MIP using PULP not approaching result












0















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.






python pulp







share|improve this question























  • Are you sure that the problem is feasible with the last constraint included? What happens if you change the right-hand-side of the constraint to a very large number - does it solve then? Also I tend to use square brackets within the pulp.lpSum() as it makes it clear then your generating a list using list comprehension to be summed over.

    – kabdulla
    Jan 1 at 8:04













  • Thanks for the suggestion. The problem is feasible. With a very large number on the right hand side, the solution becomes "Undefined".

    – user8996561
    Jan 3 at 4:25











  • My recommendation would be to clarify the formulation by pre-generating the sets and lists of interest. Your having to do lots of indexing into data-frames which makes the model harder to read, more error prone, and harder to keep up to date. Also I notice in the last term you are summing over terms you don't need to date and name each only take on a single value for each constraint you are adding so summing over them is confusion. Are you able to include a sample of data so I can actually run the code?

    – kabdulla
    Jan 3 at 19:28
















0















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.






python pulp







share|improve this question























  • Are you sure that the problem is feasible with the last constraint included? What happens if you change the right-hand-side of the constraint to a very large number - does it solve then? Also I tend to use square brackets within the pulp.lpSum() as it makes it clear then your generating a list using list comprehension to be summed over.

    – kabdulla
    Jan 1 at 8:04













  • Thanks for the suggestion. The problem is feasible. With a very large number on the right hand side, the solution becomes "Undefined".

    – user8996561
    Jan 3 at 4:25











  • My recommendation would be to clarify the formulation by pre-generating the sets and lists of interest. Your having to do lots of indexing into data-frames which makes the model harder to read, more error prone, and harder to keep up to date. Also I notice in the last term you are summing over terms you don't need to date and name each only take on a single value for each constraint you are adding so summing over them is confusion. Are you able to include a sample of data so I can actually run the code?

    – kabdulla
    Jan 3 at 19:28














0












0








0








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.






python pulp







share|improve this question














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.






python pulp




python pulp






share|improve this question













share|improve this question











share|improve this question




share|improve this question










asked Dec 31 '18 at 12:53









user8996561user8996561

399




399













  • Are you sure that the problem is feasible with the last constraint included? What happens if you change the right-hand-side of the constraint to a very large number - does it solve then? Also I tend to use square brackets within the pulp.lpSum() as it makes it clear then your generating a list using list comprehension to be summed over.

    – kabdulla
    Jan 1 at 8:04













  • Thanks for the suggestion. The problem is feasible. With a very large number on the right hand side, the solution becomes "Undefined".

    – user8996561
    Jan 3 at 4:25











  • My recommendation would be to clarify the formulation by pre-generating the sets and lists of interest. Your having to do lots of indexing into data-frames which makes the model harder to read, more error prone, and harder to keep up to date. Also I notice in the last term you are summing over terms you don't need to date and name each only take on a single value for each constraint you are adding so summing over them is confusion. Are you able to include a sample of data so I can actually run the code?

    – kabdulla
    Jan 3 at 19:28



















  • Are you sure that the problem is feasible with the last constraint included? What happens if you change the right-hand-side of the constraint to a very large number - does it solve then? Also I tend to use square brackets within the pulp.lpSum() as it makes it clear then your generating a list using list comprehension to be summed over.

    – kabdulla
    Jan 1 at 8:04













  • Thanks for the suggestion. The problem is feasible. With a very large number on the right hand side, the solution becomes "Undefined".

    – user8996561
    Jan 3 at 4:25











  • My recommendation would be to clarify the formulation by pre-generating the sets and lists of interest. Your having to do lots of indexing into data-frames which makes the model harder to read, more error prone, and harder to keep up to date. Also I notice in the last term you are summing over terms you don't need to date and name each only take on a single value for each constraint you are adding so summing over them is confusion. Are you able to include a sample of data so I can actually run the code?

    – kabdulla
    Jan 3 at 19:28

















Are you sure that the problem is feasible with the last constraint included? What happens if you change the right-hand-side of the constraint to a very large number - does it solve then? Also I tend to use square brackets within the pulp.lpSum() as it makes it clear then your generating a list using list comprehension to be summed over.

– kabdulla
Jan 1 at 8:04







Are you sure that the problem is feasible with the last constraint included? What happens if you change the right-hand-side of the constraint to a very large number - does it solve then? Also I tend to use square brackets within the pulp.lpSum() as it makes it clear then your generating a list using list comprehension to be summed over.

– kabdulla
Jan 1 at 8:04















Thanks for the suggestion. The problem is feasible. With a very large number on the right hand side, the solution becomes "Undefined".

– user8996561
Jan 3 at 4:25





Thanks for the suggestion. The problem is feasible. With a very large number on the right hand side, the solution becomes "Undefined".

– user8996561
Jan 3 at 4:25













My recommendation would be to clarify the formulation by pre-generating the sets and lists of interest. Your having to do lots of indexing into data-frames which makes the model harder to read, more error prone, and harder to keep up to date. Also I notice in the last term you are summing over terms you don't need to date and name each only take on a single value for each constraint you are adding so summing over them is confusion. Are you able to include a sample of data so I can actually run the code?

– kabdulla
Jan 3 at 19:28





My recommendation would be to clarify the formulation by pre-generating the sets and lists of interest. Your having to do lots of indexing into data-frames which makes the model harder to read, more error prone, and harder to keep up to date. Also I notice in the last term you are summing over terms you don't need to date and name each only take on a single value for each constraint you are adding so summing over them is confusion. Are you able to include a sample of data so I can actually run the code?

– kabdulla
Jan 3 at 19:28












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