Formulate a model for an Linear Programming question

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Formulate a model for an Linear Programming question

Postby xgenoriginal on Wed Apr 02, 2014 4:33 am

Here is the problem i need to form (not solve) a model for a linear programming problem .


A major airport is reviewing their staffing needs for air traffic controllers. The most recent labor agreement has specified hiring for eight different shifts consisting of eight hours per shift. FAA regulations specify that air controllers work 2-hour intervals with an hour break between.
Airport officials specify that each controller work the first 2 hours of a shift. The following figure illustrates the hours of each shift and the periods during which a controller is on duty. airport officials have determined the minimum number of controllers on duty for each hour of the day. These are also indicated in the figure
The base pay per controller is $80 per shift with differentials for certain shifts. Any shifts beginning between 4 p.m. and 11 p.m.are paid at a 10 percent premium for the entire shift; and any beginning between midnight and 6 a.m. receive a 20 percent premium.
Airport officials want to determine the number of controllers to hire for each shift so as to meet the hourly requirements at a minimum cost per day. Formulate an appropriate model. (You do NOT need to solve this LP)
Image
http://gyazo.com/98d1089d01bbff64cfc910848972d2ec

The way I read the problem is that there are 8 shifts and you must have the maximum minimum amount of workers for each time period , but It says all workers must do the first 2 hours of a shift , so does this mean they can work 2 hours leave then come back for the last hour and be paid for only 3 hours , I don't really have any idea on how to begin turning this into a model since there are no constraints only a desire for minimum costs
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Re: Formulate a model for an Linear Programming question

Postby maggiemagnet on Wed Apr 02, 2014 11:41 am

xgenoriginal wrote:The way I read the problem is that there are 8 shifts and you must have the maximum minimum amount of workers for each time period

What do you mean by "the maximum minimum"?

xgenoriginal wrote:It says all workers must do the first 2 hours of a shift , so does this mean they can work 2 hours leave then come back for the last hour and be paid for only 3 hours

It means they can't show up for work and then immediately "go on break". They have to work for the first two hours. Then they can take their first break.

xgenoriginal wrote:there are no constraints only a desire for minimum costs

The exercise says that they "have determined the minimum number of controllers on duty for each hour of the day". That's a constraint. Try starting with that.
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Re: Formulate a model for an Linear Programming question

Postby xgenoriginal on Fri Apr 04, 2014 3:09 am

i have some more questions

so you would read the question as saying if for shift one you need 14 staff at one point, you need to employ them for the whole 8 hours ( and pay them accordingly) even if you only need 2 staff most of the time.

And with the constraints so the constraint would only be something like x >= 12
then the model would just be 8 constraints like this .

how does the price come into this question then ? Is there someway to integrate the price rate for each shift into the contraints?
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Re: Formulate a model for an Linear Programming question

Postby maggiemagnet on Fri Apr 04, 2014 7:07 pm

xgenoriginal wrote:...if for shift one you need 14 staff at one point, you need to employ them for the whole 8 hours ( and pay them accordingly) even if you only need 2 staff most of the time.

Yes. I think a bit part of what they're asking for a way to staff so that you can have 14 when you need it, but not 14 when you only need 2. So maybe 12 could have their shifts end at the end of the time you need 14, so there's only the 2 left for the next shift. Or that sort of thing.
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Re: Formulate a model for an Linear Programming question

Postby xgenoriginal on Sat Apr 05, 2014 4:28 am

so no ideas on where the price rate for shifts can be used?
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