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

[Heinrich Schuchardt]

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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