Employee Scheduling Problem MIP
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I am trying to create a mathematical model for employee scheduling.
I have already got an idea on how I should model it but I do not know whether it is the best way to do it so.
Take for example a day.
A working day consists of 10 hours, from 10:00 till 20:00.
Suppose there is an employee working for 4 hours.
Now such a schedule can start from 10:00 and is dependent on the working hours of that employee.
The way that the available schedules could be written in the A Matrix ($A*x leq b$) would be one column per schedule filled with 1's and 0's.
e.g.
For the 4 hours schedule, I would have 7 different available shifts.
- 10:00 to 14:00
- 11:00 to 15:00
- ...
- 16:00 to 20:00
For that, I would need 7 columns. The first would be filled with
- 1,1,1,1,0,0,...,0
the second with
- 0,1,1,1,1,0...,0
and so goes on.
This way in the A matrix I will have many columns with 0 as matrix Elements. Is there a more efficient way to model such a schedule?
My goal is to solve it as a MIP problem.
linear-programming mathematical-modeling simplex mixed-integer-programming
asked Dec 21 '18 at 15:46
GeorgiosGeorgios
63
$endgroup$
add a comment |
$begingroup$
I am trying to create a mathematical model for employee scheduling.
I have already got an idea on how I should model it but I do not know whether it is the best way to do it so.
Take for example a day.
A working day consists of 10 hours, from 10:00 till 20:00.
Suppose there is an employee working for 4 hours.
Now such a schedule can start from 10:00 and is dependent on the working hours of that employee.
The way that the available schedules could be written in the A Matrix ($A*x leq b$) would be one column per schedule filled with 1's and 0's.
e.g.
For the 4 hours schedule, I would have 7 different available shifts.
- 10:00 to 14:00
- 11:00 to 15:00
- ...
- 16:00 to 20:00
For that, I would need 7 columns. The first would be filled with
- 1,1,1,1,0,0,...,0
the second with
- 0,1,1,1,1,0...,0
and so goes on.
This way in the A matrix I will have many columns with 0 as matrix Elements. Is there a more efficient way to model such a schedule?
My goal is to solve it as a MIP problem.
linear-programming mathematical-modeling simplex mixed-integer-programming
asked Dec 21 '18 at 15:46
GeorgiosGeorgios
63
$endgroup$
1
$begingroup$
This is a good approach. And if you cannot generate all the feasible columns a priori you can do column generation (which does it dynamically). But can be tricky to implement.
$endgroup$
– Kuifje
Dec 21 '18 at 16:07
$begingroup$
@Kuifje Thank you for your comment. Could you please provide an example or a link of the dynamical creation of the columns? I still find it performance-wise quite "expensive". If I I would implement it for multiple employees and days that would create a massive Matrix.
$endgroup$
– Georgios
Dec 21 '18 at 22:29
$begingroup$
Check this for example : gist.github.com/Bart6114/8414730
$endgroup$
– Kuifje
Dec 21 '18 at 22:48
$begingroup$
See link for an example of CG applied to employee scheduling (the links at the bottom show alternative approaches).
$endgroup$
– Erwin Kalvelagen
Dec 22 '18 at 14:26
$begingroup$
@Erwin Kalvelagen Lovely! Thank you for the link. This is what I was looking for. I still have to read multiple times the content on your page to comprehend it. To that, the first reference (Loren Shure) on your page is what I have in my mind. I find such methods so fascinating but I do not know, whether there is already commercial software that is applied in practice e.g. Starbucks employee Scheduling.
$endgroup$
– Georgios
Dec 22 '18 at 15:39
add a comment |
$begingroup$
I am trying to create a mathematical model for employee scheduling.
I have already got an idea on how I should model it but I do not know whether it is the best way to do it so.
Take for example a day.
A working day consists of 10 hours, from 10:00 till 20:00.
Suppose there is an employee working for 4 hours.
Now such a schedule can start from 10:00 and is dependent on the working hours of that employee.
The way that the available schedules could be written in the A Matrix ($A*x leq b$) would be one column per schedule filled with 1's and 0's.
e.g.
For the 4 hours schedule, I would have 7 different available shifts.
- 10:00 to 14:00
- 11:00 to 15:00
- ...
- 16:00 to 20:00
For that, I would need 7 columns. The first would be filled with
- 1,1,1,1,0,0,...,0
the second with
- 0,1,1,1,1,0...,0
and so goes on.
This way in the A matrix I will have many columns with 0 as matrix Elements. Is there a more efficient way to model such a schedule?
My goal is to solve it as a MIP problem.
linear-programming mathematical-modeling simplex mixed-integer-programming
asked Dec 21 '18 at 15:46
GeorgiosGeorgios
63
$endgroup$
I am trying to create a mathematical model for employee scheduling.
I have already got an idea on how I should model it but I do not know whether it is the best way to do it so.
Take for example a day.
A working day consists of 10 hours, from 10:00 till 20:00.
Suppose there is an employee working for 4 hours.
Now such a schedule can start from 10:00 and is dependent on the working hours of that employee.
The way that the available schedules could be written in the A Matrix ($A*x leq b$) would be one column per schedule filled with 1's and 0's.
e.g.
For the 4 hours schedule, I would have 7 different available shifts.
- 10:00 to 14:00
- 11:00 to 15:00
- ...
- 16:00 to 20:00
For that, I would need 7 columns. The first would be filled with
- 1,1,1,1,0,0,...,0
the second with
- 0,1,1,1,1,0...,0
and so goes on.
This way in the A matrix I will have many columns with 0 as matrix Elements. Is there a more efficient way to model such a schedule?
My goal is to solve it as a MIP problem.
linear-programming mathematical-modeling simplex mixed-integer-programming
linear-programming mathematical-modeling simplex mixed-integer-programming
asked Dec 21 '18 at 15:46
GeorgiosGeorgios
63
asked Dec 21 '18 at 15:46
GeorgiosGeorgios
63
asked Dec 21 '18 at 15:46
GeorgiosGeorgios
63
asked Dec 21 '18 at 15:46
GeorgiosGeorgios
63
asked Dec 21 '18 at 15:46
GeorgiosGeorgios
63
63
1
$begingroup$
This is a good approach. And if you cannot generate all the feasible columns a priori you can do column generation (which does it dynamically). But can be tricky to implement.
$endgroup$
– Kuifje
Dec 21 '18 at 16:07
$begingroup$
@Kuifje Thank you for your comment. Could you please provide an example or a link of the dynamical creation of the columns? I still find it performance-wise quite "expensive". If I I would implement it for multiple employees and days that would create a massive Matrix.
$endgroup$
– Georgios
Dec 21 '18 at 22:29
$begingroup$
Check this for example : gist.github.com/Bart6114/8414730
$endgroup$
– Kuifje
Dec 21 '18 at 22:48
$begingroup$
See link for an example of CG applied to employee scheduling (the links at the bottom show alternative approaches).
$endgroup$
– Erwin Kalvelagen
Dec 22 '18 at 14:26
$begingroup$
@Erwin Kalvelagen Lovely! Thank you for the link. This is what I was looking for. I still have to read multiple times the content on your page to comprehend it. To that, the first reference (Loren Shure) on your page is what I have in my mind. I find such methods so fascinating but I do not know, whether there is already commercial software that is applied in practice e.g. Starbucks employee Scheduling.
$endgroup$
– Georgios
Dec 22 '18 at 15:39
add a comment |
1
$begingroup$
This is a good approach. And if you cannot generate all the feasible columns a priori you can do column generation (which does it dynamically). But can be tricky to implement.
$endgroup$
– Kuifje
Dec 21 '18 at 16:07
$begingroup$
@Kuifje Thank you for your comment. Could you please provide an example or a link of the dynamical creation of the columns? I still find it performance-wise quite "expensive". If I I would implement it for multiple employees and days that would create a massive Matrix.
$endgroup$
– Georgios
Dec 21 '18 at 22:29
$begingroup$
Check this for example : gist.github.com/Bart6114/8414730
$endgroup$
– Kuifje
Dec 21 '18 at 22:48
$begingroup$
See link for an example of CG applied to employee scheduling (the links at the bottom show alternative approaches).
$endgroup$
– Erwin Kalvelagen
Dec 22 '18 at 14:26
$begingroup$
@Erwin Kalvelagen Lovely! Thank you for the link. This is what I was looking for. I still have to read multiple times the content on your page to comprehend it. To that, the first reference (Loren Shure) on your page is what I have in my mind. I find such methods so fascinating but I do not know, whether there is already commercial software that is applied in practice e.g. Starbucks employee Scheduling.
$endgroup$
– Georgios
Dec 22 '18 at 15:39
1
1
$begingroup$
This is a good approach. And if you cannot generate all the feasible columns a priori you can do column generation (which does it dynamically). But can be tricky to implement.
$endgroup$
– Kuifje
Dec 21 '18 at 16:07
$begingroup$
This is a good approach. And if you cannot generate all the feasible columns a priori you can do column generation (which does it dynamically). But can be tricky to implement.
$endgroup$
– Kuifje
Dec 21 '18 at 16:07
$begingroup$
@Kuifje Thank you for your comment. Could you please provide an example or a link of the dynamical creation of the columns? I still find it performance-wise quite "expensive". If I I would implement it for multiple employees and days that would create a massive Matrix.
$endgroup$
– Georgios
Dec 21 '18 at 22:29
$begingroup$
@Kuifje Thank you for your comment. Could you please provide an example or a link of the dynamical creation of the columns? I still find it performance-wise quite "expensive". If I I would implement it for multiple employees and days that would create a massive Matrix.
$endgroup$
– Georgios
Dec 21 '18 at 22:29
$begingroup$
Check this for example : gist.github.com/Bart6114/8414730
$endgroup$
– Kuifje
Dec 21 '18 at 22:48
$begingroup$
Check this for example : gist.github.com/Bart6114/8414730
$endgroup$
– Kuifje
Dec 21 '18 at 22:48
$begingroup$
See link for an example of CG applied to employee scheduling (the links at the bottom show alternative approaches).
$endgroup$
– Erwin Kalvelagen
Dec 22 '18 at 14:26
$begingroup$
See link for an example of CG applied to employee scheduling (the links at the bottom show alternative approaches).
$endgroup$
– Erwin Kalvelagen
Dec 22 '18 at 14:26
$begingroup$
@Erwin Kalvelagen Lovely! Thank you for the link. This is what I was looking for. I still have to read multiple times the content on your page to comprehend it. To that, the first reference (Loren Shure) on your page is what I have in my mind. I find such methods so fascinating but I do not know, whether there is already commercial software that is applied in practice e.g. Starbucks employee Scheduling.
$endgroup$
– Georgios
Dec 22 '18 at 15:39
$begingroup$
@Erwin Kalvelagen Lovely! Thank you for the link. This is what I was looking for. I still have to read multiple times the content on your page to comprehend it. To that, the first reference (Loren Shure) on your page is what I have in my mind. I find such methods so fascinating but I do not know, whether there is already commercial software that is applied in practice e.g. Starbucks employee Scheduling.
$endgroup$
– Georgios
Dec 22 '18 at 15:39
add a comment |
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1
$begingroup$
This is a good approach. And if you cannot generate all the feasible columns a priori you can do column generation (which does it dynamically). But can be tricky to implement.
$endgroup$
– Kuifje
Dec 21 '18 at 16:07
$begingroup$
@Kuifje Thank you for your comment. Could you please provide an example or a link of the dynamical creation of the columns? I still find it performance-wise quite "expensive". If I I would implement it for multiple employees and days that would create a massive Matrix.
$endgroup$
– Georgios
Dec 21 '18 at 22:29
$begingroup$
Check this for example : gist.github.com/Bart6114/8414730
$endgroup$
– Kuifje
Dec 21 '18 at 22:48
$begingroup$
See link for an example of CG applied to employee scheduling (the links at the bottom show alternative approaches).
$endgroup$
– Erwin Kalvelagen
Dec 22 '18 at 14:26
$begingroup$
@Erwin Kalvelagen Lovely! Thank you for the link. This is what I was looking for. I still have to read multiple times the content on your page to comprehend it. To that, the first reference (Loren Shure) on your page is what I have in my mind. I find such methods so fascinating but I do not know, whether there is already commercial software that is applied in practice e.g. Starbucks employee Scheduling.
$endgroup$
– Georgios
Dec 22 '18 at 15:39