Positive variable

GAMS
1

Hi,

How come I still get negative value even though I have set the variable to be positive variable?

It still give me negative answer even if I have set a demand constraint, meaning that each plant can not receive a negative demand for any circumstances.

Is there any other methods to avoid negative value in answer?
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Regards,
Jun Keat

2

Have you checked the model and solve status? Perhaps, the solver did not give you a feasible solution:

               S O L V E      S U M M A R Y

     MODEL   transport           OBJECTIVE  z
     TYPE    LP                  DIRECTION  MINIMIZE
     SOLVER  CPLEX               FROM LINE  65

**** SOLVER STATUS     1 Normal Completion         
**** MODEL STATUS      4 Infeasible                
**** OBJECTIVE VALUE              245.8800

It helps if you send reproducible code to the forum.

-Michael

3

Hi Michael,

Thanks for the reply. The model is really infeasible. However, I don’t know how to make it feasible. Can you help me to check on my code? Thanks so much!

Sets
i ‘waste type’ / waste-1 * waste-5 /
j ‘power plant’ / plant-1 * plant-7 / ;

Parameters
w(i) ‘waste amount(mil)’
/ waste-1 40
waste-2 39
waste-3 29
waste-4 57
waste-5 46 /

c(j) ‘capacity of plant’
/ plant-1 20
plant-2 19
plant-3 19
plant-4 17
plant-5 16
plant-6 17
plant-7 16 /;

Table o(i,j) ‘operating cost of waste’
plant-1 plant-2 plant-3 plant-4 plant-5 plant-6 plant-7
waste-1 4 2 4 5 7 6 7
waste-2 4 2 4 4 6 4 5
waste-3 3 1 3 3 5 4 5
waste-4 5 3 5 3 3 5 2
waste-5 4 2 4 5 2 4 8 ;

Variables
x(i,j) ‘waste to be operated in each plant’
opex ‘operating cost’ ;

Positive variables x;

Equations
opcost ‘definition of operation cost’
mascon1(i) ‘constraint - mass balance of waste to plant’
capcon(j) ‘constraint - waste amount cannot exceed the capacity of plant’;


opcost … opex =e= sum((i,j), o(i,j)*x(i,j));
mascon1(i) … sum(j, x(i,j)) =g= w(i) ;
capcon(j) … sum(i, x(i,j)) =l= c(j) ;


Model msw /all/ ;
Solve msw using lp minimizing opex ;
Display x.l, opex.l;

4

There are many ways how to deal with infeasibility. Bruce McCarl Newsletter vol. 40 gives good recommendations on how to deal with infeasible models (see section 3 of https://www.gams.com/fileadmin/community/mccarlarchive/news40.pdf).

-Michael