Originally posted by: CDN3_Daniel_Cramer

Hello there,

I got a problem using the discontinuous piecewise-linear function...

dvar float x;
dvar float signx;
 
minimize signx;
   subject to {
 
   x == 5;
   signx == piecewise{0->0; 4->0; 0->10; -0.5->10; 0->20; -0.75->20; 0} (0,0) x;
}

I want to model sales discount. A discount should be allowed after reaching a limit in the function.
For an amount of 5 - the price should be 4 and the whole costs 20.
For an amount of 15 - the price should be 3.5 and the whole costs 52.5.
and so on...

But there is a mistake -- I am not able to realize, that the function starts in (0,0).
Otherwise, the amount of the objective isn't right, too...

Do you have any conclusions??

Regards
#DecisionOptimization
#OPLusingCPLEXOptimizer

Originally posted by: CDN3_Daniel_Cramer

After hours, I implemented the example in the help file...
mod

{string
} products   = ...; 
{

int
}    time       = ...;   

int   NBdiscount = ...; 

float discount[products][1..NBdiscount] = ...; 

float breakpoint[products][1..NBdiscount-1] = ...;   

float d[products][time]       = ...; 

float s[products]                         = ...; 

float h[products]                       = ...; 

float g[products]                       = ...;   

float Wert[k in products]   = sum(t in time) d[k][t];   dvar int+           q[products][time]; dvar int+                y[products][time]; dvar 

boolean      gamma[products][time];   dexpr 

float Lagerkosten = sum(k in products, t in time) (h[k] * y[k][t]); dexpr 

float Versandkosten = sum(k in products, t in time) (s[k] * gamma[k][t]); dexpr 

float Bestellpreis = sum(t in time, k in products) piecewise (i in 1..NBdiscount-1) 
{ discount[k][i] -> breakpoint[k][i]; discount[k][NBdiscount] 
} (5,4) q[k][t];   minimize Lagerkosten + Versandkosten + Bestellpreis;   subject to 
{ forall(k in products, t in time) q[k][t] <= Wert[k] * gamma[k][t];   forall(k in products, t in time : t > 0) y[k][t-1] + q[k][t] - y[k][t] == d[k][t];   forall (k in products) y[k][0] == d[k][0];   forall (k in products) q[k][0] == 0; 
};

dat

products = 
{ 
"12" 
}; time = 
{0 1 2 3 4 5 6 7 8 9 10 11 
};   NBdiscount = 7;   discount = #[ 
"12"   : #[1:0 2:4 3:0 4:-0.5 5:0 6:-0.75 7:0]#]#; breakpoint = #[ 
"12"   : #[1:0 2:0 3:100 4:100 5:500 6:500]#]#;   g = [2,]; s = [1]; h = [0.05];   d = #[
"12" :  #[0:0 1:0 2:0 3:0 4:500 5:0 6:0 7:0 8:100 9:0 10:0 11:0]#      ]#;

q is a dvar int+ and should be multiplied with the value in the discontinous piecewise-function.
OPL chooses the right value from the .dat - but it isn't multiplied with q...
Any tips?
#DecisionOptimization
#OPLusingCPLEXOptimizer

Hi,

q is the parameter in the pwl function. When q moves, then the pwl moves. This is not a multiplication by q.

Regards
#DecisionOptimization
#OPLusingCPLEXOptimizer