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

[Heinrich Schuchardt]

Hello Wouter,

I was thinking of something like:

param max_ingredients := 5; # maximum number of ingredients per product/element
param M := 1; # maximum value for concentrations
var concentration {Product, Ingredients, Elements}, >= 0;
var x{Product, Ingredients, Elements}, binary;
s.t. c1{p in Products, e in Elements} :
  sum{i in Ingredients} x[p,i,e] <= max_ingredients;
s.t. c2{p in Products, i in Ingredients, e in Elements} :
  concentration[p,i,e] <= M * x[p,i,e];

Best regards

Heinrich Schuchardt

http://www.xypron.de


> Gesendet: Donnerstag, 20. Februar 2014 um 14:05 Uhr
> Von: "Baake, Wouter" <address@hidden>
> An: "Heinrich Schuchardt" <address@hidden>
> Cc: "'address@hidden'" <address@hidden>
> Betreff: RE: [Help-glpk] How to code restriction on number of variables > 0
>
> 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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> of its subsidiaries can accept any responsibility for any use or misuse of 
> the transmission by anyone.
> 
> For address and company registration details of certain entities within the 
> Tata Steel Europe group of companies, please visit 
> http://www.tatasteeleurope.com/entities
> 
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