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I am trying to figure out how I can write this objective function into python using Gurobi. I have to minimize the sum of the product of three dictionary's values. The reason I am confused is that while the first two dictionaries I am multiplying are the same length (somewhere in the thousands), the third has only 12 items. Also the first two dictionaries have tuple keys and the third does not.

The first dictionary ASSG is a decision variable that has the format:

ASSG = {('Abilene, TX', 'Boston, MA'): <gurobi.Var ASSG[Abilene, TX,Boston, MA]>, 
        ('Abilene, TX', 'Chicago, IL'): <gurobi.Var ASSG[Abilene, TX,Chicago, IL]>,
        ('Abilene, TX', 'Dallas, TX'): <gurobi.Var ASSG[Abilene, TX,Dallas, TX]>,
        ('Abilene, TX', 'Denver, CO'): <gurobi.Var ASSG[Abilene, TX,Denver, CO]>,
        ...}

The second dictionary is miles and it has the following format:

miles = {('Abilene, TX', 'Boston, MA'): 2091.92,
         ('Abilene, TX', 'Chicago, IL'): 1148.37,
         ('Abilene, TX', 'Dallas, TX'): 189.87,
         ('Abilene, TX', 'Denver, CO'): 775.6,
        ...}

The third dictionary is called Demand and it looks like:

Demand = {'Boston, MA': 1051,
          'Chicago, IL': 940,
          'Dallas, TX': 1131,
          'Denver, CO': 466,
          'Los Angeles, CA': 1301,
          'Richmond, VA': 1171,
          'Miami, FL': 1463,
          'New York, NY': 1120,
          'Phoenix, AZ': 665,
          'Pittsburgh, PA': 1280,
          'San Fransisco, CA': 615,
          'Seattle, WA': 528}

I think what I need to do is multiply all of the values where the keys in Demand match the second element in the tuple of ASSG and miles's keys. i.e. All the items with 'Boston, MA' get multiplied, all the Chicagos, all the Dallases...

I have tried multiplying them separately and then using quicksum but I receive an error:

a = {k: ASSG[k]*miles[k] for k in ASSG}
b = {k:Demand.get(k[1], 1)* v for k,v in x.items()}

m.setObjective(quicksum(b.values()))
m.ModelSense = GRB.MINIMIZE
m.update()

GurobiError: Variable not in model
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  • $\begingroup$ If there is any other portion of this model that you think I need to share please let me know! $\endgroup$ – Jacob Myer Oct 17 '19 at 1:03
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    $\begingroup$ 1) What is x that you used in definining b? Is it ASSG variable? 2) If what you want is something like $\sum\limits_{ij}\text{demand}_i\times \text{miles}_{ij}\times \text{ASSG}_{ij}$ then just loop over i and j. something like: quicksum(Demand[i]*miles[i,j]*val for (i,j), val in ASSG.items()) $\endgroup$ – EhsanK Oct 17 '19 at 5:17
  • $\begingroup$ @EhsanK thankyou. That is the equation that I am looking for, but that code returns ValueError: too many values to unpack (expected 2) $\endgroup$ – Jacob Myer Oct 18 '19 at 0:51
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    $\begingroup$ check my edit. I forgot to put items() after ASSG. Without that, you're just looping over the keys and that's why it told you expected only 2. $\endgroup$ – EhsanK Oct 18 '19 at 1:31
  • $\begingroup$ that was one of the first things I tried and it returned KeyError: 'Abilene, TX' , I fixed this by changing Demand[i] to Demand[j]. This allowed the model to run but there is another issue: no solution was found. I am assuming this has to do with the constraints we discussed here (or.stackexchange.com/questions/2837/…) as this is the same model @EhsanK $\endgroup$ – Jacob Myer Oct 18 '19 at 2:31

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