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

[Baake, Wouter]

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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