M1 Practice Problems Littles Law
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School
University of Wisconsin, Platteville *
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Course
4120
Subject
Industrial Engineering
Date
Jan 9, 2024
Type
xlsx
Pages
7
Uploaded by SuperHumanBook14421
1. Butternut is a ski resort in Massachusetts. One of their triple chair lifts unloads 1296 skiers per hour at the top of the slope. (A triple chair lift can carry three passengers per chair.) The ride from the bottom to the top takes 5 minutes. How many skiers are riding on the lift at any one time?
Solution:
Given data:
Process: Ski Lif
Flow unit: Skier
I = R x T
I = ?
skiers
R=
1296 skiers/hr
T=
5 minutes =
0.083333 hour
I =
108.00 skiers
Q2.2 page 30
Consider the baggage check-in of a small airline. Check-in data indicate that from 9 a.m. to 10 a.m.,
255 passengers checked in. Moreover, based on counting the number of passengers waiting in line, airport management found that the average number of passengers waiting for check-in was 35.
How long did the average passenger have to wait in line? (Round the answer to 2 decimal places.)
Solution:
Given data:
Process: Baggage Check-in
Flow unit: Passenger
I = R x T
I =
35 passengers
R=
255 passengers/hr
T= ?
T= I/R
T=
0.14 hour or
8.24 minutes
What does T represent?
The flow time represents waiting time + check-in time.
What would you do if you were asked to cut back T by 50%?
Show using Little's Law.
Install check-in kiosks
Online check-in service
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3. The following table shows annual financial data for Dirt Cheap Wholesale and Kwik
Dirt Cheap
Kwik-E-Mart
Inventories (x$1000)
$ 4,754 $ 40,894 Sales (x $1000)
$ 59,217 $ 397,206 COGS (x $1000)
$ 52,762 $ 326,606 Assume that both companies have an average annual holding cost rate of 20% (i.e. it costs both retailers $2 to hold an item that they procured for $10 for one entire year). How many days, on average, does a product stay in Dirt Cheap’s inventory before it is sold? Assume that stores operate 365 days a year.
Solution:
Given data:
Process: Retailing
Flow unit: Grocery
I = R x T
I = $ 4,754 R= $ 52,762 T=I/R =
0.09 years ==>
32.89 days
11.09844
How much lower (expressed in $’s) is, on average, the inventory cost for Dirt Cheap compared to Kwik-E-Mart of a house hold cleaner valued at $5 COGS? Assume that the unit cost of the house hold cleaner is the same for both companies and that the price and the inventory turns of an item are independent.
Solution:
Consider Dirt Cheap.
Inv. Turns =
1/T
Inv. Cost =
Annual Inv Cost / Inv. Turns
Input Data:
T =
0.09 years
Holding cost rate per annum =
20%
Product value in COGS per unit =
$5 Annual Inv Cost per unit = holding cost rate x COGS/unit=
$1 Step 1: Compute Dirt Cheap's Inv. Turns and Cost.
Inv. Turns = 1/T = 11.10
Step 2: Compute Dirt Cheap's actual Inv. Cost
Inv. Cost = Annual Inv Cost per unit / I
=
$0.090 per unit
Step 3: Compute Kwik-E-Mart's Inventory Cost (repeat the above)
Input Data:
I=
$ 40,894 R=
$ 326,606 0.13
year
T=I/R ==>
Holding cost rate per annum =
20%
Product value in COGS per unit =
$5 Annual Inv Cost per unit = holding cost rate x COGS/unit=
$1 Step 1: Compute Inv. Turns and Cost.
Inv. Turns = 1/T = 7.99
Step 2: Compute actual Inv. Cost
Inv. Cost = Annual Inv Cost per unit / I
=
$0.125 per unit
Final Ans: Dirt Cheap is
$0.035 lower
or
39% lower
ki-Mart.
turns
Inv. Turns
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turns
Inv. Turns