Question: The reference desk of a university library receives requests for assistance. Assume that a Poisson probability distribution with an arrival rate of 10 requests per hour can be used to describe the arrival pattern and that service times follow an exponential probability distribution with a service rate of 12 requests per hour.
a. What is the probability that no requests for assistance are in the system?
b. What is the average number of requests that will be waiting for service?
c. What is the average waiting time in minutes before service begins?
d. What is the average time at reference desk in minutes (waiting time plus service time)?
e. What is the probability that a new arrival has to wait for service?
[2]. Assume that the following quantity discount schedule is appropriate. If annual demand is 120 units, ordering costs are $20 per order, and annual holding cost rate is 25%, what order quantity would you recommend?
|
Order Size
|
Discount (%)
|
Unit Cost
|
|
0 to 49
|
0
|
$30.00
|
|
50 to 99
|
5
|
$28.50
|
|
100 or more
|
10
|
$27.00
|
[3]. Westside Auto purchases a component used in the manufacture of automobile generators directly from the supplier. Westside's generator production operation, which is operated at a constant rate, will require 1000 components per month throughout the year (12,000 units annually). Assume that the ordering costs are 20% of the value of the inventory. Westside has 250 working days per year and a lead time of 5 days. Answer the following inventory policy questions:
a. What is the EOQ for this component?
b. What is the reorder point?
c. What is the cycle time?
d. What are the total annual holding and ordering costs associated with your recommended EOQ?
[4]. Colonial State College is considering building a new multipurpose athletic complex on campus. The complex would provide a new gymnasium for intercollegiate basketball games, expanded office space, classrooms, and intramural facilities. The following activities would have to be undertaken before construction can begin:
|
Activity
|
Description
|
Immediate Predecessor
|
Time (Weeks)
|
|
A
|
Survey building site
|
------
|
6
|
|
B
|
Develop initial design
|
------
|
8
|
|
C
|
Obtain board approval
|
A,B
|
12
|
|
D
|
Select architect
|
C
|
4
|
|
E
|
Establish budget
|
C
|
6
|
|
F
|
Finalize design
|
D,E
|
15
|
|
G
|
Obtain financing
|
E
|
12
|
|
H
|
Hire contrator
|
F,G
|
8
|
a. Draw a project network.
b. Identify the critical path.
c. Develop an activity schedule for the project.
d. What is the expected completion time for the project?