Re: [Help-glpk] min() & max() functions alternatives to use non numeric parameters

[Suleyman Demirel]

When the objective function is z = maximize minimum of (x,y), this is not a linear program. So, you cannot use min() function. However, you may convert this to an LP by modifying your objective function and adding additional constraints. Depending on your problem structure, you may have to add a binary variable, as well.

Similarly, you cannot use min() function in constraints for the same reasons.

On Wed, Apr 27, 2011 at 2:38 PM, nikel90 <address@hidden> wrote:

Good evining!

I've got a problem with the max() and min() functions...

i need to do something like this:
min(120,ScorteIniziali+PrimoStd+PrimoStra)*70
in my "objective function"

but min() accepts only numeric parameters..

is there any alternatives?

thank you!

Nikel

the entire model:

#
#
/* Trimestri*/
var PrimoStd >=0, integer;
var SecondoStd >=0, integer;
var TerzoStd >=0, integer;
var QuartoStd >=0, integer;
var PrimoStra >=0, integer;
var SecondoStra >=0, integer;
var TerzoStra >=0, integer;
var QuartoStra >=0, integer;
var ScorteIniziali >=0, integer;
#
/* Objective function */
maximize z:
(min(120,ScorteIniziali+PrimoStd+PrimoStra)*70)-(((max(PrimoStd,SecondoStd,TerzoStd)*3*10)+(PrimoStra*3*15))+(max(0,ScorteIniziali+PrimoStd+PrimoStra-120)*6)+((PrimoStd+PrimoStra)*15))
+
(min(310,ScorteIniziali+PrimoStd+PrimoStra-120+SecondoStd+SecondoStra)*70)-(((max(PrimoStd,SecondoStd,TerzoStd)*3*10)+(SecondoStra*3*15))+(max(0,ScorteIniziali+PrimoStd+PrimoStra-120+SecondoStd+SecondoStra-310)*6)+((SecondoStd+SecondoStra)*15))
+ (min(180,ScorteIniziali+PrimoStd+PrimoStra-120 +
SecondoStd+SecondoStra-310+TerzoStd+TerzoStra)*70)-(((max(PrimoStd,SecondoStd,TerzoStd)*3*10)+(TerzoStra*3*15))+(max(0,ScorteIniziali+PrimoStd+PrimoStra-120
+
SecondoStd+SecondoStra-310+TerzoStd+TerzoStra-180)*6)+((TerzoStd+TerzoStra)*15))
+ (min(120,ScorteIniziali+PrimoStd+PrimoStra-120 +
SecondoStd+SecondoStra-310 +
TerzoStd+TerzoStra-180+QuartoStd+QuartoStra)*70)-(((max(PrimoStd,SecondoStd,TerzoStd)*3*10)+(QuartoStra*3*15))+(max(0,ScorteIniziali+PrimoStd+PrimoStra-120
+ SecondoStd+SecondoStra-310 +
TerzoStd+TerzoStra-180+QuartoStd+QuartoStra-120)*6)+((QuartoStd+QuartoStra)*15))
- (ScorteIniziali*45 + ScorteIniziali+PrimoStd+PrimoStra-120 +
SecondoStd+SecondoStra-310 + TerzoStd+TerzoStra-180 +
QuartoStd+QuartoStra-120*45);

/* Constraints */
#
s.t. a: ScorteIniziali - ScorteIniziali+PrimoStd+PrimoStra-120 +
SecondoStd+SecondoStra-310 + TerzoStd+TerzoStra-180 +
QuartoStd+QuartoStra-120  <= 0;
end;

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Suleyman Demirel - Office: (734) 647-3167

PhD Candidate in Operations Management
Stephen M. Ross School of Business
University of Michigan, Ann Arbor
Web: http://www.umich.edu/~sdemirel
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