101
Assignment OPIM 2
Spring 2012
Instructions:
Submit your answers using the Take the Quiz link at the bottom of this page.
You must submit your assignment by 9:30am, Tuesday, February 14, 2012.
Late assignments receive zero credit.
You must submit your own assignment.
Your assignment is submitted only once you click the "submit" button!
Do NOT forget to click submit.
Once you click submit, you will be allowed to submit a different set of answers, if you
submit before the due date. However, ALL of your previous responses will be deleted if you click RESUBMIT, then you will have to type in all of your answers again.
To promote learning (and NOT the mere copying of answers), Spring 2012 OPIM 101
students are permitted to consult with one another while working on this assignment.
Make sure your answers are in the correct units.
Unless otherwise noted, report your answers to the 2nd decimal point (e.g., 4.04
rather than 4.1 or 4).
There are 10 questions in this assignment, each worth 1 point. There is no partial
credit.
(Q1-2) The local Department of Motor Vehicles issues new licenses and renews licenses. (See
the diagram below.) The office receives 110 customers per hours. All customers first see a
receptionist. The receptionist directs them in one of three directions. 75% go directly to Issue
License (staffed by 9 workers) where a new photo and license are done. 15% are required to
take an eye test (staffed by one worker) and 10% must first take a multiple-choice electronic
written test (on one of three computers). Only 85% of people pass the eye test and the
remaining 15% exit. The customers who pass the eye test proceed on to the Written Test.
10% of the people who take the written test fail it, while 90% pass the test and then proceed
to Issue License.
75%
Reception
15%
Eye Test
15%
Exit
Issue
License
Exit
85%
10%
90%
Written
Test
10%
Exit
Data on each station are provided in the following table:
Reception
Eye Test
Written Test
Issue License
Workers
1
1
3
9
Processing time per worker (min)
0.4
5
15
6
OPIM 101
Assignment 2
Spring 2012
Q1. What is the utilization of the Receptionist (as a %)?
Solution:
Reception
Eye Test
Written Test
Issue License
Wor
kers
1
1
3
9
Processin
g time
(min)
0.4
5
15
6
Flow rate
110
110*0.15=16.5
110*0.1+16.5*0.85=25.025
110*0.75+25.025*0.9=105.0225
Capacity
per hour
150
12
12
90
Implied
utilization
73
138%
209%
117%
Utilization of the receptionist = 73%.
Q2. What is the implied utilization of Issue License (as a %)?
Solution: the implied utilization of Issue License is 117%.
(Q3-4) The Yum and Yee food truck near the business school serves customers during lunch
hour by taking orders and making fresh batches of stir fry. Customers have only one choice
during the lunch hour, since the objective is to maximize the number of customers served.
Assume that each customer places just one lunch order, and all lunch orders are the same
size one unit of stir-fry.
The stir fry cooking works in this manner. First, a batch of orders is cooked in a wok by one
person. The cooking depends upon the number of order s in the batch. The time to cook just
one order is 3 minutes. For each additional order in the batch, it takes 0.5 minutes more to
cook. Thus, cooking two orders in a batch takes 3.5minutes, cooking three orders takes 4
minutes, and so on.
The other process is bagging and accepting payments (done by a separate person), which
takes 0.80 minutes per order.
Q3. If Yum and Yee operates with batch sizes of 8 units, what is their process capacity (in
orders per minute)?
Solution: the capacity for cooking: setup time is 2.5 min. processing time per order =
0.5min. The food truck produces 8 units with 2.5min + 0.5min*8=6.5min. The capacity is
8/6.5min=1.23units/min.
The capacity for bagging and accepting payments: 1min/0.8min=1.25units/min.
The process capacity is the capacity of cooking(bottleneck)=1.23unit/min.
OPIM 101
Assignment 2
Spring 2012
Q4. Calculate the batch size (in orders) that will maximize the overall flow rate (assume there
is ample demand)? Do NOT round the batch size (i.e., assume for this calculation that a noninteger batch size is possible).
Solution: optimal order size should equalize the capacity of the cooking step and the
bagging step. That is, suppose the batch size is denoted by x, then we have
(2.5+0.5*x)/x=0.8min. Solve for x, x=8.33 units/batch.
Or use the formula:
Capacity = 1/0.8min=1.25 orders/min
Batch size = Capacity * setup time / (1- capacity * processing time) = 1.25 * 2.5 / (1- 1.25 8.33 *
0.5)= units/batch.
(Q5-7) Sarahs Organic Soap Company makes four kinds of organic liquid soap - regular,
lavender, citrus and tea tree. Demand for the four scents are 150, 120, 75 and 50 kgs
per hour respectively. Sarahs production process can produce any soap at the rate of 450
kgs per hour but 1.5 hours are needed to switch between scents. During those switchover
times, the process doesnt produce any soap. Sarah wants to choose a production schedule
that (i) cycles repeatedly through the four scents, (ii) meets the required demand and (iii)
minimizes the amount of inventory held.
Q5. How many kgs of regular should Sarah produce before switching over to another scent?
Solution:
total setup time=1.5*4=6hours. Total demand for all four scents per hour =
150+120+75+50 =395 kgs/hour. The process capacity equals the demand, which is 395
kgs/hr. Processing time = 1/ 450 hr. Batch Size = capacity * setup time / (1- capacity *
processing time ) = 395 * 6 /( 1- 395/450)= 19390.91 kgs.
In each batch, 150/395*19390.91 =7363.636kgs of regular should be produced.
Q6. Sarah needs to purchase organic Palm oil to make her soaps. She needs 1,000 kgs of Palm
oil per day on average. The supplier charges a $60 delivery fee per order (which is
independent of the order size) and $4.75 per kg. Sarahs annual holding cost is 25%. Assume
52 weeks per year and 5 days per week. If Sarah wants to minimize inventory holding and
ordering costs, how much Palm oil should she purchase with each order (in kgs)?
Solution: Use EOQ formula, Q=sqrt(2*fixed cost*flow rate/holding cost) =
sqrt(2*$60*1000/($4.75*0.25/(52*5))) =5125.786 kgs.
OPIM 101
Assignment 2
Spring 2012
Q7. Sarahs supplier is willing to sell her Palm oil at a 5% discount if she purchases 10,000 kgs
at a time. If she were to purchase 10000 kgs per order what would be her average inventory
holding and delivery fees per day (in $s)? (Note, do NOT include her purchasing costs per day,
which would be 1000 x 4.75 x 95%.)
Solution:
delivery cost per day will be $60/(10,000kgs/1000kgs/day)=$6/day
The average inventory level is 10,000/2=5000kgs. Inventory cost per day will be $4.75 *(15%)*(25%/52/5)*5000kgs=$21.6947. The sum of the two is $27.6947
Q8. It is costly to hold inventory (e.g., storage costs, obsolescence costs, etc.) but inventory
can also be useful in a process because(choose the best answer)
a) Adding inventory to a process will shorten the average time a unit spends in a process.
b) Adding inventory to a process can increase the capacity of the process.
c) Adding inventory to a process is likely to increase quality.
d) None of the above
e) All of the above
Solution: B.
Adding inventory (or adding buffer) reduces chances that the process starving for items
to work on, thus improve the process capacity.
The average time that a unit spends in a process is the sum of processing time at each
step and the time spend waiting for servers to be available. Adding inventory will not
affect the processing time nor the waiting time, as waiting time is determined by the
processing time of each step. Thus, A is not correct. Inventory does not influence quality
either.
Q9. Which of the following most directly expresses the motivation behind the expression Do
not block the bottleneck!?
a) If the bottleneck has nothing to work on, the overall capacity of the process will be
lower than it could be.
b) If the bottleneck is prevented from working (e.g., it has nowhere to put its output), the
overall capacity will be reduced.
c) Blocking the bottleneck will increase the coefficient of variation of the arrival process,
which decreases capacity.
d) Blocking the bottleneck increases inventory turns, which increases the annual holding
costs.
e) It is not good to block the bottleneck because there are economies of scale in
inventory management.
Solution: B.
OPIM 101
Assignment 2
Spring 2012
Q10. Which of the following most directly expresses the motivation behind the expression
Buffer or Suffer?
a) Adding product variety to a process with setup times is likely to increase the average
amount of inventory needed.
b) To increase capacity, it is important to reduce setup times in a process.
c) If you want to increase the capacity of a process, add capacity f irst to the bottleneck.
d) If there is variability in the arrival process or in processing times, make sure there is
sufficient inventory between stages, otherwise capacity will be reduced.
e) When there are setup costs, producing in large enough batches is important to avoid
reducing capacity.
Solution: D.