MIP using PULP not approaching result

问题

I am trying to solve a MIP problem. I am trying to find the number of exams to be done by each tech on a date for a week by minimizing the total number of techs used. I have demand, time taken by each tech, list of techs etc. in separate dataframes.

Initially, I was using the cost function as minimizing the total time used to finish demand which @kabdulla helped me solve, linkhere!

Now, with the new cost function, the script gets stuck and doesn't seem to converge and I am not able to identify the reason.

Below is my code so far:

# Instantiate problem class
model = pulp.LpProblem("Time minimizing problem", pulp.LpMinimize)

capacity = pulp.LpVariable.dicts("capacity",
                                 ((examdate , techname, region) for examdate, techname, region in tech_data_new.index),
                                 lowBound=0,
                                 cat='Integer')

tech_used = pulp.LpVariable.dicts("techs",
                             ((examdate,techname) for examdate,techname,region in tech_data_new.index.unique()),
                             cat='Binary')

model += pulp.lpSum(tech_used[examdate, techname] for examdate,techname in date_techname_index.index.unique())

for date in demand_data.index.get_level_values('Exam Date').unique():
    for i in demand_data.loc[date].index.tolist():
        model += pulp.lpSum([capacity[examdate,techname,region] for examdate, techname, region in tech_data_new.index if (date == examdate and i == region)]) == demand_data.loc[(demand_data.index.get_level_values('Exam Date') == date) & (demand_data.index.get_level_values('Body Region') == i), shiftname].item()

for examdate, techname,region in tech_data_new.index:
    model += (capacity[examdate, techname, region]) <= tech_data_new.loc[(examdate,techname,region), 'Max Capacity']*tech_used[examdate, techname]

# Number of techs used in a day should be less than 8    
for examdate in tech_data_new.index.get_level_values('Exam Date').unique():
    model += pulp.lpSum(tech_used[examdate, techname] for techname in tech_data_new.index.get_level_values('Technologist Name').unique()) <=8


# Max time each tech should work in a day should be less than 8 hours(28800 secs)    
for date in tech_data_new.index.get_level_values('Exam Date').unique():
    for name in tech_data_new.loc[date].index.get_level_values('Technologist Name').unique():
        #print(name)
        model += pulp.lpSum(capacity[examdate,techname,region] * tech_data_new.loc[(examdate,techname,region), 'Time taken'] for examdate, techname, region in tech_data_new.index if (date == examdate and name == techname)) <= 28800

The last condition seems to be the problem, if I remove it, the problem converges. However, I am not able to understand the problem.

Please let me know, what I am missing in my understanding. Thanks.

来源：https://stackoverflow.com/questions/53987761/mip-using-pulp-not-approaching-result