Pulp obtains results as problem is infeasible, while problem is not feasible

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I'm trying to solve an assignment problem with pulp. The basic part of the code is as follows:


set_I = range(1, numberOfPoints)
set_J = range(1, numberOfCentroids)

tau = 0.15
Q = 15

# decision variable
x_vars = LpVariable.dicts(name="x_vars", indexs=(set_I, set_J), lowBound=0, upBound=1, cat=LpInteger)

# model name
prob = LpProblem("MIP_Model", LpMinimize)

# constraints
for i in set_I:
   prob += lpSum(x_vars[i][j] for j in set_J) == 1, ""

for j in set_J:
   prob += lpSum(x_vars[i][j] for i in set_I) >= 1, ""

for j in set_J:
   prob += lpSum(x_vars[i][j] for i in set_I) <= Q*(1-tau), ""

for j in set_J:
   prob += lpSum(x_vars[i][j] for i in set_I) >= Q*(1+tau), ""

# objective
prob += lpSum(d[i, j]*x_vars[i][j] for i in set_I for j in set_J)

prob.solve()

The result is like this:

Problem MODEL has 31 rows, 76 columns and 304 elements

Coin0008I MODEL read with 0 errors

Problem is infeasible - 0.01 seconds

Option for printingOptions changed from normal to all

However, the problem is not infeasible and results are obtained with other solvers.

I wonder if there is a syntax error and is the problem caused by this?

I have asked a similar question in the next link:

Infeasible solution by pulp

pulp python
1 Answers

When I run the problem locally, with d a matrix of ones, 20 points, and 3 centroids. It also becomes infeasible for me. Look at the constraints:

_C22: x_vars_10_1 + x_vars_11_1 + x_vars_12_1 + x_vars_13_1 + x_vars_14_1
 + x_vars_15_1 + x_vars_16_1 + x_vars_17_1 + x_vars_18_1 + x_vars_19_1
 + x_vars_1_1 + x_vars_2_1 + x_vars_3_1 + x_vars_4_1 + x_vars_5_1 + x_vars_6_1
 + x_vars_7_1 + x_vars_8_1 + x_vars_9_1 <= 12.75

_C23: x_vars_10_2 + x_vars_11_2 + x_vars_12_2 + x_vars_13_2 + x_vars_14_2
 + x_vars_15_2 + x_vars_16_2 + x_vars_17_2 + x_vars_18_2 + x_vars_19_2
 + x_vars_1_2 + x_vars_2_2 + x_vars_3_2 + x_vars_4_2 + x_vars_5_2 + x_vars_6_2
 + x_vars_7_2 + x_vars_8_2 + x_vars_9_2 <= 12.75

_C24: x_vars_10_1 + x_vars_11_1 + x_vars_12_1 + x_vars_13_1 + x_vars_14_1
 + x_vars_15_1 + x_vars_16_1 + x_vars_17_1 + x_vars_18_1 + x_vars_19_1
 + x_vars_1_1 + x_vars_2_1 + x_vars_3_1 + x_vars_4_1 + x_vars_5_1 + x_vars_6_1
 + x_vars_7_1 + x_vars_8_1 + x_vars_9_1 >= 17.25

_C25: x_vars_10_2 + x_vars_11_2 + x_vars_12_2 + x_vars_13_2 + x_vars_14_2
 + x_vars_15_2 + x_vars_16_2 + x_vars_17_2 + x_vars_18_2 + x_vars_19_2
 + x_vars_1_2 + x_vars_2_2 + x_vars_3_2 + x_vars_4_2 + x_vars_5_2 + x_vars_6_2
 + x_vars_7_2 + x_vars_8_2 + x_vars_9_2 >= 17.25

You require

x_vars_10_2 + x_vars_11_2 + x_vars_12_2 + x_vars_13_2 + x_vars_14_2
 + x_vars_15_2 + x_vars_16_2 + x_vars_17_2 + x_vars_18_2 + x_vars_19_2
 + x_vars_1_2 + x_vars_2_2 + x_vars_3_2 + x_vars_4_2 + x_vars_5_2 + x_vars_6_2
 + x_vars_7_2 + x_vars_8_2 + x_vars_9_2

to be greater than 17.25 and smaller than 12.75 at the same time. That's not possible, of course.

user_50153560
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