Module 4 assignment

Module 4

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Queuing Analysis
PROBLEM #8
The ticket booth on the Tech campus is operated by one person, who is selling tickets for the annual Tech versus
State football game on Saturday. The ticket seller can serve an average of 12 customers per hour;on average, 10
customers arrives to purchase tickets each hour (poisson distributed). Determine the average time a ticket buyer must wait
and the portion of time the ticket seller is busy.
Arrival Rate
Service Rate
Average waiting time in queue (Wq)
Average waiting time in the system (W)
The portion of time the ticket seller is busy

10
12
0.4167
0.5
83.33%

PROBLEM #10
The Dynaco Manufacturing Company produces a particular product in an assembly line operation. One of the machines
on the line is a drill press that has a single assembly line feeding into it. A partiallycompleted unit arries at the press to be worked
on every 7.5 minutes on average. The machine operator can process an average of 10 parts per hour. Determine the average
number of parts waiting to be worked on, the percentage of time the operator is working, and the percentage of time the
machine is idle.
Arrival Rate
Service Rate
The average number of parts waiting to be worked on
The pecentage of time the operator is working
The percentage of time the machine is idle

7.5
10
14.0625
75.00%
0.4

PROBLEM #12
The Peachtree Airport in Atlanta serves light aircraft. It has a single runway and one air traffice controller to land planes. It takes
an airplane 12 minutes to land and clear the runway. Planes arrive at the airport at the rate of four per hour.
a. determine the average number of planes that eill stack up, waiting to land
b. find the average time a plane must wait in line before it can land.
c. Calculate the average time it takes a plane to clear the runway once it has notified the airport that it is in the vicinity and wants to land.
d. The FAA has a rule than an air traffic controller can, on average, land planes a maximum of 45 minutes out of every hour. There
must be 15 idle time available to releive the tension. Will this airport have to hire an extra air traffic controller?
Problem #14
During registration at State University every semester, students in the college of business must have their courses approved
by the college advisor. It takes the advisor an average of 2 minutes to approve each schedule, and students arrive at the advisor's
office at the rate of 28 per hour.
a. compute L, Lq,W,Wq, and U.
b. the dean of the college has received a number of complaints from students about the length of time they must wait to have their schedules
approved. The dean feels that waiting 10.00 minutes to get a schedule approved is not unreasonable. Each assistant the dean assigns to
the adviser's office will reduce the average time required to approve a schedule by 0.25 minute, down to a minimum time of 1.00 minute to
approve a schedule. How many assistants should the dean assign to the advisor?

Inventory Management
Problem # 2

Hayes electronics assumed with certainty that the ordering cost is $450 per order and the inventory
carrying cost is $170 per unit per year. However, the inventory model parameters are frequently only
estimates that are subject to some degree of uncertainty. Consider four cases of variation in the model
parameters as follows: (a) both ordering cost and carrying cost are 10% less that originally estimated,
(b) both ordering cost and carrying cost are 10% higher than originally estimated, (c) ordering cost is
10% higher and carrying cost is 10% lower than originally estimated, and (d) ordering cost is 10%
lower and carrying cost is 10% higher than originally estimated. Determine the optimal order quantity
and total inventory cost for each of the four cases. Prepare a table with values from all four cases and
compare the sensitivity of the model solution to changes in parameter values.

Problem #4

The Western Jeans Company purchases denim from Cumberland Textile Mills. The Western Jeans
Company uses 235,000 yards of denim per year to make jeans. The cost of ordering denim from the
textile company is $250 per order. It costs Western $1.65 per yard annually to hold a yard of denim in
inventory. Determine the optimal number of yards of denim the Western Jeans Company should
order, the minimum total annual inventory cost, the optimal number of orders per year, and the
optimal time between orders.

Problem 3