Solving Cow Industrials Ltd's Production Problem for Board of Directors

soph.
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Looking for guidance on the following: The text outlines a company's problem, and ways to solve it. Results are hypothetically to be presented to the 'Board of Directors' ina week's time. Help please!

Cow Industrials Ltd is a medium sized Engineering Company. A number of their regular customers have made complaints over the last few orders they have received from Cow Ltd. These complaints are as follows:

• Products have been of a substandard nature
• Products are arriving late
• A combination of the above

Some of the customers have threatened that if this continues, then they will cancel their future orders and find another local supplier.

Consequently, the Managing Director has asked the Production Manager to investigate this immediately. He has replied, saying that he cannot meet production and deadline targets, because a large number of his workforce is constantly absent. He has done some basic statistical calculations and says there is strong correlation between production and workers attendance. Clearly something must be done about this, as the company does not want to lose their valued customer base.

The company has therefore called you in, the Information Analyst, to help the Production Manager. You are being asked to give advice regarding the absenteeism of the production workforce, and your brief is to analyze certain factors to try and reduce this high absenteeism and therefore increase production.

After an initial discussion with the Production Manager, you have decided to take a representative sample of ten employees and look at three possible factors – the age of the employee, their holiday entitlement and their hourly rate of pay (grade) - that may affect absenteeism. The Production Manager has given you the required data for each employee in your sample:

Employee Days Absent Pay Scale Holiday AGE
Entitlement
A 12 B 25 18
B 14 C 25 57
C 10 B 25 44
D 18 C 20 32
E 6 A 30 21
F 4 A 30 19
G 20 E 20 23
H 19 D 20 39
I 28 E 15 45
J 7 B 30 52
N.B. Employees are paid different hourly rates depending on their grade. These are as follows:

Grade A - £ 10.00 per hour
Grade B - £ 8.00 per hour
Grade C - £ 7.00 per hour
Grade D - £ 6.00 per hour
Grade E - £5.00 per hour
Grade F - £4.75 per hour

In a week’s time, the Production Manager and Managing Director will be asking a variety of questions regarding the above data. You are therefore advised to comprehensively analyze this data and do your calculations.
 
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I think, I need to ask - Can production targets be met if attendance is improved? Which is obviously yes, it's fundamental, surely? There's already been stated a positive correlation between production and workers' attendance.

I'm stuck which relationships are relevant and those that are not, for example pay vs attendance. What relevance does holiday entitlement have? Argh!

Thanks for your patience, hehe.
 
oops, sorry!

Do you have any suggestions to my problem though?

Thanks!
 
soph. said:
oops, sorry!

Do you have any suggestions to my problem though?

Thanks!

I guess I'd start with some sort of multiple regression analysis. I think a package like SPSS should have this function. http://www.statsoft.com/textbook/stmulreg.html
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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