Homework #4 - Classes

IE 368: Facility Design and Operations Management
Winter 2012
Homework #4: Production System Design Concepts
Due Date: Tuesday, February 7 th , 2012
(NOTE: To obtain full credit in this homework, make sure to show all your work in each
problem.)
1. Suppose jobs arrive to a workstation at a rate of 20 jobs per hour.
a. If the workstation processes a single job at a time with an average process time per
job of 2.5 minutes, what is the utilization of the workstation?
b. If the workstation processes two jobs at a time with an average process time per job
of 5 minutes, what is the utilization of the workstation?
c. If the workstation processes two jobs at a time with an average process time per job
of 2.5 minutes, what is the utilization of the workstation?
d. If the workstation processes two jobs at a time with an average process time for
server 1 (or machine 1) in the workstation of 2.5 minutes, and 5 minutes for server 2
(or machine 2), what is the utilization of the workstation?
2. Consider a workstation with 11 machines (in parallel), each with an average effective process
time of one hour with CV e2 = 5 . Each machine costs $10,000. Orders arrive at a rate of 10
per hour with CV a2 = 1 and must be filled. The maximum allowable average time-in-system
is two hours. Currently, it is a little more than three hours. Analyze the following options for
decreasing response time and make a recommendation.
a. Add another machine to the workstation at a cost of $10,000.
b. Modify the existing machines (all eleven) to make them faster. Assume the
coefficient of variation for the shorter effective processing times does not change.
The cost will be $8,500 and the new t = 0. 96 hours.
3. Consider two machines A and B that could be used at a workstation.
Avg. Effective Process Time
2
CV
e
Machine A 1.0 hour 0.25
Machine B 0.85 hours 5
e
a. For an arrival rate of 0.92 jobs per hour with CV
a2 = 1, which machine has a shorter
average time-in-system?
b. Double the number of machines and the arrival rate, leaving the CVs the same. What
happens to the average time-in-system for machine A vs. B and how does this compare to
part a?

4. Consider two machines (i.e., A and B) that are used at workstations 1 and 2, respectively,
arranged in series. Each workstation has a single machine.
Avg. Effective Process Time
2
CV
e
Machine A 1.0 hour 0.25
Machine B 0.85 hours 5
For an arrival rate of 0.92 jobs per hour with CV
a2 = 1, calculate the total system WIP and
TIS if:
a. The workstations are visited in the sequence 12.
b. The workstations are visited in the sequence 21.
5. Suppose in problem 4 that the sequence is 21, but now there are two machines at each
workstation with a single queue feeding both machines at each workstation. The average
effective processing times are double the values in problem 4, but the CVs are the same.
Estimate total system WIP and TIS.
6. Using the concepts of t
e
, ta
, CVe
, CVa
, explain the results of the following activities on TIQ.
a. Reducing the repair times at a workstation when it goes down during job processing.
b. Reducing the frequency of failures at a workstation through preventive maintenance.
c. Maintaining an inventory of different types of finished products to permit a similar
production schedule each day.
d. Producing small lots on a workstation with large setup times.
e. Accepting orders for a new product (in addition to existing production) that differs (has
larger times) in effective process time.

IE 368: Facility Design and Operations Management
Homework #4: Production System Design Concepts
Due Date: Tuesday, February 7 th , 2012
Name: _______________________________________________
1a) Utilization: __________________ %
1b) Utilization: __________________ %
1c) Utilization: __________________ %
1d) Utilization: __________________ %
RESULTS
2a) TIS = _________________ hrs Meets requirements?: YES NO
2b) TIS = _________________ hrs Meets requirements?: YES NO
3a) Machine A TIS: _________________ hrs
Machine B TIS: _________________ hrs
3b) Machine A TIS: _________________ hrs
Machine B TIS: _________________ hrs
4a) Total TIS: _________________ hrs
Total WIP: _________________ jobs
4b) Total TIS: _________________ hrs
Total WIP: _________________ jobs
5) Total TIS: _________________ hrs
Total WIP: _________________ jobs
6) Explain your answers on your workspace.