## Lineair Programming

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
WBREEN
Posts: 1
Joined: Sun Sep 13, 2015 9:24 am
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### Lineair Programming

Hello Guys,

I have a problem which I can't figure out how to solve. Even with Excel Solver I could't manage to complete this.

A company accepts calls 7 days a week during the period 9 A.M. to 5 P.M. Based on analysis of historical data, the following number of staffers are needed each day in the call center to cover incoming calls:

Sunday Monday Tuesday Wednesday Thursday Friday Saturday
12 17 8 9 10 11 8

The company hires staff to work 5 consecutive days a week. It is not possible to offer part-time jobs. Thus, a staffer can start at any day of the week, and then works for 5 days in a row. The company pays these staffers €100/day to work on weekdays (Monday through Friday) and €150/day to work on the weekends (Saturday and Sunday). A continuous schedule must be created that can be used for the whole year and specifies the number of staffers that start each day (On every Sunday the same number of staffers will start, as on Tuesday, as on Wednesday, etc.). The objective is to minimise the total costs paid. Formulate this problem as an integer/binary/linear programming model.

maggiemagnet
Posts: 358
Joined: Mon Dec 08, 2008 12:32 am
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### Re: Lineair Programming

Even with Excel Solver I could't manage to complete this.
If you got as far as having the Solver try to finish this, then you did most of the work already. Please write back showing this. Thanks!
A company accepts calls 7 days a week during the period 9 A.M. to 5 P.M. Based on analysis of historical data, the following number of staffers are needed each day in the call center to cover incoming calls:

Sunday: 12, Monday: 17, Tuesday: 8, Wednesday: 9,
Thursday: 10, Friday: 11, Saturday: 8

The company hires staff to work 5 consecutive days a week. It is not possible to offer part-time jobs. Thus, a staffer can start at any day of the week, and then works for 5 days in a row. The company pays these staffers €100/day to work on weekdays (Monday through Friday) and €150/day to work on the weekends (Saturday and Sunday). A continuous schedule must be created that can be used for the whole year and specifies the number of staffers that start each day (On every Sunday the same number of staffers will start, as on Tuesday, as on Wednesday, etc.). The objective is to minimise the total costs paid. Formulate this problem as an integer/binary/linear programming model.
I think the setup is probably close to what they do here. The PDF here explains how to use Solver and has a good example starting at the bottom of page 10.