Re: [Help-glpk] How to code restriction on number of variables > 0

[Baake, Wouter]

Hi Heinrich,

Thanks for your answer, but I'm having some trouble implementing it.

My original model would look something like this:
set Products;
set Unit_operations;
set Ingredients;
set Elements;

param cost {Products};
param aim {Products};
param concentration {Ingredients,Elements};

var ingredient_used {Products, Unit_operations,Ingredients} >= 0;

minimize total_cost: sum{p in Products,u in Unit_operations, i in Ingredients}  
cost[i] * ingredient_used [p,u,i];
Subject to {p in Products, e in Elements}: sum {u in Unit_operations, i in 
Ingredients} (ingredient_used [p,u,i]*concentration[i,e]) = aim[p,e];

To add the binary variable, I would then write this as:
set Products;
set Unit_operations;
set Ingredients;
set Elements;

param cost {Products};
param aim {Products};
param concentration {Ingredients,Elements};

var ingredient_used {Products, Unit_operations,Ingredients} >= 0;
var ingredient_used_yes_no {Products, Unit_operations,Ingredients} binary;

minimize total_cost: sum{p in Products,u in Unit_operations, i in Ingredients}  
cost[i] * ingredient_used [p,u,i];

Subject to {p in Products, e in Elements}: sum {u in Unit_operations, i in 
Ingredients} (ingredient_used [p,u,i]*concentration[i,e]) = aim[p,e];
Subject to {p in Products,u in Unit_operations,i in Ingredients :  
ingredient_used_yes_no[p,u,i]=0}: ingredient_used[p,u,i]=0;


Unfortunately, I then get an error: "operand preceding = has invalid type" 
which I do not understand.
You write "Add a constraint limiting the ingredient quantity to zero if the 
binary is" but my attempts to do this result in errors when I run glpsol. Do 
you have an example of how to write this constraint?

Regards,
Wouter


-----Original Message-----
From: Heinrich Schuchardt [mailto:address@hidden
Sent: Thursday, February 20, 2014 12:37 PM
To: Baake, Wouter
Cc: Help Glpk
Subject: Re: [Help-glpk] How to code restriction on number of variables > 0

Hello Wouter,

you can add a binary variable per ingredient.

Add a constraint limiting the ingredient quantity to zero if the binary is 0.

aim <= M *x;

Choose M as small as possible.

Add a constraint for the sum of the binaries.

Best regards

Heinrich Schuchardt

http://www.xypron.de


On 20.02.14 at 11:49, Baake, Wouter wrote:

> Hi,
>
>
>
> I'm modelling a problem where I need to make several products with different 
> specifications. Each product undergoes several unit operations where 
> ingredients are added.
>
> var ingredient_used {Products, Unit_operations,Ingredients} >= 0;
>
>
>
> Each ingredient has a cost and the total cost is to be minimized:
>
> minimize total_cost: sum{p in Products,u in Unit_operations, i in 
> Ingredients}  cost[i] * ingredient_used [p,u,i];
>
>
>
> Each ingredient consists of several elements in different concentrations. 
> Each of the products has an aim value for concentration of each of the 
> elements in the product:
>
> Subject to {p in Products, e in Elements}: sum {u in Unit_operations, i in 
> Ingredients} (ingredient_used [p,u,i]*concentration[i,e]) = aim[p,e];
>
>
>
> This problem I can model and solve, but I need to add some more constraints.
>
> One constraint is that there is a maximum number of ingredients that can be 
> kept in stock at a given unit operation. As an example, at the first unit 
> operation, I cannot keep more than 10 ingredients in stock, but the amount 
> per ingredient is unlimited.
>
>
>
> How could I translate this into a mathprog constraint?
>
>
>
> Regards,
>
> Wouter
>
>
>
>
>
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transmission by anyone.

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Tata Steel Europe group of companies, please visit 
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