[HELP] Translation of Algebraic Mathematical Model to using python gurobi api
AnsweredI have a max flow problem for an emergency evacuation planning. The model is based on the Cell Transmission Model (CTM), basically the entire area to be evacuated is partitioned into cells using square grid, where cells=nodes and the passage/links between adjacent cells = arcs. G=(V,A). The whole idea is to find the maximum number of evacuated at each time slot.
The model will be run for tau = 1, 2, ...until a solution for N is found.
NB: My degree/life literally depends on this and I have Tuesday to submit and present it on Thursday.
I I have the mathematical formulation of the problem I am working on but I honestly cant do the python formulation for the problem to be solved by gurobi. I would be very grateful in the kind people here could help me out with the implementation because my whole life literally depends on it and I will be indebted to you guys forever. Thanks

Hi Evans,
here is an implementation of your problem in Python using Gurobi:
First, we define a few basics. Since I don't know anything about your problem‚ I just generated some random data.
import gurobipy as gp
import numpy as np
# The nodes
nodes = 10
V = range(nodes)
n = np.random.rand(nodes) # max capacity of node i
# The arcs
A = [(i,j) for i in V for j in V] # The set of arcs. This may have to be adjusted for your problem
c = np.random.rand(nodes, nodes) # max capacity of arc ijNext, we formulate and solve the problem:
solution_found = False
tau = 2
while not solution_found:
T = range(tau)
m = gp.Model()
# Add the variables
y = m.addVars(nodes,tau)
x = m.addVars(A, tau, lb=gp.GRB.INFINITY)
# This picks the last element from y and maximizes that
m.setObjective(y[nodes1,tau1], sense=gp.GRB.MAXIMIZE)
# The constraints
for t in T:
for j in V:
if t > 0:
m.addConstr(y[j,t]  y[j,t1]  x.sum('*',j,t1) + x.sum(j,'*',t1) == 0)
m.addConstr(y[j,t] <= n[j])
for i,j in A:
m.addConstr(x[i,j,t] + x[j,i,t] >= 0)
m.addConstr(x[i,j,t] + x[j,i,t] <= c[i,j])
m.optimize()
if m.Status == gp.GRB.OPTIMAL:
solution_found = True
tau += 1Note that Python indexes at 0, which leads to the "1" in a few places. Also, note that I assume that the super sink is the last node for convenience.
Good luck
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Thanks very much Richard for the solution. You are a life saver.
Honestly I have 5 more constraints. Please help me out if am not asking for too much. Attached is a picture of the other constraints.
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Hi Evans,
I think you should give it shot yourself based on the code that I sent. You can see that the gurobipy interface is quite easy to use, so it should be possible for you to add the additional constraints.
Best regards
Richard
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Thanks. I have been able to implement it. Thanks very much. Your code was very intuitive and and straightforward.
You are need very helpful
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