In many industries and
institutions, retaining workers is an important issue in building
community and continuity. McLane Company is a large distribution
center owned by WalMart that distributes goods and products to
convenience stores nationwide. The management at McLane have been
working hard to reduce turnover through their Leadership 2000 project
in order to make a stronger company–stronger in morale, which,
they implied, leads to stronger commitment from workers and stronger
financial health. Perhaps this drive to keep the people they hire
could also be seen as a necessary step in their goal to be the number
one distributor to convenience stores worldwide.
They provided the
following data on turnover rates at McLane since 1996:
Year

%
turnover, McLane overall

% turnover, Distr.
Center only

1996

62.8

90

1997

38

42.44

1998

29.9

35

1999

19.5

22

What
is turnover?
1) Explain
in words what it means to have 90% turnover in the distribution
center in 1996:
______________________________________________________________________________
2) Explain
why you think that the turnover rates in the distribution center
alone are higher than the turnover rates for McLane as a whole:
______________________________________________________________________________
3) List
some factors that might contribute to turnover:
4) List
some factors that might contribute to reducing turnover:
Some natural questions…
…might be:
How are the turnover
rates decreasing? Is there a pattern? Several possible patterns?
What can McLane expect
the turnover rates to be in the year 2000? In the year 2005?
What might have been
the turnover rates in 1995? In 1990?
Will McLane ever
reduce the turnover rate to zero? Why or why not?
5)
What other questions would you want to ask about the data?
________________________________________________________________________
________________________________________________________________________
Examining the Data
and Making Predictions
6)
Recode the year data so that 1996 = year 1. We do this to simplify
the regression equations we will use to model the data. Using
a graphing calculator, graph year versus % turnover in McLane
and year versus % turnover in the Distribution Center only.
Describe the trend(s)
you see and suggest possible types
Make
a sketch of the graphs here:
of functions to model
the data.
_______________________________________________
_______________________________________________
_______________________________________________
_______________________________________________
_______________________________________________
7) Fit an exponential
model to the year versus % turnover in McLane data, using
your graphing calculator.
a) Write down
your model for the data. Round all values to three decimal
places.
___________________________________________________________________
b) How well does
model fit the data? Explain your answer.
______________________________________________________________
c) Your model
is likely in the form of y = a .
bx.
Explain what the values of a and b mean in the
context of the situation.
_________________________________________________________
_________________________________________________________
d) Use the model
to predict the turnover rate at McLane overall in the year
2000 and 2005. Are the predictions reasonable? Explain why
or why not.
_____________________________________________________________
______________________________________________________________
e) Use the model
to suggest the turnover rates at McLane overall in 1995 and
1990. Are the predictions reasonable? Explain why or why not.
_____________________________________________________________
______________________________________________________________
8)
Fit an exponential model to the year versus % turnover in the
Distribution Center only data, using your graphing calculator.
a) Write down
your model for the data. Round all values to three decimal
places.
_______________________________________________________________
b) How well does
model fit the data? Explain your answer.
_______________________________________________________________
c) Your model
is likely in the form of y = a .
bx.
Explain what the values of a and b mean in the
context of the situation.
_______________________________________________________________
________________________________________________________________
d) Use the model
to predict the turnover rate in the distribution center in
the year 2000 and 2005. Are the predictions reasonable? Explain
why or why not.
_______________________________________________________________
_______________________________________________________________
e) Use the model
to suggest the turnover rates in the distribution center in
1995 and 1990. Are the predictions reasonable? Explain why
or why not.
_______________________________________________________________
_______________________________________________________________
Deep Thoughts
9) According
to the models given, will McLane ever reduce the turnover rate
to zero?
Why or why not?
Explain.
_______________________________________________________________
_______________________________________________________________
10)
According to the models, will the percent turnover rate in the
distribution center alone ever equal the percent turnover rate
at McLane overall? Demonstrate and explain how you determined
your answer.
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
11)
Would a different function provide a better model for the data?
Try a linear model for the each set of data. Compare the predictions
for turnover rates in 1990, 1995, 2000, and 2005 with exponential
models and linear models. Which seem the most reasonable? Why?
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
12)
Are there any other functions you might use to model the data?
Explain why or why not. If you have an idea for another model,
try it out. Which model tried above seems to fit the data the
best? Explain.
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
13) Imagine
you are a consultant, helping McLane to improve itself as a company.
Write a memo to the management in which you explain your analysis
of their decreasing turnover rate. Indicate what they might expect
over the next five years according to the model you chose in #12.
Also explain any limitations of this model, and suggest ways that
McLane might overcome those limitations–that is, how they
might adapt the model so that it can be a better prediction tool.
