"KeyError: (0, 'num')" when using List Comprehension to create PuLP LPConstraint

Question

I thought what I was creating for optimization was a fairly simple problem. I have the following data in a csv file:

I'm trying to create an "optimal" day of rides using the PuLP package, but keep getting errors when creating one of my constraints. The constraint simply summarized is: The amount of time on each ride (# times ridden * ride time, plus # times ridden * wait time), plus 15 minutes between rides, has to be equal to or less than the time the park is open (minus a fixed amount of time for meals and restrooms)

I keep getting a KeyError: (0, 'num') when I run the line for the constraint. (I can print the ride_list.loc[0,'num'] without a problem - first step to troubleshoot.) Any tips or thoughts would be appreciated.

import pandas as pd
import pulp

ride_list = pd.read_csv('RideData.csv')
num_rides = ride_list.shape[0]
rides = list(range(num_rides))
min_times = 0 #minimum # times for each ride
max_times = 2 #maximum # times for each ride
time_between = 0.25 #how long to allow between rides
food_time = 2.5 #how long to allow for meals
hours_open = 12 #how many hours the park is open

# Set default values for testing
for i in rides:
    ride_list.loc[i, 'my_min'] = min_times
    ride_list.loc[i, 'my_max'] = max_times
    ride_list.loc[i, 'my_rating'] = ride_list.loc[i, 'rating']
    ride_list.loc[i, 'num'] = 0

# Initialize model
model = pulp.LpProblem('Maximimize ride enjoyment', pulp.LpMaximize)

# Add calculation to be optimized
model += pulp.lpSum([ride_list.loc[i,'ride'] * ride_list.loc[i,'rating'] * ride_list.loc[i,'num'] for i in rides])

# Add constraint to # times for each ride
x = pulp.LpVariable.dicts("times",[ride_list.loc[i, 'num'] for i in rides], 
                          lowBound = min_times,
                          upBound = max_times,
                          cat = 'Integer')

# Add constraint for total amount of time
total_rides = pulp.lpSum([ride_list[i,'num'] for i in rides])
model += pulp.LpConstraint('total_ride_time',
                          (pulp.lpSum([((ride_list.loc[i,'wait'] * ride_list.loc[i,'num']) + 
                          (ride_list.loc[i,'ride'] * ride_list.loc[i,'num'])) for i in rides]) + 
                          ((total_rides - 1) * time_between)) <= 
                          (hours_open - food_time))

Answer 1

So the problem you are having with the indexing is due to the fact that you are not constructing the variable correctly in pulp. When you do this:

x = pulp.LpVariable.dicts("times",[ride_list.loc[i, 'num'] for i in rides], ...

you are passing in a list of the values of the data frame, which is incorrect. The call should provide a key set for the variable to be created, in this case, x and the logical index is just a count of the number of rides. In your case, you are providing a list of 3 zeros, as you have filled the df with those values. That collapses down to a set with one zero in it. See my example below. Also, in the remainder of your effort, you are not using the variable you created... ?? You are using ride_list.loc[i,'num'] which is just some fixed value in a data frame, not a variable in the problem.

Here is an example that shows a better way to construct the variable, etc. Note the output results from printing x [poorly formed] and y. Also note the usage of the variable created in a notional constraint.

import pulp
import pandas as pd

data = { 'wait':        [1, 5, 10],
         'ride_time':   [2, 6, 8],
         'num' :        [0, 0, 0]}

df = pd.DataFrame(data)
print (df)

model = pulp.LpProblem("ride_plan", pulp.LpMaximize)
x = pulp.LpVariable.dicts("rides", [df.loc[i, 'num'] for i in range(len(df))])  # <-- bad
print(x)

y = pulp.LpVariable.dicts("rides", range(len(df)), cat="Integer")
print(y)

# example constraint for notional max wait time of 15 minutes...
model += pulp.LpConstraint(pulp.lpSum(df.loc[i, 'wait'] * y[i] for i in range(len(df)))) <= 15

print(model)

Yields:

   wait  ride_time  num
0     1          2    0
1     5          6    0
2    10          8    0

{0: rides_0}    # <--- x
{0: rides_0, 1: rides_1, 2: rides_2}   # <--- y

ride_plan:
MAXIMIZE
None
SUBJECT TO
_C1: rides_0 + 5 rides_1 + 10 rides_2 <= 15

VARIABLES
rides_0 free Integer
rides_1 free Integer
rides_2 free Integer

[Finished in 220ms]