Constraints subject to multiple conditions

[anonp...@gmail.com]

Hi all,

I am trying to create a constraint that would only get used if two conditions apply. 

I know if I only had one condition, it would look like this:

subject to Time {t in 1..T}:
   avail[t] > 0 ==> sum {p in PROD} (1/rate[p]) * Make[p] <= avail;

But if I want both "avail[t] > 0" , and another condition, say "cost[t] > 0", essentially have an and function, how would I do it?

Cheers,

[Robert Fourer]

It appears from the context that both avail and cost are parameters. Thus you should put the conditions in the indexing rather than the constraint expression:

subject to Time {t in 1..T: avail[t] > 0 and cost[t] > 0}:
sum {p in PROD} (1/rate[p]) * Make[p,t] <= avail[t];

Bob Fourer
am...@googlegroups.com

=======

[jonathan...@u.northwestern.edu]

Hi Bob,

Appreciate the response! If they were variables instead, how would I proceed?

Once again, thanks!

[Robert Fourer]

If avail[t] and cost[t] are variables then you need to reformulate using additional binary (zero-one) variables to put the constraint into a form that standard solvers will accept.  To start you can define

   var za {1..T} binary;
   ...
   subject to zadef {t in 1..T}: za[t] = 0 ==> avail[t] = 0;

Then avail[t] > 0 will imply za[t] = 1.  The same can be done for binary variables zc[t] associated with cost[t].  Next you can define binary variables z[t] constrained by

   subject to zdef {t in 1..T}: z[t] = 0 ==> za[t] + zc[t] <= 1;

Then za[t] = zc[t] = 1 will imply z[t] = 1.  Finally you can have "z[t] = 1 ==> (your constraint);".  Because these constraints are all of the form "binary-var = 0 ==> linear-constraint" or "binary-var = 1 ==> linear-constraint" they are in the form of "indicator" constraints accepted by CPLEX or Gurobi (vers 7.0).  For other solvers these constraints can be reformulated to linear constraints by using well-known tricks; there are some examples in the Integer Programming chapter of the AMPL book (http://ampl.com/BOOK/CHAPTERS/23-integer.pdf).

Bob Fourer
am...@googlegroups.com

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[Bred]

Hi,

Could you please also explain, how one could write the code incase the model requires a seperation of different values for one of the two variables?

For example  "avail[t] > 0" but for cost[t] the condition depends on either "cost[t]=0.33" or "cost[t]=0.66" or "cost[t]=1"

Thank you alot in advance!