The movie, Star Wars VII , is coming out Friday, Dec. 15 th . Emagin e Saline, a
ID: 382908 • Letter: T
Question
The movie,
Star Wars VII
,
is coming out Friday, Dec. 15
th
. Emagin
e Saline, a movie theater
south of Ann Arbor with ridiculously comfortable seats, is planning to sell an opening day poster
that can be purchased only on Friday. It costs Emagine $1.50 to purchase each poster from their
distributor, and they’re planning t
o sell them for $10 each. Because they are required to recycle
any unsold posters after Friday, there is no salvage value.
They don’t know what the demand for the posters will be so they have decided to assume it is
uniformly distributed between 75 and
130 posters.
The inverse of the
(
,
)
distribution is
1
(
)
=
+
(
)
.
(a)
How many posters should Emagine Saline purchase? Note, they would like to purchase
an integer quantity.
One of your friends
, Phillip,
does stock
-
keeping for Emagine
. He
mentioned his boss aske
d him
to figure out how many boxes of popcorn kernels to order and how often. He isn’t sure what to
do. Conveniently you took at IOE 202
, and you
tell him that you’ll help him out as long as he
nabs you one of those sweet
Star Wars VII
posters.
He rolls
his eyes but agrees.
Phillip tells you each week, Emagine uses 235 boxes of popcorn kernels. Each time an order is
placed, it costs $15, and orders take ½ week to arrive. The cost per box of popcorn varies based
on how many boxes are ordered at the sam
e time, see table below. The cost to hold a box per
week is
5
% of the value of the box.
The cost per box is:
Number of boxes
Cost per box
0
-
150
$3
151
-
4
00
$2.7
4
01
-
1000
$2.4
>1000
$2.25
(b)
How many boxes should Emagine order each time an order is plac
ed?
They would like
to order an integer quantity.
Show all work.
(c)
How much will this order policy cost
per week?
(d)
How often should Emagine place an order?
(e)
What is the re
-
order point?
(f)
If the lead time were to increase, would you expect the re
-
order poin
t to increase or
decrease?
(g)
If boxes of popcorn kernels are perishable (i.e., go bad after enough time has passed),
how would this change how we model this problem?
Explanation / Answer
I only understood the first problem. For the second problem, all texts are coming as jumbled up. So, please psot again for the second problem.
-----------
Co = Cost of overstocking = Purchase cost - salvage value = $1.5 - 0 = $1.5
Cu = Cost of understocking = Selling price - purchase cost = $10 - $1.5 = $8.5
Critical ratio = CR = Cu / (Co+Cu) = 8.5 / (8.5+1.5) = 0.85
Note that according to the theory of the newsvendor model, the optimum order size is that order size where the critical ratio equals the service level.
So, service level = 0.85
The demand distribution is uniform with D ~ U(75, 130)
So, the optimal order quantity(Q*) = 75 + 0.85*(130 - 75) = 121.75 or 122 (rounded off)