1) Sketch a picture of
a portion of McLane's floor plan, showing at least one aisle, one
bay, and the five shelves and five slots per shelf in each bay.
2) What other questions
might you ask in order to answer the natural question?
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3) Answer the natural
question in multiple ways, if necessary (depending on the answers
to the questions in #2.) Explain your process(es) and answer(s).
Deep Thoughts
4) Let's say McLane wants
to renumber its bins, but they still plan to use threedigit numbers.
How many slot locations will be possible if
a) they use every
other number?
b) they use every
third number?
c) they use every
number?
d) Why is your
answer to part (b) not a whole number?
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e) If a small distribution
center wanted to have only about 1 million possible slot locations,
how many numbers should they skip in numbering their bays? (Assume
they use the same system as McLanethat is, the only aspect they
will change is how many threedigit numbers to skip.)
5) As
you have seen in #4, how we count the bays can increase or decrease
the total available slots. Find the percent increase each
case. Assume that McLane allows repetition of letters when naming
aisles.
a) Instead of using
every fifth number, use every fourth number:
b) Instead of using
every fourth number, use every third number:
c) Instead of using
every third number, use every second number:
d) Instead of using
every second number, use every number:
e) Describe at least
one way you can simplify your calculations for parts (a)(d) above:
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f) Why are the percent
increases NOT constant?
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6) Let's say McLane does
NOT repeat letters when naming aisles. (That is, they do
not have aisles AA, BB, etc.) What percent increase in available
slots will there be if they decide to allow repetition of letters?
a) Answer this
question with a specific example, as in #3 and/or #4 above.
Show your work.
b) Will your answer
always be the same for a given number of bays, shelves and slots?
Prove it or refute
it!
7) How will the number
of available slots be reduced if twodigit numbers are used
to identify bays? Explain your answer.
8) Assume McLane doubles
the number of shelves and doubles the number of slots on
each shelf.
a) How many times
bigger are the total number available slots compared with
the "original" number of slots in #3?
b) Predict how many
times bigger the number of available slots will be if the number
of shelves and number of slots on each shelf are both tripled.
Explain your answer.
c) Predict how many
times bigger the number of available slots will be if the number
of shelves is doubled and the number of slots per shelf
is tripled.
d) How many times
smaller will the number of available slots be if the number
of shelves is reduced to three and the number of slots
to four per shelf?
9) Design a numbering
scheme for McLane that would yield about 10 million possible slots.
(Get as close to 10 million as you can!) Assume that McLane will
still have aisles, bays, shelves, and slots, but you may determine
restrictions on any or all of these four elements. Write a memo
to the management at McLane explaining how you determined your scheme,
and how it could help them expand the capacity of their distribution
center.
