test 1Suppose that you are using the simple mean to make a forecast.  This period’s forecast was equal to 200 units, and it was based on 5 periods of demand.  This period’s actual demand was 300 units.  What is your forecast for next period?5*200+3001300simple mean = 1300/6= 216.7 217 rounded answerThe school’s cafeteria has three service lines (pizza, salads, and sandwiches). The pizza line has one server and serves 90 pizzas per hour. The salad line has two servers and they handle 140 customers in 70 minutes. The sandwich line has three servers and they supply 360 sandwiches in 90 minutes. Which service line has the highest hourly productivity?Your answer should just note down one of the three lines pizza, salads, or sandwich? For instance, if you conclude that the salads line has the highest productivity you will just write salads in your answer.Pizza P P= O/ISalad P=O/Isandwich P=O/I90/1140/(70/60)*2360/(90/60)*390 pizzas per hour 140/2.33360/4.560 salads per hour 80 slalads per hour pizza is the highestSuppose that you want to set up a 3-month weighted moving average forecasting system.  You want the weights to be percentages (that add to 100%). Furthermore, you want weights for the most recent two months to be equal but you want each of those weights to be twice as large as the weight for the oldest month.  What should the weight be for the oldest month?x=2yso, x+x+y = 100%or 2y +2y + y =100%y=20%Which of the following would not be considered a core competency that a company might have:insuffcient distribution centerThe definition of quality that involves the product functioning as expected without failure is:realiability Cover Me, Inc. sells umbrellas in three cities.  Management assumes that annual rainfall is the primary determinant of umbrella sales, and it wants to generate a linear regression equation to estimate potential sales in other cities.  Given the data below, what is the forecast for 20 in. of rain? (Round your answer to the nearest whole number)                                                Rainfall                       Sales                                                      X                                Y    b=3(152400)-(78)(5100)/3(2340)-(78)^2            City A               36 in.                          2300b=63.5            City B               30 in.                          2000            City C               12 in.                            800y=63.5+50xSuppose that a product has two parts, both of which must be working in order for the product to function.  The reliability of the first part is .85, and the reliability of the second part is .82.  In addition, the second part comes with a backup that is 50% reliable.  What is the overall reliability of the product?  Please answer as a percentage to the second decimal place (so your answer should be of the form xx.xx%)0.82+0.5(1-0.82)=0.91(0.85)(0.91)=(0.7735)Which of the following forecasting methods would be most accurate if demand were rapidly decrea.

1. test 1Suppose that you are using the simple mean to make a
forecast. This period’s forecast was equal to 200 units, and it
was based on 5 periods of demand. This period’s actual demand
was 300 units. What is your forecast for next
period?5*200+3001300simple mean = 1300/6= 216.7 217
rounded answerThe school’s cafeteria has three service lines
(pizza, salads, and sandwiches). The pizza line has one server
and serves 90 pizzas per hour. The salad line has two servers
and they handle 140 customers in 70 minutes. The sandwich line
has three servers and they supply 360 sandwiches in 90 minutes.
Which service line has the highest hourly productivity?Your
answer should just note down one of the three lines
pizza, salads, or sandwich? For instance, if you conclude that
the salads line has the highest productivity you will just write
salads in your answer.Pizza P P= O/ISalad P=O/Isandwich
P=O/I90/1140/(70/60)*2360/(90/60)*390 pizzas per hour
140/2.33360/4.560 salads per hour 80 slalads per hour pizza is
the highestSuppose that you want to set up a 3-month weighted
moving average forecasting system. You want the weights to be
percentages (that add to 100%). Furthermore, you want weights
for the most recent two months to be equal but you want each of
those weights to be twice as large as the weight for the oldest
month. What should the weight be for the oldest
month?x=2yso, x+x+y = 100%or 2y +2y + y
=100%y=20%Which of the following would not be considered a
core competency that a company might have:insuffcient
distribution centerThe definition of quality that involves the
product functioning as expected without failure is:realiability
Cover Me, Inc. sells umbrellas in three cities. Management
assumes that annual rainfall is the primary determinant of
umbrella sales, and it wants to generate a linear regression
equation to estimate potential sales in other cities. Given the
data below, what is the forecast for 20 in. of rain? (Round your
answer to the nearest whole

2. number) Rainfall
Sales X
Y b=3(152400)-(78)(5100)/3(2340)-(78)^2 City
A 36 in. 2300b=63.5 City
B 30 in. 2000 City C
12 in. 800y=63.5+50xSuppose that a product
has two parts, both of which must be working in order for the
product to function. The reliability of the first part is .85, and
the reliability of the second part is .82. In addition, the second
part comes with a backup that is 50% reliable. What is the
overall reliability of the product? Please answer as a
percentage to the second decimal place (so your answer should
be of the form xx.xx%)0.82+0.5(1-
0.82)=0.91(0.85)(0.91)=(0.7735)Which of the following
forecasting methods would be most accurate if demand were
rapidly decreasing?3 month moving
averagehttps://howard.blackboard.com/webapps/assessment/revi
ew/review.jsp?attempt_id=_6260548_1&course_id=_1098933_1
&content_id=_2360185_1&outcome_id=_5990310_1&outcome_
definition_id=_901219_1https://howard.blackboard.com/webapp
s/assessment/review/review.jsp?attempt_id=_6260548_1&cours
e_id=_1098933_1&content_id=_2360185_1&outcome_id=_5990
310_1&outcome_definition_id=_901219_1
test 2Eight samples of n = 50 were taken by an operator at a
workstation in a production process. The number of defective
items in each sample was recorded as
follows. Sample Number of
Defects 1
10 2
0 3
12 4
8 5
10 6
16 7
14 8 101. What is the
upper control limit (round to 4 decimals)? [1]2. What is the

3. lower control limit (round to 4 decimals)? [2]3. Is the process in
control? [3]question 2Johnson Enterprises sells no-spill syrup in
bottles. The specification limits 11.95 and 12.05 ounces.
Management is evaluating four different machines with standard
deviations of each machine provided in the options
below. Check all the machines that are statistically
"capable."question 3Consider a p-chart measuring the
percentage of defective light bulbs. If the LCL is .04 and a
sample has 1% defects, what is the implication?question 4 The
best operating level is the volume of output that results in the
____________________.question 5A firm must choose between
remaining where it is, with current capacity, and building a new
facility with 50% more capacity. The probability of high
demand is estimated to be 75%. The current facility would
provide $100,000 profit if there is high demand or $50,000
profit if there is low demand. The replacement facility would
provide $160,000,000 profit if there is high demand but would
only break even if there is low demand. What is the expected
value of remaining where it is? [1] (answer in the format
$xxxxxxx, so $ sign and then numbers without "," as separator,
so if the answer is 50,000 it should be types as $50000)What is
the expected value of of building a new or replacement
facility? [2] (answer in the format $xxxxxxx, so $ sign and then
numbers without "," as separator, so if the answer is 50,000 it
should be types as $50000) question 6 One limitation with
quantitative forecasting models is:they are linited on a quality
of avaviable data question 7 A company used to produce 300
units every day, but 20% of the units were defective. After
installing a new process, the defect rate has been reduced to 5%,
while output has remained the same. What is the percent
increase in productivity due to installing the new process?
(Answer should be rounded to 2 decimals in the format
xx.xx%)Which of the following is not a factor in capacity
planning?labor hours consumed proximity to suppliers
https://howard.blackboard.com/webapps/assessment/review/revi
ew.jsp?attempt_id=_6263503_1&course_id=_1098933_1&conte

4. nt_id=_2378048_1&outcome_id=_5992371_1&outcome_definiti
on_id=_913056_1
test 3practice questions Howard University Hospital has a
current layout as follows (please assume each department
resides in its own block even if the borders are not showing in
the diagram and B and A are in adjacent blocks. Similarly E and
F are in adjacent blocks and so on and so forth):BACDEFThe
movement between departments is as follows:Table 10-11:
From-To Matrix for Howard University HospitalTrips between
DepartmentsDepartmentABCDEFA-5205-8B--301010C-20155D-
--E-17F-What is the ld-score of the current layout? [1]If
Howard University Hospital decides to swap departments A and
C (that is department A is moved to where department C is and
vice-versa), what would be the new ld-score? [2]Note: ld-score
is the total score used for evaluation of which layout is
considered to a better layoutTen samples of n = 200 were taken
by an operator at a workstation in a production process. The
number of defective items in each sample was recorded as
follows:SampleNumber of
Defects1122253104155166307288129111014To assess if the
process is in control:What is the UCL? [1] (format of answer
should be rounded to four decimals)What is the LCL? [2]
(format of answer should be rounded to four decimals)Is the
process in control? [3] (answer should be yes or no)Howard
University Hospital has a current layout as follows (please
assume each department resides in its own block even if the
borders are not showing in the diagram and B and A are in
adjacent blocks. Similarly E and F are in adjacent blocks and so
on and so forth):BACDEFThe movement between departments
is as follows:Table 10-11: From-To Matrix for Howard
University HospitalTrips between
DepartmentsDepartmentABCDEFA-5205-8B--301010C-20155D-
--E-17F-What is the ld-score of the current layout? [1]If
Howard University Hospital decides to swap departments A and
C (that is department A is moved to where department C is and
vice-versa), what would be the new ld-score? [2]Note: ld-score

5. is the total score used for evaluation of which layout is
considered to a better layout.You have your own
"Dunkin" manufacturing company that makes packaged mini-
donut box for sale. You operate 50 weeks in a year and the total
demand is 50,000 boxes. The setup costs are $21 and the
holding cost per box on an annual basis is $1. You
can make 1500 boxes in a week. How many mini-donut boxes
should you plan to produce each cycle? [1] (round your answer
to the nearest whole number)If Dunkin produces in batches of
1900, what is the penalty cost? [2] (note your answer to the
nearest whole number without the $ sign)Investments in
building or purchasing long-term production facilities are
inherently risky due to __________.You have a system with a
component reliability of 97.2%. If you can add a backup
component, what should be the reliability of the backup
component [1] to achieve a system reliability of 99.1%? (your
answer should be rounded to 1 decimal and in the formal xx.x%)
test 4Question #2LocationFixed Costs Variable Costs
A=BB=CC=DA$ 85,000.00260006666.66666666677500B$
55,000.007C$ 35,000.0010D$ 65,000.006Question #3average
weekly demand50unitsstandard deviation 8units95%1.645Safety
Stock13units (the correct answer is 26 you have to multiply by
2) therefore target inventory level= lead time demand +safety
stocklead time2weekslead time demand 100target inventory
level=113answer should be 226 again you have to multiply by 2
so correct answer safety stock = 26 units and target inventory
level = 226 Question 1 An auto-mechanic charges $60 per job.
Labor costs average $15 per job, materials costs are $20 per job,
and overhead costs are averaged at $20 per job.a. What is the
multifactor productivity ratio for the mechanic? What does your
finding mean?b. If the auto-mechanic reduces his overhead
costs by 25% all else remaining the same, what will be the
percentage change in productivity?problem and solution are
correct MFP1.09090909091.2Question #4 change
10.0917431193Using the information provided in the table
below, find the probability of completing the project in 44

6. weeks?probablilty 0.71problem and solution correct keep same
process Question 5 Given the following data, use exponential
smoothing with α = 0.2 and 2-period moving average to
generate forecasts for periods 2 through 4. Calculate MAD to
determine the better forecasting method. (In your answer, note
the MAD for both methods and then make a determination as to
which one is a better forecasting
method).PeriodActualForecastSigmamoving average 115170.22-
222187.510.510.532016.53.53.541619-
3319PeriodActualForecast MAD4.7511517-
2221816.61.41.432016.883.123.1241617.504-
1.5041.5048.024MAD2.006
chapters 3+4 (for test 5)chapter 4 Analysis will look at the
expected sales levels and cost of internal operations vs. cost of
purchasing the product or serviceTotal Cost of Outsourcing :T C
B u y = F C B u y + (V C B u y ´ Q ) Total Cost of Insourcing:T
C M a k e = F C M a k e + (V C M a k e ´ Q ) Indifference Point
:F C B u y + (V C B u y ´ Q ) = F C M a k e + (V C M a k e ´ Q
)example Mary and Sue decide to open a bagel shop. Their first
decision is whether they should make the bagels on- site or buy
the bagels from a local bakery. If they buy from the local
bakery they will need airtight containers at a fixed cost of
$1000 annually. They can buy the bagels for $0.40 each. If they
make the bagels in-house they will need a small kitchen at a
fixed cost of $15,000 annually. It will cost them $0.15 per bagel
to make. They believe they will sell 60,000 bagels.Mary and
Sue wants to know if they should make or buy the bagels?⚫
FCBuy + (VCBuy x Q) = FCMake + (VCMake x Q)⚫ $1,000 +
($0.40 x Q) = $15,000 + ($0.15 x Q)Q = 56,000 bagelsnext
steps total costs for 60000 buy
1000+0.4*600002500025000>24000total costs for 60000 make
better option would be to make 15000 +
0.15*6000024000chapter 3A company is planning to establish a
chain of movie theaters. It estimates that each new theater will
cost approximately $1 Million. The theaters will hold 500
people and will have 4 showings each day with average ticket

7. prices at $8. They estimate that concession sales will average $2
per patron. The variable costs in labor and material are
estimated to be $6 per patron. They will be open 300 days each
year.Break-Even PointWhat must average occupancy be to
break-even? Total revenues = Total costs @ break-even point Q
Selling price*Q = Fixed cost + variable cost*Q($8+$2)Q=
$1,000,000 + $6*QQ = 250,000 patrons (42% occupancy)⚫
What is the gross profit if they sell 300,000 ticketsProfit =
Total Revenue – Total CostsP = $10*300,000 – (1,000,000 +
$6*300,000) P = $200,000⚫ If concessions only average
$.50/patron, what is break-even Q now? (sensitivity
analysis)($8.50)Q = 1,000,000 - $6*QQ = 400,000 patrons (67%
occupancy)
Project Management
(Chapter 16)
Production & Operations Management
INFO 335-71
Week 4
Learning Objectives

8. f completing a project
by a specific time
effectively
management
Project Management Applications
• Any unique endeavor with specific objectives
• With multiple activities
• With defined precedent relationships
• With a specific time period for completion
• A major event like a wedding
• Any construction project
• Designing a political campaign
Project Life Cycle
Conception: identify the need

9. Network Planning Techniques
iew Technique (PERT):
• Developed to manage the Polaris missile project
• Used to determine a project’s planned completion
date and identify the critical path
• Developed to coordinate maintenance projects in the
chemical industry
• An algorithm for scheduling a set of project activities;
identification of the critical path/s (longest)
Network Planning Techniques –
Activity Time Estimates
Probabilistic
optimistic, most likely,
and pessimistic time
estimates

10. uncertainty about
duration
• Example: bad weather,
delays, unexpected labor
issues
Deterministic
duration is a known
certainty
estimates can be made
based on similar activities
in the past
PERT and CPM Benefits
relationships & sequence of activities
without delaying the project

11. non-critical activities
Network Diagrams
-on-Node (AON):
• Uses nodes to represent the activity
• Uses arrows to represent precedence relationships
Project Management and
Network Planning – 4 Steps
1. Describe the Project
a. Objective, project end date
b. Define project activities (resource requirements
such as labor, equipment, funds) and
precedence relationships
2. Diagram the Network
3. Estimate Project’s Completion Time
4. Monitor Project’s Progression
a. Quality, audit, measurements
Step 1-Define the Project: Cables By Us is bringing a
new product on line to be manufactured in their
current facility in existing space. The owners have
identified 11 activities and their precedence
relationships. Develop an AON for the project.

12. Activity Description
Immediate
Predecessor
Duration
(weeks)
A Develop product specifications None 4
B Design manufacturing process A 6
C Source & purchase materials A 3
D Source & purchase tooling & equipment B 6
E Receive & install tooling & equipment D 14
F Receive materials C 5
G Pilot production run E & F 2
H Evaluate product design G 2
I Evaluate process performance G 3
J Write documentation report H & I 4
K Transition to manufacturing J 2
Step 2- Diagram the Network
Cable By Us
Activity Description
A Develop product specifications
B Design manufacturing process
C Source & purchase materials
D Source & purchase tooling & equipment
E Receive & install tooling & equipment
F Receive materials
G Pilot production run
H Evaluate product design

13. I Evaluate process performance
J Write documentation report
K Transition to manufacturing
Step 3 (a) - Estimate Project’s
Completion Time
Add Deterministic Time Estimates and Connected Paths
Step 3 (a) - Estimate Project’s
Completion Time – cont’d
project’s duration (project cannot finish in less
time than its longest path)
Paths Path duration
ABDEGHJK 40
ABDEGIJK 41
ACFGHJK 22
ACFGIJK 23
Activity
A Develop product specifications
B Design manufacturing process
C Source & purchase materials
D Source & purchase tooling & equipment
E Receive & install tooling & equipment
F Receive materials

14. G Pilot production run
H Evaluate product design
I Evaluate process performance
J Write documentation report
K Transition to manufacturing
Some Network Definitions
-critical activities can be
delayed without delaying the project
its late start minus its early start)
preceding activity
(EF) = is the ES plus the activity time
activity can start (LS) or finish (LF) without delaying the
project completion
ES, EF Network (Deterministic)
LS, LF Network (Deterministic)
Delay H = LS – ES = 33 – 32 = 1 Week = LF

15. Calculating Slack
Step 3 (b) - Estimate Project’s
Completion Time
• Beta Probability Distribution model to calculate; definite
end points; weighted average for each activity
Step 3 (b) - Estimate Project’s
Completion Time – cont’d
Activity
Optimistic
tim e
M ost likely
tim e
Pessim istic
tim e
Expected
tim e
A 2 4 6 4
B 3 7 10 6.83
C 2 3 5 3.17
D 4 7 9 6.83

16. E 12 16 20 16
F 2 5 8 5
G 2 2 2 2
H 2 3 4 3
I 2 3 5 3.17
J 2 4 6 4
K 2 2 2 2
6
cpessimistilikelymost 4optimistic
timeExpected
Best Case Worst Case
Step 3 (b) - Estimate Project’s
Completion Time – cont’d
Network Diagram with Probabilistic expected activity times
Step 3 (b) - Estimate Project’s
Completion Time – cont’d
project has an expected duration of 44.83
weeks

17. Activities on paths Expected duration
ABDEGHJK 44.66
ABDEGIJK 44.83
ACFGHJK 23.17
ACFGIJK 23.34
ES, EF Network (Probabilistic)
Gantt Chart - Each Activity
Finished at the ES Date
LS, LF Network (Probabilistic)
Gantt Chart - Each Activity
Finished at the LS Date
Project Is to Be Completed in 44.83 Weeks
Step 4 – Monitor The Project’s
Progression
success/failures

18. slack, processes
improvements
Estimating The Probability
of Completion Dates
of predicting the probability of project completion dates
using three time estimates; Now we need to calculate
the variance for each activity
p=pessimistic activity time estimate
o=optimistic activity time estimate
2
2
6
op

19. Project Activity Variance
Activity Optimistic Most Likely Pessimistic Variance
A 2 4 6 0.44
B 3 7 10 1.36
C 2 3 5 0.25
D 4 7 9 0.69
E 12 16 20 1.78
F 2 5 8 1.00
G 2 2 2 0.00
H 2 3 4 0.11
I 2 3 5 0.25
J 2 4 6 0.44
K 2 2 2 0.00
Variances of Each Path
Through The Network

20. Path
Number
Activities on
Path
Path Variance
(weeks)
1 A,B,D,E,G,H,J,k 4.82
2 A,B,D,E,G,I,J,K 4.96
3 A,C,F,G,H,J,K 2.24
4 A,C,F,G,I,J,K 2.38
Calculating Probability of
Completing a Project in Less
Than a Specified Time
• The expected completion time
• Its variance
“X” weeks with the following formula:
Where
DT = the specified completion date
EFPath = the expected completion time of the path

21. 2
Pσ
EFD
time standard path
time expected pathtime specified
z
PT
Calculating Probability of
Completing a Project in Less
Than a Specified Time – cont’d
Example – 48 weeks
to determine probabilities

22. Path
Number
Activities on
Path
Path Variance
(weeks)
z-value Probability of
Completion
1 A,B,D,E,G,H,J,k 4.82 1.5216 0.9357
2 A,B,D,E,G,I,J,K 4.96 1.4215 0.9222
3 A,C,F,G,H,J,K 2.24 16.5898 1.000
4 A,C,F,G,I,J,K 2.38 15.9847 1.000
1.52
4.82
weeks 44.66weeks 48

23. Expected duration
0.00
0.0 0.5000
0.1 0.5398
0.2 0.5793
0.3 0.6179
0.4 0.6554
0.5 0.6915
0.6 0.7257
0.7 0.7580
0.8 0.7881
0.9 0.8159
1.0 0.8413
1.1 0.8643
1.2 0.8849
1.3 0.9032
1.4 0.9192
1.5 0.9332
1.6 0.9452
1.7 0.9554
1.8 0.9641
1.9 0.9713
2.0 0.9772
2.1 0.9821
2.2 0.9861
2.3 0.9893
2.4 0.9918
2.5 0.9938
2.6 0.9953
2.7 0.9965
2.8 0.9974
2.9 0.9981
3.0 0.9987

24. Reducing Project Completion Time
oject completion times may need to be shortened
because:
• Different deadlines
• Penalty clauses
• Need to put resources on a new project
• Promised completion dates
Reducing Project
Completion Time – cont'd
• Shorten a project duration
• Cost to shorten the project duration
• Normal activity time/costs
• Crash time/costs of each activity
• Activities on the critical path
Crash cost/duration = (crash cost-normal cost)/(normal time –
crash time)
Reducing Project Completion
Time With Crashing
Activity Normal
Time (wk)

25. Normal
Cost ($)
Crash
Time
Crash
Cost ($)
Max. weeks
of reduction
Reduce cost
per week
A 4 8,000 3 11,000 1 3,000
B 6 30,000 5 35,000 1 5,000
C 3 6,000 3 6,000 0 0
D 6 24,000 4 28,000 2 2,000
E 14 60,000 12 72,000 2 6,000
F 5 5,000 4 6,500 1 1500
G 2 6,000 2 6,000 0 0
H 2 4,000 2 4,000 0 0
I 3 4,000 2 5,000 1 1,000
J 4 4,000 2 6,400 2 1,200

26. K 2 5,000 2 5,000 0 0
Normal Time –
Crash Time
(Crash Cost – Normal Cost) /
(Normal Time – Crash Time)
Crashing Example: Suppose the
Cables By Us project manager wants to
reduce a product project from 41 to 36
weeks.
sidered to be linear
path first (based on cost per week)
• Crash activity I from 3 weeks to 2 weeks $1000
• Crash activity J from 4 weeks to 2 weeks $2400
• Crash activity D from 6 weeks to 4 weeks $4000
• Recommend Crash Cost $7400
Question: Will crashing 5 weeks return more in benefits
than it costs?
Crashed Network Diagram
The Critical Chain Approach

27. han on individual
activities and the following realities:
• Project time estimates are uncertain > add safety time
• Multi-levels of organization may add additional time to be
“safe”
• Individual activity buffers may be wasted on lower-priority
activities
• Best approach > place project safety buffer at the end
Original critical path
Activity A Activity B Activity C Activity D Activity E
Critical path with project buffer
Activity A Activity B Activity C Activity D Activity E Project
Buffer
Inventory
(Chapter 12)
Production & Operations Management
INFO 335-71
Week 3 and 4
2

28. Learning Objectives
⚫ Describe the different types and uses of
inventory
⚫ Describe the objectives of inventory
management
⚫ Calculate inventory performance measures
⚫ Understand relevant costs associated with
inventory
⚫ Perform ABC inventory control & analysis
⚫ Understand the role of cycle counting in
inventory record accuracy
3
Learning Objectives – cont'd
⚫ Understand inventory’s role in service
organizations
⚫ Calculate order quantities
⚫ Evaluate the total relevant costs of different
inventory policies

29. ⚫ Understand why companies don’t always use the
optimal order quantity
⚫ Understand how to justify smaller order sizes
⚫ Calculate appropriate safety stock inventory
policies
⚫ Calculate order quantities for single-period
inventory
Functions of Inventory
⚫ Geographical specialization allows us to specialize
production across different locations
⚫ Decoupling allows us to run processes for
maximum economic lot sizes within a single facility
⚫ Supply/Demand balancing accommodates the
elapsed time between inventory availability and
consumption
⚫ Buffering uncertainty accommodates uncertainty
related to
• Demand in excess of forecast or
• Unexpected delays in delivery (aka safety stock)

30. 5
Types of Inventory
© Wiley 2013 6
Objectives of Inventory Management
7
Inventory Investment Measures Example: The Coach
Motor Home Company has annual cost of goods sold
(COGS) of $10,000,000. The average inventory value
at any point in time is $384,615. Calculate inventory
turnover and weeks/days of supply.
⚫ Inventory Turnover:
⚫ Weeks/Days of Supply:
turnsinventory 26
$384,615
0$10,000,00

31. valueinventory average
sold goods ofcost annual
Turnover ===
2weeks
0/52$10,000,00
$384,615
dollarsin usage weekly average
dollarsin handon inventory average
Supply of Weeks ===
days 10
0/260$10,000,00
$384,615
Supply of Days ==
Relevant Inventory Costs
Name Definition
Item Cost Includes price paid for the item plus
other direct costs associated with
the purchase
Holding Costs Include the variable expenses
incurred by the plant related to the

32. volume of inventory held (15-25%)
Capital Costs The higher of the cost of capital or
the opportunity cost for the company
8
Relevant Inventory Costs – cont’d
Item Definition
Ordering/Setup
Cost
Fixed, constant dollar amount incurred
for each order placed
Shortage Costs Loss of customer goodwill, back order
handling, and lost sales
Risk costs
(Inventory
Shrink)
Obsolescence, damage, deterioration,
theft, insurance and taxes

33. Storage costs Included the variable expenses for
space, workers, and equipment related
to the volume of inventory held
9JIT – Just-in-time; VMI – Vendor managed inventory
10
Inventory Record Accuracy
⚫ Inaccurate inventory records can cause:
• Lost sales
• Disrupted operations
• Poor customer service
• Lower productivity
• Planning errors and expediting
11
Inventory Record Accuracy
⚫ Two methods for checking record accuracy:
• Cycle counting - daily counting of pre-specified items
provides the following advantages:
• Timely detection and correction of inaccurate records
• Elimination of lost production time due to unexpected

34. stock outs
• Structured approach using employees trained in cycle
counting
• Periodic counting - physical inventory is taken
periodically, usually annually
• Steps: Count, Verify, Collect tickets, Reconcile
Which type of counting method to use?
12
ABC Inventory Classification
ABC classification is a method for determining level of
control and frequency of review of inventory items
⚫ A Pareto analysis (80/20 rule) can be done to segment
items into value categories depending on annual dollar
volume
A Items typically 20% of the items accounting for 80% of the
inventory value-use Q system
B Items typically an additional 30% of the items accounting for
15%
of the inventory value-use Q or P
C Items Typically the remaining 50% of the items accounting

35. for
only 5% of the inventory value-use P
13
Example: The AAU Corp. is considering doing an
ABC analysis on its entire inventory but has
decided to test the technique on a small sample
of 15 of its SKU’s. The annual usage and unit
cost of each item is shown below
ABC Inventory Analysis Procedure
Step 1: Calculate the annual dollar usage for each item
Step 2: List the items in descending order based on
annual dollar usage
Step 3: Calculate the cumulative annual dollar volume
Step 4: Classify the items into groups
14

36. 15
Step 1. Calculate the
annual dollar volume for
each item
16
Step 2: Descending list/$ usage
Step 3: Calculate cumulative $
Step 4: Classify the ABC items
17
Graphical ABC Classification
of Materials
⚫ The A items (106 and
110) account for 60.5%
of the value and 13.3%
of the items
⚫ The B items
(115,105,111,and 104)
account for 25% of the
value and 26.7% of the
items

37. ⚫ The C items make up
the last 14.5% of the
value and 60% of the
items
⚫ How might you control
each item
classification?
Different ordering
rules for each?
AAU Corporation
18
Determining Order Quantities
Inventory management and control are managed
with SKU (stock control units)
Term Definition
Lot-for-lot Order exactly what is needed
Fixed-order quantity Specifies the number of units to order
whenever an order is placed
Min-max system Places a replenishment order when the on-
hand inventory falls below the predetermined
minimum level.
Order n periods Order quantity is determined by total

38. demand for the item for the next n periods
Replenishment policy – how much to order and when
19
Mathematical Models for
Determining Order Quantity
⚫ Economic Order Quantity (EOQ)
• An optimizing method used for determining order quantity
and reorder points
• Part of continuous review system which tracks on-hand
inventory each time a withdrawal is made
⚫ Quantity Discount Model
• Modifies the EOQ process to consider cases where
quantity discounts are available
⚫ Economic Production Quantity (EPQ)
• A model that allows for incremental product delivery
20
EOQ Assumptions
⚫ Demand is known & constant

39. - no safety stock is required
⚫ Lead time is known &
constant
⚫ No quantity discounts are
available
⚫ Ordering (or setup) costs are
constant
⚫ All demand is satisfied (no
shortages)
⚫ The order quantity arrives in a
single shipment
Economic Order Quantity,
essentially the quantity placed on
order with the supplier
Reorder Point
Saw-tooth model
21
Total Annual Inventory Cost with
EOQ Model (Q System)
Total annual cost =

40. annual ordering cost + annual holding costs
H
2DS
Q and H;
2
Q
S
Q
D
=

41. 22
Continuous (Q) Review System Example: A computer
company has annual demand of 10,000. They want to
determine EOQ for circuit boards which have an annual
holding cost (H) of $6/unit, and an ordering cost (S) of
$75. They want to calculate TC and the reorder point
(R) if the purchasing lead time is 5 days.
⚫ EOQ (Q)
⚫ Reorder Point (R)
⚫ Total Inventory Cost (TC)
units 500
$6
$75*10,000*2
H
2DS
Q ===
units 200days 5*
days 250
10,000

42. Time Leadx Demand DailyR ===
$3000$1500$1500$6
2
500
$75
500
10,000
=
Net operating days
23

43. Why Companies Don’t Always
Use Optimal Order Quantity
⚫ It is not unusual for companies to order less or
more than the EOQ for several reasons:
• They may not have a known uniform demand;
• Some suppliers have minimum order quantity that
are beyond the demand.
⚫ EOQ provides a benchmark for other policies; is
more expensive; need to justify
24
Justifying Smaller Order Quantities
⚫ JIT or “Lean Systems” would recommend reducing order
quantities to the lowest practical levels
⚫ Benefits from reducing Q’s:
• Improved customer responsiveness (inventory = Lead time)
• Reduced Cycle Inventory
• Reduced raw materials and purchased components
⚫ Justifying smaller EOQ’s:

44. ⚫ Reduce Q’s by reducing setup time. “Setup reduction” is a
well documented, structured approach to reducing S
H
2DS
Q =
25
Quantity Discount Model
⚫ Same as the EOQ model, except:
• Unit price depends upon the quantity ordered
⚫ The total cost equation becomes:

45. = H
2
Q
S
Q
D
TC
QD CD+
C = unit price
D = annual demand in units
26
Quantity Discount Procedure
⚫ 9 Steps
1. Calculate the EOQ at the lowest price
2. Determine whether the EOQ is feasible at
that price (Will vendor sell quantity at that price?)
3. If yes, stop – if no, continue
4. Check the feasibility of EOQ at the next
higher price

46. 27
Quantity Discount Procedure
- cont'd
5. Continue until you identify a feasible EOQ
6. Calculate the total costs (including total item
cost) for the feasible EOQ model
7. Calculate the total costs of buying at the
minimum quantity required for each of the
cheaper unit prices
8. Compare the total cost of each option &
choose the lowest cost alternative
9. Any other issues to consider?
28
Quantity Discount Example: Collin’s Sport store is
considering going to a different hat supplier. The
present supplier charges $10/hat and requires lots of
490 hats. The annual demand is 12,000 hats, the
ordering cost is $20, and the inventory carrying cost

47. is 20% of the hat cost, a new supplier is offering hats
at $9 in lots of 4000. Who should he buy from?
⚫ EOQ at lowest price $9. Is it feasible?
⚫ Since the EOQ of 516 is not feasible, calculate the total cost
(C) for
each price to make the decision
⚫ 4000 hats at $9 each saves $19,320 annually. Space?
hats 516
$1.80
20)2(12,000)(
EOQ$9 ==
( ) ( ) ( )
( ) ( ) ( ) $101,66012,000$9$1.80
2
4000
$20
4000
12,000
C
$120,98012,000$10$2
2
490
$20

48. 490
12,000
C
$9
$10
=++=
=++=
111,660
© Wiley 2013 29
Economic Production
Quantity (EPQ)
Same assumptions as the EOQ except: inventory arrives
in increments & draws down as it arrives
© Wiley 2013 30
Calculating EPQ
⚫ Total cost:
⚫ Maximum inventory:

49. • d=avg. daily demand rate
• p=daily production rate
⚫ Calculating EPQ
= H
2
I
S
Q
D
TC
MAX

50. EPQ
−=
p
d
1QI
MAX
−
=
p
d
1H

51. 2DS
EPQ
EXAM 3 – up until this point
31
32
Determining Safety Stock and
Service Levels
⚫ If demand or lead time is
uncertain, safety stock can be
added to improve order-cycle
service levels
• R = dL +SS
• Where SS =zσdL, and Z is the
number of standard deviations
and σdL is standard deviation of
the demand during lead time
⚫ Order-cycle service level
• The probability that demand
during lead time will not
exceed on-hand inventory

52. • A 95% service level (stockout
risk of 5%) has a Z=1.645
Normal Distribution
33
340.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279
0.5319 0.5359
0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675
0.5714 0.5753
0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064
0.6103 0.6141
0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443
0.6480 0.6517
0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808
0.6844 0.6879
0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157
0.7190 0.7224
0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486
0.7517 0.7549
0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794
0.7823 0.7852

53. 0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078
0.8106 0.8133
0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340
0.8365 0.8389
1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577
0.8599 0.8621
1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790
0.8810 0.8830
1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980
0.8997 0.9015
1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147
0.9162 0.9177
1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292
0.9306 0.9319
1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418
0.9429 0.9441
1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525
0.9535 0.9545
1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616
0.9625 0.9633
1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693
0.9699 0.9706
1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756
0.9761 0.9767

54. 2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808
0.9812 0.9817
2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850
0.9854 0.9857
2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884
0.9887 0.9890
2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911
0.9913 0.9916
2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932
0.9934 0.9936
2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949
0.9951 0.9952
2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962
0.9963 0.9964
2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972
0.9973 0.9974
2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979
0.9980 0.9981
2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985
0.9986 0.9986
3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989
0.9990 0.9990
How many σ
are needed for

55. a 99% service
level?
Z=2.33
What is the
service level
if .85 σ are
kept (z=.85)?
80%
35
Periodic Review Systems (P
System)
⚫ Orders are placed at specified, fixed-time intervals (e.g.
every Friday), for a order size (Q) to bring on-hand
inventory (OH) up to the target inventory (TI), similar to
the min-max system.
⚫ Advantages are:
• No need for a system to continuously monitor item
• Items ordered from the same supplier can be reviewed on
the same day saving purchase order costs

56. ⚫ Disadvantages:
• Replenishment quantities (Q) vary
• Order quantities may not qualify for quantity discounts
• On the average, inventory levels will be higher than Q
systems; more stockroom space needed
Fixed Time-Period Inventory System:
Cycle Stock, Safety Stock and Lead Time
Courtesy: Jacobe and Chase, Operations and SCM, 3e
T = Review Period or RP
L= Lead Time
T+L = Protection Period
Protection Period
37
Periodic Review Systems:
Calculations for TI
⚫
Demand for the bird feeder is normally distributed with a mean
of

57. 18 units per week and a standard deviation in weekly demand of
5
units. The review period is 4 weeks with a lead time of 2 weeks,
and the business operates 52 weeks per year. Calculate the
target
inventory level for a cycle-service level of 90 percent.
We now find the standard deviation of demand over the
protection
interval (P + L) = 6:
Before calculating TI, we also need a z value. For a 90 percent
cycle-service level z = 1.28. The safety stock becomes
Safety stock = zσRP + L = 1.28(12.25) = 15.68 or 16 units
We now solve for T:
= (18 units/week)(6 weeks) + 16 units = 124 units
T = Average demand during the protection interval + Safety
stock
= d(RP + L) + safety stock
units 12.2565 ==+=
+
LRP
dLRP

58. 39
Inventory Management Across
The Organization
⚫ Inventory management policies affect functional
areas throughout
• Accounting is concerned of the cost implications of
inventory
• Marketing is concerned as stocking decision affect
the level of customer service
• Information Systems tracks and controls inventory
records
• Other:
• Purchasing is concerned with workload
• Manufacturing is concerned with cost efficiency
BACKUP SLIDES
41
Customer Service Level

59. Measurements
⚫ Percentage of Orders Shipped on Schedule
• Good measure if orders have similar value (Doesn’t capture) .
• If one company represents 50% of your business but only 5%
of
your orders, 95% on schedule could represent only 50% of
value
⚫ Percentage of Line Items Shipped on Schedule
• Recognizes not all orders are equal, but doesn’t capture $
value
of orders. More expensive to measure. Ok for finished goods.
• A 90% service level might mean shipping 225 items out of the
total 250 line items totaled from 20 orders scheduled
⚫ Percentage Of $ Volume Shipped on Schedule
• Recognizes the differences in orders in terms of both line
items
and $ value
Customer Service
Unit fill rate = Total units delivered / Total units ordered
Line fill rate = # of order lines delivered complete / Total
order lines

60. Order fill rate = Total complete orders delivered / Total
orders
(Orders shipped complete)
42
Customer Service
⚫Fill rate example
43
Orders
Received
Total
Units
Ordered
Total
Order
Lines
Total
Units

61. Delivered
Total
Complete
Order
Lines
Delivered
Total
Complete
Orders
Delivered
1,000 20,000 5,000 19,500 4,800 910
What is the Unit Fill Rate?
Line Fill Rate?
Order Fill Rate?
44
Single Period Inventory Model
⚫ The SPI model is designed for products that share the

62. following characteristics:
• Sold at their regular price only during a single-time period
• Demand is highly variable but follows a known probability
distribution
• Salvage value is less than its original cost so money is lost
when these products are sold for their salvage value
⚫ Objective is to balance the gross profit of the sale of
a unit with the cost incurred when a unit is sold after
its primary selling period
Extra Material
45
SPI Model Example: T-shirts are purchase in multiples
of 10 for a charity event for $8 each. When sold
during the event the selling price is $20. After the
event their salvage value is just $2. From past events
the organizers know the probability of selling
different quantities of t-shirts within a range from 80
to 120

63. Payoff Table
Prob. Of Occurrence .20 .25 .30 .15 .10
Customer Demand 80 90 100 110 120
# of Shirts Ordered Profit
80 $960 $960 $960 $960 $960 $960
90 $900 $1080 $1080 $1080 $1080 $1040
Buy 100 $840 $1020 $1200 $1200 $1200 $1083
110 $780 $ 960 $1140 $1320 $1320 $1068
120 $720 $ 900 $1080 $1260 $1440 $1026
Sample calculations:
Payoff (Buy 110)= sell 100($20-$8) –((110-100) x ($8-$2))=
$1140
Expected Profit (Buy 100)= ($840 X .20)+($1020 x .25)+($1200
x .30) +
($1200 x .15)+($1200 x .10) = $1083
Extra Material
Facility Layout
(Chapter 10)
Production & Operations Management

64. INFO 335-71
Week 3
2
Learning Objectives
⚫ Define layout planning and explain its importance
⚫ Identify and describe different types of layouts
⚫ Compare process layouts & product layouts
⚫ Describe the steps involved in designing a process
layout
⚫ Describe the steps involved in designing a product
layout
⚫ Define the meaning of group technology (cell)
layouts
3
Types of Layouts
⚫ Four basic layout types:
• Process layouts - Group similar resources

65. together based on similar processes/functions
• Product layouts - Designed to produce a specific
product efficiently
• Hybrid layouts - Combine aspects of both
process and product layouts
• Fixed-Position layouts - Product is too large to
move; e.g. a building
4
Process vs. Product Layouts
Characteristic differences:
5
Designing Process Layouts
Step 1: Gather information:
Space needed, space available, identify closeness
measures (From-to Matrix, REL, SLP)
Step 2: Develop alternative block plans:
Using trial-and-error or decision support tools (load-
distance model, ALDEP, CRAFT)
Step 3: Develop a detailed layout:

66. Consider exact sizes/shapes of departments and work
centers including aisles and stairways
Tools like drawings, 3-D models, and CAD software
are available to facilitate this process
Load-Distance Model
6
Warehouse Layout
7
Warehouse Layout
8
Trips/block
9
Designing Product Layouts
⚫ Designing product layouts requires consideration of:
• Sequence of tasks to be performed by each workstation

67. • Logical order
• Speed considerations – line balancing
WS1 WS2 WS3 WS4
Work In-
process
Inventory
t t t t
Raw After
WS1
After
WS2
After
WS3
Finished
Product
10
Designing Product Layouts – cont'd
Step 1: Identify tasks & immediate predecessors

68. Step 2: Determine output rate
Step 3: Determine cycle time
Step 4: Compute the Theoretical Minimum number
of Stations
Step 5: Assign tasks to workstations
(balance the line)
Step 6: Compute efficiency, idle time &
balance delay
11
Step 1: Identify Tasks &
Immediate Predecessors
Example 10.4 Vicki's Pizzeria and the Precedence Diagram
Immediate Task Time
Work Element Task Description Predecessor (seconds
A Roll dough None 50
B Place on cardboard backing A 5
C Sprinkle cheese B 25

69. D Spread Sauce C 15
E Add pepperoni D 12
F Add sausage D 10
G Add mushrooms D 15
H Shrinkwrap pizza E,F,G 18
I Pack in box H 15
Total task time 165
Precedence Diagram
bottleneck
12
Step 2: Determine Output Rate
⚫ Output Rate is the number of units to be produced
over a specific period of time
• Vicki needs to produce 60 pizzas per hour
• Vicki will need to divide the work among a number of
people simultaneously at workstations
⚫ The goal is to design a product layout that can
produce the desired number of units with the least

70. amount of work centers and a balance of workload
hourper pizzas 8.12
sec./unit 165
sec./hr. 3600
output M aximum ==
Minimum
13
Step 3: Determine Cycle Time
⚫ Determine cycle time calculations
• The amount of time each workstation is allowed to
complete its tasks
• Limited by the bottleneck task (the longest task):
• Minimum cycle time = bottleneck (50 sec.)
• Maximum cycle time = sum of the task times (165
sec.)
( )
( )
sec./unit 60
units/hr 60
sec/min 60x min/hr 60

71. units/hroutput desired
sec./day time available
)(sec./unit time Cycle ===
hourper pizzas 72
sec./unit 50
sec./hr. 3600
output Maximum ==
Seconds/hr
60 pizzas per hour
60 pizzas per 3600 seconds
1 pizza every 3600/60 = 60 seconds
14
Step 4: Theoretical Minimum
Number of Stations
⚫ Computing the theoretical minimum (TM) number
of stations
• TM = number of stations needed to achieve 100%
efficiency (every second is used)
• Always round up (no partial workstations)
• Serves as a lower bound for our analysis

72. ( )
stations 3or 2.75,
itseconds/un 60
itseconds/un 165
timecycle
task times
TM ===
Round it up
15
Step 5: Assign Tasks to
Workstations
⚫ Assigning tasks to workstations (Balance the Line)
• Start at the first station & choose the longest eligible task
following
precedence relationships
• Continue adding the longest eligible task that fits without
going over the
desired cycle time
• When no additional tasks can be added within the desired
cycle time,
begin assigning tasks to the next workstation until finished

73. Workstation Eligible task Task Selected Task time Idle time
A A 50 10
B B 5 5
C C 25 35
D D 15 20
E, F, G G 15 5
E, F E 12 48
F F 10 38
H H 18 20
I I 15 5
1
2
3
WS1
WS2
WS3
16

74. Step 6: Efficiency and Balance
Delay
⚫ Computing efficiency and balance delay
• Efficiency (%) is the ratio of total productive time
divided by total time
• Balance delay (%) is the amount by which the line
falls short of 100%
( ) 91.7%100
sec. 60x stations 3
sec. 165
NC
t
(%) Efficiency ===
8.3%91.7%100%delay Balance =−= (15/180)*100
17
Other Product Layout
Considerations
⚫ Shape of the line (S, U, O, L):
• Share resources, enhance communication & visibility,

75. impact location of loading & unloading
⚫ Paced versus Un-paced lines
• Paced lines use an automatically enforced cycle time
• Un-paced has more autonomy; product may be
removed off assembly line
⚫ Number of Product Models produced
• Single-model lines – one version of a product
• Mixed-model lines – many versions of a product
© Wiley 2013 18
Group Technology
(CELL) Layouts
⚫ One of the most popular hybrid layouts uses Group
Technology
(GT) and a cellular layout
⚫ GT has the advantage of bringing the efficiencies of a
product layout
to a process layout environment
19
Problem – Facility Layout
•The items listed below are stored in a one-dock warehouse.

76. How should the item
areas be allocated to the warehouse layout below (assume all
blocks are equal in
area)?
Item Trips Area Needed (blocks)
A 300 2
B 220 1
C 72 1
D 50 1
E 24 1
Dock
XYZ Company is designing a new product layout. It plans to
use this
production line eight hours a day in order to meet a schedule of
50 units
per hour. The task necessary to produce this product are
detailed in the
table below,
(a) Draw the precedence Diagram 3pt
(b) What is the required cycle time (seconds) in order to meet
the
schedule? 2pts
(c) What is the minimum number of work stations needed to
meet the

77. Schedule? 2pts
(d) Balance the line by assigning tasks to workstations 3pts20
Problem – Product Layout
Task Predecessor Time (seconds)
A - 50
B A 36
C B 26
D - 52
E C,D 70
F C,E 30
Capacity Planning & Facility Location
(Chapter 9)
Production & Operations Management
INFO 335-71
Week 2

78. 2
Learning Objectives
⚫ Define capacity planning
⚫ Define location analysis
⚫ Describe the decision support tools used for capacity
planning
⚫ Identify key factors in location analysis
⚫ Describe the decision support tools used for location
analysis
3
Capacity Planning
⚫ Capacity is the maximum output rate of a facility
⚫ Capacity planning is the process of establishing
the output rate that can be achieved at a facility:
• Capacity is usually purchased in “chunks”
• Strategic issues: how much and when to spend capital for
additional facility & equipment
• Tactical issues: workforce & inventory levels, & day-to-day
use of equipment

79. 4
Measuring Capacity Examples
⚫ There is no one best way to measure capacity
⚫ Output measures like kegs per day are easier to
understand
⚫ With multiple products, input measures work better
Type of Business
Input Measures of
Capacity
Output Measures
of Capacity
Car manufacturer Labor hours Cars per shift
Hospital Available beds Patients per month
Pizza parlor Labor hours Pizzas per day
Retail store
Floor space in
square feet
Revenue per foot

80. Measuring Capacity
⚫ Two types of information needed:
1. Amount of available capacity
▪ design capacity (max. possible output rate
▪ effective capacity (max. sustainable output rate)
2. Effectiveness of capacity use
▪ How effectively we are using the available capacity
5
( )100%
capacity
rateoutput actual
nUtilizatio =
6
Example of Computing Capacity Utilization: A bakery’s
design capacity is 30 custom cakes per day with an
effective capacity of 20 per day. Currently the bakery
is producing 28 cakes per day. What is the bakery’s

81. capacity utilization relative to both design and
effective capacity?
93%(100%)
30
28
(100%)
capacity design
output actual
nUtilizatio
140%(100%)
20
28
(100%)
capacity effective
output actual
nUtilizatio
design
effective
===
===
⚫ The current utilization is only slightly below its design
capacity and

82. considerably above its effective capacity
⚫ The bakery can only operate at this level for a short period of
time
7
Capacity Considerations - Best
Operating Level and Size
⚫ When expanding capacity, there are two alternatives:
1. Purchase one large facility, requiring one large initial
investment
2. Add capacity incrementally in smaller chunks as needed
Fixed Cost = $100,000
Variable Cost =
$2/unit
If you produce 150,000 units, then total cost = 100,000 +
150,000*2 =
$400,000
Per unit cost = $400,000/150,000 units = $2.67/unit
8

83. Making Capacity Planning
Decisions
The three-step procedure for making capacity planning
decisions is as follows:
1. Identify Capacity Requirements
2. Develop Capacity Alternatives
3. Evaluate Capacity Alternatives
9
Decision Trees
Diagramming technique
• Decision points – points in time when decisions are
made, squares called nodes
• Decision alternatives – branches or arrows leaving a
decision point (nodes)
• Chance events – events that could affect a decision,
branches or arrows leaving circular chance nodes
• Outcomes – each possible alternative listed
10

84. Example Using Decision Trees: A restaurant owner has
determined that she needs to expand her facility.
Alternatives are to expand large now and risk smaller
demand, or expand on a smaller scale now, knowing
that she might need to expand again in three years.
Which alternative would be most attractive?
D1 – Expand Small: High Demand (O1 = 200,000, p1 = .7); Low
Demand (O2 = 80,000, p2 = .3)
Expected Value (D1) = ∑Oi*Pi = O1*p1 + O2*p2 = 200,000*.7
+ 80,000*.3
11
Evaluating the Decision Tree
⚫ Refer to previous slide
• Calculate Expected Value (EV) of small expansion:
• EVsmall = 0.30($80,000) + 0.70($200,000) = $164,000
• Calculate EV of large expansion:
• EVlarge = 0.30($50,000) + 0.70($300,000) = $225,000
Take the calculated risk!

85. 12
Location Analysis
⚫ Three most important factors in real estate: Location,
Location, Location
⚫ Facility location is the process of identifying the best
geographic location for a service or production facility
⚫ Long term commitment
⚫ Sizable financial investment and impact
13
Factors Affecting Location Decisions
⚫ Proximity to source of supply
⚫ Proximity to customers
⚫ Proximity to labor
⚫ Community considerations
⚫ Site considerations
⚫ Quality-of-life issues
⚫ Other considerations:

86. • Options for future expansion, local competition,
transportation access and congestion, etc.
⚫ Globalization
14
Making Location Decisions
⚫ Analysis should follow 3 step process:
1. Identify dominant location factors
2. Develop location alternatives
3. Evaluate locations alternatives
⚫ Procedures/tools for evaluating location alternatives
include
• Factor rating method
• Load-distance model
• Center of gravity approach
• Break-even analysis
15
Factor Rating (with example)
A procedure to evaluate multiple alternative locations
based on a number of selected factors.

87. 16
A Load-Distance Model Example: Matrix Manufacturing
is considering where to locate its warehouse to service
its four Ohio stores located in Cleveland, Cincinnati,
Columbus, Dayton. Two sites are being considered;
Mansfield and Springfield, Ohio.
Use the load-distance model to make the decision.
⚫ Calculate the rectilinear distance:
⚫ Multiply by the number of loads between each site and four
cities
miles 4515401030dAB =−+−=
A procedure for evaluating location alternatives based on
distance.
Dayton-Mansfield = |3 – 11| + |6 -14| = 16
17
Calculating Load-Distance Score:
Springfield vs. Mansfield
⚫

88. The load-distance score for Mansfield is higher than for
Springfield. The
warehouse should be located in Springfield.
Computing the Load-Distance Score for Springfield
City Load Distance ld
Cleveland 15 20.5 307.5
Columbus 10 4.5 45
Cincinnati 12 7.5 90
Dayton 4 3.5 14
Total Load-Distance Score(456.5)
Computing the Load-Distance Score for Mansfield
City Load Distance ld
Cleveland 15 8 120
Columbus 10 8 80
Cincinnati 12 20 240
Dayton 4 16 64
Total Load-Distance Score(504)

89. 18
The Center of Gravity Approach
Requires the analyst to find the center of gravity of the
geographic area
being considered for an alternative site.
⚫ Computing the Center of Gravity for Matrix Manufacturing
⚫ Is there another possible warehouse location closer to the
C.G. that
should be considered?? Why?
10.6
41
436
l
Yl
Y ; 7.9
41
325
l
Xl
X
i
ii

90. c.g.
i
ii
c.g. ======
19
Example using Break-even Analysis: Clean-Clothes
Cleaners is considering four possible sites for its new
operation. They expect to clean 10,000 garments. The
table and graph below are used for the analysis.
Example 9.6 Using Break-Even Analysis
Location Fixed Cost ($) Variable Cost ($) Total Cost ($) for
Quanity Q
A 350,000.00 5 350,000 + 5*Q
B 170,000.00 25 170,000 + 25*Q
C 100,000.00 40 100,000 + 40*Q

91. D 250,000.00 20 250,000 + 20*Q
⚫ Breakeven point or point of
indifference:
100,000 + 40*Q = 170,000 +25*Q
40Q – 25Q = 170,000 – 100,000
15Q = 70,000
Q = 4667 A: 350,000 + 5*Q = 350,000 + 5*9000 = 350,000 +
45,000 = 395,000
B: 170,000 +25*Q = 170,000 + 25*9000 = 170,000 + 225,000 =
395,000
Forecasting
(Chapter 8)
Production & Operations Management
INFO 335-71
Week 1
2

92. Learning Objectives
⚫ Identify Principles of Forecasting
⚫ Explain the steps in the forecasting process
⚫ Identify types of forecasting methods and their
characteristics
⚫ Describe time series and causal models
⚫ Generate forecasts for data with different patterns:
level, trend, seasonality, and cyclical
⚫ Describe causal modeling using linear regression
⚫ Compute forecast accuracy
⚫ Explain how forecasting models should be selected
3
Principles of Forecasting
Many types of forecasting models differ in complexity
and amount of data & way they generate forecasts.
Common features include:
1. Forecasts are rarely perfect
2. Forecasts are more accurate for grouped
data than for individual items

93. 3. Forecast are more accurate for shorter than
longer time periods
Steps in the Forecasting Process
1. Determine the purpose of the forecast
2. Establish a time horizon
3. Select a forecasting technique
4. Obtain, clean, and analyze appropriate data
5. Make the forecast
6. Monitor the forecast
5
Types of Forecasting Models
⚫ Qualitative methods – judgmental methods
• Forecasts generated subjectively by the forecaster
• Educated guesses
⚫ Quantitative methods – based on mathematical
modeling:
• Forecasts generated through mathematical

94. modeling
Executive Decisions : Market Research : Delphi Method
Time Series : Causal/Associative Method
6
Time Series Models
⚫ Forecaster looks for data patterns as
• Data = historic pattern + random variation
⚫ Historic pattern to be forecasted:
• Level (long-term average) – data fluctuates around a constant
mean
• Trend – data exhibits an increasing or decreasing pattern
• Seasonality – any pattern that regularly repeats itself and is of
a constant length
• Cycle – patterns created by economic fluctuations
⚫ Random Variation cannot be predicted
P
A
T
T

95. E
R
N
7
Time Series Models
⚫ Naive:
⚫ Simple Mean:
⚫ Simple Moving Average:
tA=
+1t
F
n/AF
t1t
n/AF
8
Time Series Models cont'd
⚫ Weighted Moving Average:

96. • Method in which “n” of the most recent observations
are averaged and past observations may be
weighted differently
• All weights must add to 100% or 1.00
e.g. Ct .5, Ct-1 .3, Ct-2 .2 (weights add to 1.0)
• Allows emphasizing one period over others; above
indicates more weight on recent data (Ct=.5)
• Differs from the simple moving average that weighs
all periods equally - more responsive to trends
Weights
⚫ Future period is
Wednesday – create a
forecast (t+1)
⚫ Tuesday’ Demand = 50
widgets (t)
⚫ Monday’ Demand = 40
widgets (t-1)
9

97. Simple 2-period Moving Average
= (50+40)/2 = 45
=50/2 + 40/2
=(1/2)*50 + (1/2)*40
=.5*50 + .5*40
2-period Weighted Moving Average
60% weight to the most recent period of
demand, and 40% to the next most recent
Weights in the ratio 6:4 with greater
weight to the more recent period
=0.6*50 + 0.4*40 = 30 + 16 = 46 widgets
10
Time Series Models cont'd
⚫ Exponential Smoothing:
• Most frequently used time series method because of
ease of use and minimal amount of data needed
• Need just three pieces of data to start:
• Last period’s forecast (Ft)
• Last periods actual value (At)

98. • Select value of smoothing coefficient, ,between 0 and 1.0
• If no last period forecast is available, average the last
few periods or use naive method
• Higher values (e.g. .7 or .8) place a lot of weight on
current periods actual demand and influenced by
random variation
( )
tt1t
Fα1αAF −+=
+
Exponentially Weighted Moving Average (EWMA)
11
Time Series Problem
Determine forecast for periods 7 &
8:
⚫ 2-period moving average - 340

99. ⚫ 4-period moving average
⚫ 2-period weighted moving average
with t-1 weighted 0.6 and t-2
weighted 0.4 - 344
⚫ Exponential smoothing with
alpha=0.2 and the period 6 forecast
being 375
Period Actual
1 300
2 315
3 290
4 345
5 320
6 360
7 375
8
( )
tt1t
Fα1αAF −+=

100. +
375
372
372.6
12
Time Series Problem
Solution
Period Actual 2-Period 4-Period 2-Per.Wgted.
Exponential
Smoothing
1 300
2 315

101. 3 290
4 345
5 320
6 360
7 375 340.0 328.8 344.0 372.0
8 367.5 350.0 369.0 372.6
13
Questions?
Which of the following is the least useful sales forecasting
model to use
when sales are increasing?
a) Simple mean
b) Exponential smoothing

102. c) Weighted moving average
d) Naïve
Over the long term, which of the following forecasting models
will likely
require carrying the least amount of data?
a) Naïve
b) Simple mean
c) Exponential smoothing
d) Weighted moving average
e) Moving average
14
Questions?

103. Suppose that Sally’s company uses exponential smoothing to
make forecasts. Further
suppose that last period’s demand forecast was for 20,000 units
and last period’s
actual demand was 21,000 units. Sally’s company uses a
smoothing constant (α)
equal to 40%. What should be the forecast for this period?
a) 20,000
b) 21,000
c) 20,600
d) 20,400
e) 19,600
Suppose that you are using the four-period weighted moving
average forecasting
method to forecast sales and you know that sales will be

104. increasing every period for
the foreseeable future. What of the following would be the best
set of weights to use
(listed in order from the most recent period to four periods ago,
respectively)?
a) 0.25, 0.25, 0.25, 0.25
b) 0.40, 0.30, 0.20, 0.10
c) 1.00, 0.00, 0.00, 0.00
d) 0.10, 0.20, 0.30, 0.40
e) 0.00, 0.00, 0.00, 1.00.
15
Questions?
⚫ In exponential smoothing, what values can the smoothing

105. ⚫ a) [−1, 1]
⚫
⚫
⚫ d) [0, 1]
⚫
16
Linear Trend Line
⚫ A time series technique that computes a
forecast with trend by drawing a straight line
through a set of data using this formula:
Y = a + bx
where
Y = forecast for period X

106. X = the number of time periods from X = 0
A = value of y at X = 0 (Y intercept)
B = slope of the line
17
Causal Model - Linear Regression
( )( )
−
−
=
XXX
YXXY

107. b
2
⚫ Identify dependent (y) and
independent (x) variables
⚫ Solve for the slope of the line
⚫ Solve for the y intercept
⚫ Develop your equation for
the trend line
Y=a + bX
XbYa −=
−

108. −
=
2
2
XnX
YXnXY
b
18
Linear Regression Problem: A maker of golf shirts has
been tracking the relationship between sales and
advertising dollars. Use linear regression to find out
what sales might be if the company invested $53,000
in advertising next year.

109. −
−
=
2
2
XnX
YXnXY
bSales $
(Y)
Adv.$
(X)
XY X^2 Y^2
1 130 32 4160 1024 16,900
2 151 52 7852 2704 22,801

110. 3 150 50 7500 2500 22,500
4 158 55 8690 3025 24964
5 153.85 53
Tot 589 189 28202 9253 87165
Avg 147.25 47.25
( )( )
( )
( )
( ) 153.85531.1592.9Y
1.15X92.9bXaY
92.9a
47.251.15147.25XbYa
1.15
47.2549253

111. 147.2547.25428202
b
2
=+=
+=+=
=
−=−=
=
−
−
=
19
Correlation Coefficient -

112. How Good is the Fit?
⚫ Correlation coefficient (r) measures the direction and
strength of the linear
relationship between two variables. The closer the r value is to
1.0 the better
the regression line fits the data points.
⚫ Coefficient of determination ( ) measures the amount of
variation in the
dependent variable about its mean that is explained by the
regression line.
Values of ( ) close to 1.0 are desirable.
( ) ( )( )
( ) ( ) ( ) ( )
( ) ( )
( ) ( )

113. ( ) .964.982r
.992
58987,1654*(189)-4(9253)
58918928,2024
r
YYn*XXn
YXXYn
r
22
22
2
2
2
2
==

114. =
−
−
=
−−
−
=
2
r
2
r
20

115. Questions?
What are the two categories of quantitative models?
a) Delphi and non-causal
b) Causal and non-causal
c) Delphi and time series
d) Causal and time series
e) Causal and Delphi
A causal research model is based on the assumption that
a) the independent variable is related to the dependent variable
b) there is a relationship between the time series and the
dependent variable
c) the variable being forecast is related to other variables in the
environment
d) there is a relationship between the time series and the

116. independent
variable
e) the information is contained in a time series of data
Techniques for Seasonality
⚫ Seasonality – regularly repeating movements in series
values that can be tied to recurring events
• Expressed in terms of the amount that actual values
deviate from the average value of a series
• Models of seasonality
• Additive
• Seasonality is expressed as a quantity that gets added to or
subtracted from the time-series average in order to
incorporate seasonality
• Multiplicative
• Seasonality is expressed as a percentage of the average (or

117. trend) amount which is then used to multiply the value of a
series in order to incorporate seasonality
21
Models of Seasonality
22
⚫ A coffee shop owner wants to predict quarterly demand for
hot chocolate for periods 9 and 10, which happen to be the
1st and 2nd quarters of a particular year. The sales data
consist of both trend and seasonality. The trend portion
of demand is projected using the equation Ft = 124 + 7.5 t.
Quarter relatives are

118. Q1 = 1.20, Q2 = 1.10, Q3 = 0.75, Q4 = 0.95,
Seasonal Relatives Example
20
⚫ Use this information to predict for periods 9 and 10.
⚫ F9 = 124 +7.5( 9) = 191.5
F10= 124 +7.5(10) = 199.0
Multiplying the trend value by the appropriate quarter relative
yields a forecast that includes both trend and seasonality.
Given that t =9 is a 1st quarter and t = 10 is a 2nd quarter.
The forecast demand for period 9 = 191.5(1.20) = 229.8
The forecast demand for period 10 = 199.0(1.10) = 218.9

119. Seasonal Relatives Example
(cont’d)
22
25
Measuring Forecast Error
⚫ Forecasts are never perfect
⚫ Need to measure over time
⚫ Need to know how much we should rely on
our chosen forecasting method
⚫ Measuring forecast error:
⚫ Note that over-forecasts = negative errors and
under-forecasts = positive errors
ttt

120. FAE −=
26
Measuring Forecasting Accuracy
⚫ Mean Absolute Deviation
(MAD)
• measures the total error in a
forecast without regard to sign
⚫ Cumulative Forecast Error
(CFE)
• Measures any bias in the forecast
⚫ Mean Square Error (MSE)
• Penalizes larger errors
⚫ Tracking Signal
• Measures if your model is working;
quality

121. ( )
n
forecast - actual
MSE
2
=
MAD
CFE
TS =
n
forecastactual
MAD
=

122. tualCFE
27
Selecting the Right Forecasting
Model
1. The amount & type of available data
▪ Some methods require more data than others
2. Degree of accuracy required
▪ Increasing accuracy means more data
3. Length of forecast horizon
▪ Different models for 3 month vs. 10 years
4. Presence of data patterns

123. ▪ Lagging will occur when a forecasting model
meant for a level pattern is applied with a trend
28
Collaborative Planning
Forecasting & Replenishment
(CPFR)
• Establish collaborative relationships between buyers and
sellers
• Create a joint business plan
• Create a sales forecast
• Identify exceptions for sales forecast
• Resolve/collaborate on exception items
• Create order forecast
• Identify exceptions for order forecast
• Resolve/collaborate on exception items
• Generate order

124. CPFR is an
iterative
process.
Backup Slides (to circle back at
the end of the term based on
time)
30
Accuracy & Tracking Signal Problem: A company is
comparing the accuracy of two forecasting methods.
Forecasts using both methods are shown below along with
the actual values for January through May. The company

125. also uses a tracking signal with ±4 limits to decide when a
forecast should be reviewed. Which forecasting method is
best?
Month Actual
sales
Method A Method B
F’cast Error Cum.
Error
Tracking
Signal
F’cast Error Cum.
Error
Tracking
Signal
Jan. 30 28 2 2 2 27 3 3 1

126. Feb. 26 25 1 3 3 25 1 4 2
March 32 32 0 3 3 29 3 7 3
April 29 30 -1 2 2 27 2 9 4
May 31 30 1 3 3 29 2 11 5
MAD 1 2.2
MSE 1.4 5.4
Statistical Quality Control (SQC)
(Chapter 6)
Production & Operations Management
INFO 335-71
Week 2

127. 2
What is SQC?
Statistical Quality Control (SQC)
the term used to describe the set of statistical
tools used by quality professionals to evaluate
organizational quality.
SQC
1. Categories:
1. Descriptive Statistics (mean, variance, range, distribution)
2. Statistical Process Control

128. 3. Acceptance Sampling – Not to worry about this for now
2. Causes of Variation
1. Common
2. Assignable
3
4
Descriptive Statistics
• The Mean- measure of
central tendency
• The Range- difference
between largest/smallest
observations in a set of data
• Standard Deviation
measures the amount of data

129. dispersion around mean
• Distribution of Data shape
• Normal or bell shaped or
• Skewed
n
x
x
n
1i
==
( )
1n
Xx

130. σ
n
1i
2
i
−
−
=
=
5
Normal Distribution of Data

131. Control Charts
Center
14-17 17-1912-14
Bottling
Plant ~ 16
Fl. Oz.
UCL: μ + 3σ
LCL: μ - 3σ
Variables and Attributes
⚫ Variables
• Continuous measures (height, weight, volume etc.)
• X-bar (centrality)

132. • Variance or standard deviation of operation provided
• When variance or standard deviation of operation is
unknown
• R-bar (dispersion)
⚫ Attributes
• Discrete measures (complaints, defects etc.)
• P-chart (proportions known, such as proportion of
defectives)
• C-chart (proportion unknown, just totals are known)
8
Control Charts for Variables
⚫ Use x-Bar charts to monitor
the changes in the mean of a

133. process (central tendencies)
⚫ Use R-bar charts to monitor
the dispersion or variability
of the process
⚫ System can show
acceptable central
tendencies but unacceptable
variability
⚫ System can show
acceptable variability but
unacceptable central
tendencies
Center line and control limit
formulas
9
xx

134. xx
n21
zσxLCL
zσxUCL
sample each w/in nsobservatio of# the is
(n) and means sample of # the is )( where
n
σ
σ ,
...xxx
x x
−=
+=

135. =
++
=
k
k
Time 1 Time 2 Time 3
Observation 1 15.8 16.1 16.0
Observation 2 16.0 16.0 15.9
Observation 3 15.8 15.8 15.9
Observation 4 15.9 15.9 15.8
Sample
means (X-bar)
15.875 15.975 15.9
Sample
ranges (R)

136. 0.2 0.3 0.2
Constructing an x-Bar Chart: A quality control inspector at
the Cocoa Fizz soft drink company has taken three samples
with four observations each of the volume of bottles filled. If
the standard deviation of the bottling operation is .2 ounces,
use the below data to develop control charts with limits of 3
standard deviations for the 16 oz. bottling operation.
Sample Size = number of observations per sampling activity
Number of samples = number of times we went and collected
samples
10