I am learning to solve optimization problems using CVXPY, so I started with the following simple facility location allocation problem.
The Code in CVXPY is given as:
Fi = np.array([1,1,1]) # Fixed cost of each facility
Ci = np.array([15, 10, 10]) # Capacity of each facility
Dj = np.array([5, 5, 5, 3, 3, 4]) # Demand of each facility
Cij = np.ones(m,n)
n = len(Dj)
m = len(Fi)
# Decision Variables
Xij = cvx.Bool(m,n) # (m,n) vector
Yi = cvx.Bool(m) # column vector of length (m,1)
# Objective
fixed_cost = cvx.sum_entries(Fi*Yi)
var_cost = cvx.sum_entries(Cij.T * Dj *Xij)
total_cost = fixed_cost + var_cost
objective = cvx.Minimize(total_cost)
# Maximum facility locations to be selected?
constraints.append(cvx.sum_entries(Yi)==2)
# Sum of demands allocated to a facility shall be <= facility capacity -
# Capacity Fixed Cost
constraints.append(cvx.sum_entries(Dj * Xij.T, axis=0) <= Ci*Yi)
# Every demand point shall be supplied by only one facility.
constraints.append(cvx.sum_entries(Xij, axis=1) == 1)
# Solve the problem
prob = cvx.Problem(objective, constraints)
prob.solve(solver=cvx.GLPK_MI)
# Print the values
#print("status:", prob.status)
print("optimal value", prob.value)
print("Selected Facility Locations", Yi.value)
print("Assigned Nodes", Xij.value, )
As per the last constraint, a demand location should be supplied by only one facility, however the output of Xij.value shows wrong results.
Using CVXPY version: 0.4.10
status: optimal
optimal value 91.0
Selected Facility Locations [[1.]
[0.]
[1.]]
Assigned Nodes to Facility 1) [[1. 0. 0. 0. 0. 0.]]
Assigned Nodes to Facility 2) [[1. 0. 0. 0. 0. 0.]]
Assigned Nodes to Facility 3) [[1. 0. 0. 0. 0. 0.]]
The Xij.value should be something like this:
Using CVXPY version: 0.4.10
status: optimal
optimal value 91.0
Selected Facility Locations [[1.]
[1.]
[0.]]
Assigned Nodes to Facility 1) [[1. 1. 1. 0. 0. 0.]]
Assigned Nodes to Facility 2) [[0. 0. 0. 1. 1. 1.]]
Assigned Nodes to Facility 3) [[0. 0. 0. 0. 0. 0.]]
Which means, facility 1 and 2 are selected. The first three points are allocated to facility 1 and the next three to facility 2.
