.;