# Business math HW need help

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• Aug 12th 2007, 10:30 AM
lillian
Business math HW need help
Western Family Steakhouse offers a variety of low cost meals and quick service. Other than management, the Steakhouse operates with full time employees work 8 hrs/ day. The rest of employees are part time employees who are scheduled for 4 hrs shifts during peak meal times. On the Saturdays the Steakhouse is open from 11:00AM to10:00PM management want to develop a schedule for part time employees that will minimize labor cost and provide excellent customer service. The average wage rate for the part time employees is \$7.60/ hr. The total number of full time and part-time employees needed varies with time of a day as shown.

Time
Total number of employees needed

11:00AM-noon
9
Noon- 1:00PM
9
1:00PM-2:00PM
9
2:00PM-3:00PM
3
3:00PM-4:00PM
3
4:00PM-5:00PM
3
5:00PM-6:00PM
6
6:00PM-7:00PM
12
7:00PM-8:00PM
12
8:00PM-9:00PM
7
9:00PM-10:00PM
7

One full time employee comes on duty at 11:00 AM works 4 hrs, take one hr. off , and return to an other 4 hrs. The other employees comes to work at 1:00PM work same 4hrs. and take one hr. off, 4 hours- on pattern.

• Develop a minimum cost schedule for part time employees?

• What is total payroll for the part time employees? How many part time shifts are needed? (Use the surplus variables to comment on the desirability of scheduling at least some of the part time employees for 3 hrs shifts.)
Assume hat part-time employees can be assigned either 3hrs or 4 hrs shifts. Develop a minimum cost schedule for the part time employees. How many part time shifts are needed and what is the cost saving compared to the previous schedule?
• Aug 12th 2007, 07:32 PM
TKHunny
My very first reaction is to wonder what your thoughts are on this lengthy problem statement. What is your plan of attack. What tools are available to you? What section of what book are you in?
• Aug 12th 2007, 10:26 PM
CaptainBlack
Quote:

Originally Posted by TKHunny
My very first reaction is to wonder what your thoughts are on this lengthy problem statement. What is your plan of attack. What tools are available to you? What section of what book are you in?

Now mine was to wonder where I have seen this before and why it
was deleted? Now I would not be supprised to find that I had deleted
it, but I can't see why I would have:confused:

RonL
• Aug 12th 2007, 10:33 PM
CaptainBlack
It would help if you told us what techniques you have been studying, that
this might be homework for.

Me, I would think about useing simulated annealing to develop a schedule,
but I doubt that is what you have been studying.

RonL
• Aug 12th 2007, 10:33 PM
lillian
:(
Quote:

Originally Posted by TKHunny
My very first reaction is to wonder what your thoughts are on this lengthy problem statement. What is your plan of attack. What tools are available to you? What section of what book are you in?

I am using the Quantitative methods for business for my course book.
Because this is online course so we have to read and study by ourselves and I have a lot problem with linear programming applications.

I know this is production management application of the production scheduling and workforce scheduling. We are use excel to run the problem and get answer.

This question took me for more than a week now so I really need help
1.
• Aug 13th 2007, 12:25 AM
ticbol
Quote:

Originally Posted by lillian
Western Family Steakhouse offers a variety of low cost meals and quick service. Other than management, the Steakhouse operates with full time employees work 8 hrs/ day. The rest of employees are part time employees who are scheduled for 4 hrs shifts during peak meal times. On the Saturdays the Steakhouse is open from 11:00AM to10:00PM management want to develop a schedule for part time employees that will minimize labor cost and provide excellent customer service. The average wage rate for the part time employees is \$7.60/ hr. The total number of full time and part-time employees needed varies with time of a day as shown.

Time
Total number of employees needed

11:00AM-noon
9
Noon- 1:00PM
9
1:00PM-2:00PM
9
2:00PM-3:00PM
3
3:00PM-4:00PM
3
4:00PM-5:00PM
3
5:00PM-6:00PM
6
6:00PM-7:00PM
12
7:00PM-8:00PM
12
8:00PM-9:00PM
7
9:00PM-10:00PM
7

One full time employee comes on duty at 11:00 AM works 4 hrs, take one hr. off , and return to an other 4 hrs. The other employees comes to work at 1:00PM work same 4hrs. and take one hr. off, 4 hours- on pattern.

• Develop a minimum cost schedule for part time employees?

• What is total payroll for the part time employees? How many part time shifts are needed? (Use the surplus variables to comment on the desirability of scheduling at least some of the part time employees for 3 hrs shifts.)
Assume hat part-time employees can be assigned either 3hrs or 4 hrs shifts. Develop a minimum cost schedule for the part time employees. How many part time shifts are needed and what is the cost saving compared to the previous schedule?

I don't know anything about that Quantitative Methods for business. In fact, I don't think I was interested on the Business Math subject offered us in college back then for one semester only. It was just a "filler" subject I thought then. So my "knowledge" on Business Math is based on intuition (?) or thinking power only. It's a 2+2 thing for me only.

Here is my solution for your question here, based on thinking power or reasoning only. No "formulas" used. It might not be what you expect but it might help.
[The problem is about linear programming? I couldn't see it that way---or too many variables.]

I also don't know how to use or make tables/spreadsheets here so I copy-pasted your table and then I added my comments.

The regular employees are 2 only. One, in shift "a", and one also in shift "b".
The part timers, pt, are...
...8 employees in shift "c", 3-hr shift only.
...1 employee in shift "d", 3-hr shift.
...1 employee in shift "e", 3-hr shift.
...4 employees in shift "f", 3-hr shift.
...6 employees in shift "g", 4-hr shift.

1:00PM-2:00PM
9.......................1a...1b, needs 7pt ==>...8c<---excess of 1pt.
should read,
"From 1PM to 2PM, 9 employees are needed. Regulars "a" and "b" are there, so we need 7 part timers, which are the 8 in shift "c". There is an excess of one pt---since the shifts are either in 3- or 4-hr shifts. Need to pay that excess 1pt also even if he has to sleep at the back only.

------------------------------------------------------

Time
Total number of employees needed

11:00AM-noon
9.......................1a...0, needs 8pt ==>...8c

Noon- 1:00PM
9.......................1a...0, nedds 8pt ==>...8c

1:00PM-2:00PM
9.......................1a...1b, needs 7pt ==>...8c <---excess of 1pt.

2:00PM-3:00PM
3.......................1a...1b, needs 1pt ==>...1d

3:00PM-4:00PM
3.......................0....1b, needs 2pt ==>...1d...1e

4:00PM-5:00PM
3.......................1a...1b, needs 1pt ==>...1d...1e <----excess of 1pt.

5:00PM-6:00PM
6.......................1a...0, needs 5pt ==>.....4f...1e

6:00PM-7:00PM
12.....................1a...1b, needs 10pt ==>...4f...6g

7:00PM-8:00PM
12.....................1a...1b, needs 10pt ==>...4f...6g

8:00PM-9:00PM
7.......................0....1b, needs 6pt ==>...6g

9:00PM-10:00PM
7.......................0....1b, needs 6pt ==>....6g

------------------------------------------------------
So the payroll for the part time employees should be
(8*3 +1*3 +1*3 +4*3 +6*4)(7.60) = \$501.60 -------------answer.