# Math Help - Linear Programming Formulation

1. ## Linear Programming Formulation

Hi. I need help with this formation of this problem.

A highly unethical taxi company is trying to determine the number of staff it requires to cover demand - they are most interested in keeping the number of staff to the barest of minimums to cover projected demand. They are also interested in knowing when the drivers should start work. A driver will work for 16 hours at a time which begins at the start of one of the designated shifts. The company has identified a rough demand schedule below which is broken into 8 hour segments:

3am - 11am : 2
11.01am - 7pm : 3
7.01am - 3am - 14

Formulate the problem as a linear programming problem.

Thanks

2. Originally Posted by lpd
Hi. I need help with this formation of this problem.

A highly unethical taxi company is trying to determine the number of staff it requires to cover demand - they are most interested in keeping the number of staff to the barest of minimums to cover projected demand. They are also interested in knowing when the drivers should start work. A driver will work for 16 hours at a time which begins at the start of one of the designated shifts. The company has identified a rough demand schedule below which is broken into 8 hour segments:

3am - 11am : 2
11.01am - 7pm : 3
7.01pm - 3am - 14

Formulate the problem as a linear programming problem.

Thanks
Start by identifying the variables you will use. Lets choose $x$, $y$ and $z$ being the number who start at 03:00, 11:01 and 19:01.

Then the objetive is to minimise the total number of drives:

$
Ob(x,y,z)=x+y+z
$

Now I will leave it to you to formulate the constraint/s. If you have problems then post them here with an explanation of what they are.

CB

3. Hi.

The contraints will be

x =< 2
y =< 3
z =< 14

because thats the minimum amount of demand that has to be met right?

4. Originally Posted by lpd
Hi.

The contraints will be

x =< 2
y =< 3
z =< 14

because thats the minimum amount of demand that has to be met right?
Wrong. You said the drivers work for 16 hours at a time, therefore those who start at 3am will cover the period from 3am to 11am and the one from 11am to 7pm.

Also it should be >= because the number of drivers have to cover the demand.

The constraints should then be:

z+x >= 2
x+y >= 3
y+z >= 14