How to introduce a variable in pulp environment of Python

Question

I have two sets.

S = Sources = {S1, S2, S3}
D = Desinations = {D1, D2, D3}

I have to minimize the total transportation cost subject to some constraints. I am using the pulp in Python. How can I introduce a variable such that I am allowing some specific route?

The condition is if cost $(S_i, D_j) >=$ 250 then 0 else 1.

allowed_route = []
for i in range(len(matrix)):

for j in matrix[i]:
    if j >= 250:
        allowed_route.append(0)
    else:
        allowed_route.append(1)
 np_array=np.asarray(allowed_route)
 allowed_route = np_array.reshape(6, 4) 
 allowed_route = np.array(P_allowed_PLF_cap).tolist()

In this way, I have defined the parameter but I am unable to introduce the variable.

You are describing a transportation model. It isn't clear whether you are stumped on how to declare pulp variables or on how to set up the problem as an LP. Regardless, here is a complete example: coin-or.org/PuLP/CaseStudies/a_transportation_problem.html — AirSquid
– AirSquid, Commented Jul 27, 2020 at 14:53
I am asking that how to declare a pulp variable where there are some conditions on the parameter. I know how to set up the problem as an LP. Thank you. — Manglu
– Manglu, Commented Jul 27, 2020 at 16:09

AirSquid · Accepted Answer · 2020-07-27 23:19:00Z

You should make a subset of your S X D variables that have the legal routes and use that. Here is an example:

In [4]: from pulp import *                                                      

In [5]: sources = {'S1', 'S2', 'S3'}                                            

In [6]: destinations = {'D1', 'D2', 'D3'}                                       

In [7]: legal_routes = ( ('S1', 'D2'), 
   ...:                  ('S2', 'D1') )                                         

In [8]: # note:  above is obviously infeasible...just shows idea...             

In [9]: route_select = LpVariable.dicts('route', legal_routes, 0, 1, LpBinary)

In reality, you probably have costs for each of those routes, so I would hold all of that in a dictionary and send the dictionary keys to the LpVariable.dicts call

The rest should look similar to the example I noted. If you are stuck, there are several other examples on this site if you search 'pulp transportation model' or 'pulp sparse constraints' & such.

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