Originally posted by: Thomas_321

Hello,

I do have a problem with the second decision variable of my model. I also asked the question in the "CPLEX Optimizers" Forum but they suggested to ask here. I hope you guys can help. (https://www.ibm.com/developerworks/community/forums/html/topic?id=e5026e71-abf5-42ce-86d9-f56946dc58ea&ps=25#repliesPg=0)

The optimization problem:

I have Product Categories (lets start with 2) containing Products. Each Product can be bought from One of the Two Suppliers therefore I have Two Prices for each product. I want to minimize my total costs taking into account the two constraints:

1.  60% of the total cost has to be purchased from supplier 1.
2.  60% of the total cost of one product category has to be purchased from supplier 1. 

My Code:

 // Sets
{string} A = ...;     // Product categories
{string} B = ...;     // Products
 
// Parameters
float c1[B] = ...;    // Product price supplier 1
float c2[B] = ...;    // Product price supplier 2
float rate = ...;     // Percentage rate purchased from supplier 1
float m = 10000;      // Big number

// Decision variables 
dvar boolean x[B];    
dvar boolean y[A];
 
// decision expression 
dexpr float test = sum (b in B)(c1[b]*x[b]+(1-x[b])*c2[b]);    // Minimizing total cost
 
// objective funtion  
minimize test;
 
// Constraints
subject to{

  sum (b in B)c1[b]*x[b] >= rate * sum(b in B)(c1[b]*x[b]+(1-x[b])*c2[b]);   // Percentage of total cost purchased from S1

      forall (a in A)
         sum (b in B) sum (b in B)c1[b]*x[b] >= rate * sum(b in B)(c1[b]*x[b]+(1-x[b])*c2[b])-(1-y[a])*m; // Percentage of total cost of a product category purchased from S1
 
      sum (a in A) y[a] >=1; // Number of product categories which need to reach the percentage rate 
 }
 

The Problem is the following:

The decision variable y[a] should turn 1 if the 60% of the total cost of a product category is purchased from S1 (supplier1) but it doesn´t. 

As seen below the buying rate for product category A is 38% but y[a] ==1 although the buying rate for product category B is 96% and y[a]==0.

I attached my model and the data.

Thank you, I appreciate the help! 

Originally posted by: Thomas_321

Hello,

Is it possible that the problem might be a missing connection between the product categories and the products? 

Is there a possibility to assign the products to a certain product category? 

I tried to solve this problem with tuples but I´m stuck at the same point.

Code.

// Sets
{string} Category = ...;     // Categories
{string} Product = ...;     // Products
 
// Parameters
tuple ProductCost{     //Cost of products
string pc;            // Product Category
float p1;            // Price 1
float p2;             // Price 2
}
ProductCost c[Product] = ...; 
float rate = ...;   // Buying rate of supplier 1
float m = 10000;    // Big number
// Decision variables 
dvar boolean x[Product];
dvar boolean y[Category];
 
// objective funtion  
minimize sum (b in Product)(x[b]*c[b].p1+(1-x[b])*c[b].p2);
 
// Constraints
subject to{   
     sum (b in Product)(x[b]*c[b].p1)>= rate * sum(b in Product)(x[b]*c[b].p1+(1-x[b])*c[b].p2);
 
 forall (a in Category)
     sum (b in Product)(x[b]*c[b].p1)>= rate * sum(b in Product)(x[b]*c[b].p1+(1-x[b])*c[b].p2)-(1-y[a])*m;
 }

Thanks for your help

Originally posted by: Thomas_321

Hey,

so I hope this goes in the right direction, for "productCost c" I get  [<"A", 10 11>]... witch is a good start but how can I calculate the buying rate for each product category?

In other words that for "A" and "B" the buying rate is calculated and if so, y = 1?

Does anyone have an idea?

Thank you for your help, best regards

Hi,

do you know that you are allowed to write logical constraints like:

(x[1]<=6) => (y[1]==1) // imply

?

regards

Originally posted by: Thomas_321

Hey Alex, 

thanks for your answer, but sorry I don´t understand where it would be implemented in my model?

I adjusted my model now and I´m also able to get the data from excel but the main problem still remains the same. y[a] still turns 1 when it shouldn´t. 

Yet I still think that the problem is rooted in the missing link between product categories and the rest of the constraint, so y still doesn´t  turn 1 because the buying rate within a product category has reached the given rate.

I really have no clue what else to do or where the problem is. 

I´d really appreciate your help

Thank you and best regards

Hi

in order to get rid of errors you should replace

forall (a in Category)
    Ct2[a]:
    sum (f in P) (c[f.pc].Ppc1*x[f.pc]) >= rate * sum(f in P)(c[f.pc].Ppc1*x[f.pc] + (1-x[f.pc])*c[f.pc].Ppc2)-m*(1-y[a]);

by

forall (a in Category)
    Ct2[a]:
    sum (f in P) (c[f.product].Ppc1*x[f.product]) >= rate * sum(f in P)(c[f.product].Ppc1*x[f.product] + (1-x[f.product])*c[f.product].Ppc2)-m*(1-y[a]);

regards

Originally posted by: Thomas_321

Hey Alex,

Thank you for your answer, I actually did that before and it helped with the error messages yet the main problem remains the same. The second decision variable still is not related to the rest and therefore doesn´t switch from 0 to 1 when the Product Category reaches the BR. 

I changed c[f.product].Ppc1 to c[f.pc].Ppc1 because pc is the product category and I thought that would create the connection, obviously it doesn´t work.

Do you have an idea how to achieve that y(a) turns 1 when the BR within one product category is reached?

I attached the model 

Thanks a lot and best regards! 

Originally posted by: K3P9_SAURABH_PRATAP

I have doubt

please clarify it

dvar boolean x[B];   

is it binary decision variable?

I would like to ask, how can I define binary decision variables.

x[B]= 1 If its is positive

      = 0 otherwise

?

Hi

dvar int x[1..2];

subject to
{
forall(i in 1..2) (x[i]>=1) => (x[i]==1);
forall(i in 1..2) (x[i]<=-0) => (x[i]==0);
x[1]!=x[2];
}

gives

[0 1]

regards

Originally posted by: Stanko_86

Hi Thomas,

I modified your Ct2[a] constraint as follows:

forall (a in Category)
{
    Ct2[a]:
    
    (sum (<pr, a, price1, price2> in P) (price1*x[pr]) >= rate*(sum (<pr, a, price1, price2> in P)(price1*x[pr] + price2*(1-x[pr])))) => (y[a] == 1);
    (sum (<pr, a, price1, price2> in P) (price1*x[pr]) <= rate*(sum (<pr, a, price1, price2> in P)(price1*x[pr] + price2*(1-x[pr])))) => (y[a] == 0);  
}

Now, the constraint :  sum (a in Category)  y[a] >=1;    is unnecessarily.

I got results given in the table below:

Originally posted by: Thomas_321

Thanks a lot for the help guys!!!

I managed to solve the problem.

regards