University of Texas OM 335 Spring 2014 Exam 1

Question 1.(10 points)
Consider
the Fishing Fleet and Cannery exercise. Suppose that fish is caught and brought
to the freezer
daily
according to the following pattern: (1) 100 tons/hr. between 8 a.m. and 10
a.m., (2) 150 tons/hr.
between
10 a.m. and noon, (3) and 100 tons/hr. between 1 p.m. and 5 p.m. Note that
there is no input
between
12 noon and 1 p.m. The processing capacity of the cannery is: (1) 100 tons/hr.
between 8 a.m.
and
noon, (2) 50 tons/hr. between noon and 2 p.m., and (3) 150 tons/hr. between 2
p.m. and 8 p.m.
(a)Assume that there is unlimited freezer space for unprocessed
fish.
(i) Draw an
inventory buildup diagram that shows fish inventory in the freezer starting at
8
a.m. and ending
at 8 p.m.

(ii) What is the
average inventory of fish in the freezer during 8 a.m.-8 p.m.?(1 point)

(iii) What is the average waiting time of fish
in the freezer(in minutes)?(1 point)

(iv)Consider
a fish that enters the freezer between 8 a.m. and 12 noon.What is the average
waiting time of such a fish in the freezer (in minutes)?(1 point)
0
50
100
150
8:00 AM
9:00 AM
10:00 AM
11:00 AM
12:00 PM
1:00 PM
2:00 PM
3:00 PM
4:00 PM
5:00 PM
6:00 PM
7:00 PM
8:00 PM
Inventory (tons)
Inventory (tons)
0
50
100
150
8:00 AM
9:00 AM
10:00…
11:00…
12:00…
1:00 PM
2:00 PM
3:00 PM
4:00 PM
5:00 PM
6:00 PM
7:00 PM
8:00 PM

Question 2.(10 points)
Physical
Examination on Hire- a chain of small clinics – has
contracted with a consortium of HMOs to conduct
physical
examination of prospective health insurance clients. The table below lists the
various tasks that need to
be
performed in a physical examination:
Task
Task Description Duration (in minutes)
1
Blood pressure, weight, temperature, etc. 5
2
Medical history 8
3
Nurse’s checkup 7
4
Lab work 7
5
Doctor’s consultation 6
6
Final report 9
For
any client: Task 6 has to follow every other task; Task 1 has to precede every
other task; Task 5 has to
follow
Tasks 1-4; and no two tasks can be performed at the same time.
The
current process is staffed with:
3
nurses, say A, B and C, with A performing tasks 1 and 2, B performing Tasks 3
and 4, and C
performing
Task 6; and
1
doctor, say D, who performs Task 5.
All
nurses are cross-trained to perform each other’s tasks. However, union rules
prohibit assigning a nurse to
more
than four different tasks. Task 5 can only be performed by the doctor who will
perform no other task. In
drawing
process flow diagrams for this problem please denote which employee is assigned
to which task by
writing
the initial of the employee (A, B, …) on top of the task notation.
(a)Currently, each client progresses through the six tasks in
the sequence 1-2-3-4-5-6.What is the system capacity (in clients/hour)?(1 point)Assuming adequate demand, what is the
overall labor utilization (in percentage)?(1
point)
System Capacity
Labor
Utilization =————–=

What would be
the overall utilization of nurses (in percentage) if clients arrive at the rate
of 3 per hour?(1 point)
Because
the arrival rate of clients is less than system capacity, the flow rate is
equal to the arrival rate of
2
clients per hour. So the cycle time is 20 minutes.
Labor Content
36
min.
—————-
=60%
(20
min.) (3)
Cycle Time #
Employees
Resource Capacity
(clients/hr.)
A
4.61
B
4.28
C
6.66
D
10
5
(b)Suppose that a fourth nurse (say E) is now available to you.
Redesign the process such that system
capacity
is maximized.Show
the new process flow diagram.(2
points)
What is the
system capacity (in clients/hour)?(1
point)
System Capacity
=>
What is the rush
order flow time (in minutes)?(1
point)

Suppose that one
of the four nurses, say A, is unavailable.
Show the new
process flow diagram.(2 points)What would be
the system capacity now?(1 point)
System Capacity
=>
Resource
Capacity (clients/hour)
Resource
Capacity (clients/hour)

Question 3.(20 points)
Consider
the Kristen’s Cookie Company (KCC) case when both you and your roommate are
working. Suppose that the sequence of processing stages stays the same, but the
duration of some of the process steps and labor assignment have changed. The
required sequence of steps and their durations are as follows:
Mixing
6 minutes of labor time for 1 dozen cookies;
8
minutes of labor time for 2 dozens of the same type of cookies;
10
minutes of labor time for 3 dozens of the same type of cookies;
Spooning
3 minutes of labor time per dozen cookies;
Baking
12 minutes of oven time per dozen cookies (1 minute of labor time to set up and
load the oven
followed
by 11 minutes of baking);
Cooling
8 minutes;
Packing
2 minutes of labor time per dozen cookies;
Payment
2 minutes of labor time per order.
There
is one other point of departure from the KCC case – your roommate will mix and
accept payment;
you
will spoon, set up and load the oven, and pack. You will also unload the oven
but we shall assume that this
activity
consumes negligible time and can be performed in the middle of doing something
else. Assume as we
did
in class that once you start a process step (mixing/spooning a
dozen/baking/packing a dozen/payment) you
have
to perform it without a break. Furthermore, assume that two identical ovens are
available for your use.
Answer
the following questions on the basis of the above information.
(a)Consider a particular day when each customer order is for
one dozen cookies.
(i) List the
resources (You, Roommate, Ovens) and show the capacity (in dozens per hour) of each.
(2 points)Identify the
bottleneck.(1 point)Note down the
steady-state system
capacity (in
dozens per hour).(1 point)

(ii) What is the steady-state utilization of
the ovens (in percentage)?(1 point)
(b)Suppose
that each customer order is for two dozen cookies of the same type.
(i) List the
resources (You, Roommate, Ovens) and show the capacity (in dozens per hour) of each.
(2 points)Identify the
bottleneck.(1 point)Note down the
steady-state system
capacity (in
dozens per hour).(1 point)

(ii) What is the steady-state utilization of
labor (in percentage)?(1 point)

(iii) What is the rush order flow time (in
minutes)? Explain.(2 points)

(iv) What is the cycle time (in minutes)?(1 point)

(c)Suppose
that each customer order is for three dozen cookies of the same type.
(i) List the
resources (You, Roommate, Ovens) and show the capacity (in dozens per hour) of
each.(2 points)Identify the bottleneck.(1 point)Note down the steady-state system
capacity (in
dozens per hour).(1 point)

(ii) What will be the rush order flow time if
your roommate is not working? Explain.
(2
points)
(iii) What is the cycle time (in minutes)?(1 point)