335 DSC Operations Management
Instructor: Zhibin Yang
Assistant Professor
Decision Sciences Department
DSC 335
1
Review
q
Whats Operations Management?
Process view
q Supply chain view
q Manufacturing vs. service processes
q
q
Operation strategy
q
DSC 335
Competitive priorities
2
Announcements
q
Course packet will be available by tomorrow
q
Groups
q
Computer lab policy
DSC 335
3
DSC 335 Roadmap
Operations Strategy
Decision Making Tools
Process strategy/analysis
Capacity analysis/planning
Process Management
Lean systems
Littlefield Game 1
Case: Kristens Cookie
Quality management
Inventory management
Littlefield Game 2
Case: Blanchard
Supply Chain Mgmt.
Supply chain dynamics
Case: A Pain in Chain
Beer game
DSC 335
4
Decision Making Tools
DSC 335
5
How do you make decisions?
DSC 335
6
How do you make decisions?
q
q
q
q
Brainstorming
pro and con
Relying on expert opinions
Tossing a coin
In operations management, we make decisions
using analytical (mathematical) tools.
DSC 335
7
Challenges in Decision Making
q
You are thinking of dating someone
q
q
You have to decide whom to date, or whether or
not date that particular one
Is it an easy decision?
Your criterion may vary
q Looking, charm, academic performance, etc.
q Second, you are not sure the outcome
q Will he/she like you as much as you like
him/her?
q
DSC 335
8
Challenges in Decision Making for OM
q
Multiple criteria for your decision
q
q
Uncertainty in your decisions outcome
q
q
Examples: cost, quality, delivery speed, etc.
Examples: Economic condition, Weather condition, Price of
raw materials in the spot market
Interdependency between sequential decisions
Making two or more decisions in a sequence
q Your choice for a decision is contingent on your choice for
preceding decisions
q
DSC 335
9
Outline
q
Decision making under certainty
q
q
q
Making a single decision under uncertainty
q
q
q
Single criterion: Break-even analysis
Multiple criterion: Preference matrix
When the probabilities of the possible outcomes are
unknown
When the probabilities of the possible outcomes are known
Making sequential decisions under uncertainty
q
DSC 335
Decision tree
10
Break-even Analysis
q
q
Break-even analysis is used to evaluate a new
production or service process
Note
There is a single criterion the cost (or profit)
q The outcome is (assumed to be) certain
q
DSC 335
11
Two Costs of Installing a New Process
q
Fixed cost, F: the portion of cost that does not change in
the volume of output
Fixed cost = 0, if you choose to do nothing (i.e. zero output)
q Fixed cost = F>0, if you choose to produce of any output
greater than zero.
q
q
Examples of fixed cost
Time and costs paid for installing and fine-tuning a production
line
q Costs paid for buying machines and hiring workers for
operating the production line
q
DSC 335
12
(contd) variable cost
q
Variable cost: the portion of cost that increases
(linearly) in the volume of output
Let c be the cost for a unit of product or service
q Let Q be the volume of output, e.g., # customers served, #
units produced
q Total variable cost = c*Q
q
q
Example of variable cost
Cost paid for the electricity consumption
q Cost paid for raw materials
q
DSC 335
13
(contd) Total Costs of Using a New Process
q
The total costs = F + cQ
Cost
Total costs of using
a new process, F + cQ
Rate = variable cost per unit, c
F
0
DSC 335
Q (volume)
14
Application 1: Cost-return analysis for a New
Service / Production Process
q
We compare the total costs of a new process with
1.
2.
q
The revenue of this process, or
The costs of an existing process
Two types of questions we can answer
1.
2.
DSC 335
For a given demand (the scale of operation), should we adopt
the new process?
Find the break-even quantity
q The minimum size of demand such that the costs of the
new process are justified?
15
(contd)
q
q
Given the selling price, p, per unit of product, to find the
volume, Q, at which total revenues meets total costs.
The Tradeoff
1.
2.
3.
q
Total revenues = pQ
Total costs = F + cQ
Set revenue equal to total cost: pQ = F + cQ
Break-even quantity is
Q=
DSC 335
F
pc
16
(contd) Graphic Illustration
Dollars
Total revenues
Profits
F
DSC 335
Fixed costs
Loss
0
Total costs of using
a new process, F + cQ
Quantity (Q)
Break-even quantity
F
Q* =
pc
17
Example New Procedure at a Hospital
q
q
A hospital is considering a new procedure to be offered
at $200 (p) per patient. The fixed cost per year would be
$100,000 (F), with a variable cost of $100 (c) per
patient.
Question 1: what is the break-even quantity for this
service?
Q* =
DSC 335
F
100,000
=
= 1,000 patients
pc
200 100
18
(contd)
q
q
Question 2: If the most pessimistic sales forecast of the
demand for the proposed service were 1,500 patients,
what would be the procedures total contribution to
profit?
Answer: the new procedures total contribution is the
difference between total revenues and total costs
pQ (F + cQ) = 200(1,500) [100,000 + 100(1,500)]
= $50,000
DSC 335
19
Exercise Entrepreneur
q
You are an entrepreneur, planning to enter the gourmet
soy-based burger market in Eugene. The variable unit
cost for making one burger is $0.97. The fixed cost of
making burgers for 18 months: $140,000 (rent, phone
bill, and insurance coverage).
1)
2)
DSC 335
Market survey shows that Eugene consumers would accept a
price up to $2.99 for a gourmet burger. At this price, how
many burgers will you have to sell before you make back
your total cost?
Your partner has forecast selling 150,000 burgers in 18
months. What is the lowest price you have to charge to cover
your cost of producing 150,000 burgers?
20
(contd) Solution to Question (1)
q
q
q
q
Setup cost F=$140,000; Variable cost c=$0.97
Selling price p=$2.99
Equation: F+cQ = pQ
Break-even quantity Q = F/(p-c) = 140,000/2.02 =
69,307
DSC 335
21
(contd) Solution to Question (2)
q
q
q
q
F=$140,000
c=$0.97
Q=150,000
P=(F/Q)+c = 1.91
DSC 335
22
Application 2 Comparing Two Processes:
Make-or-buy Decision
q
Two alternative processes to acquire products/services:
make: firm builds its own capacity and produces in-house
q buy: firm sources products from a supplier or outsource
services to contractor
q
q
Costs of buy
Fb: fixed cost of buy option
q cb: variable cost (per unit) of buy option
q
q
Costs of make
Fm: fixed cost of make option
q cm: variable cost of make option
q
DSC 335
23
(contd) Graphic Illustration of the Tradeoff
q
make option usually has a higher fixed cost, but has a
lower variable cost, than buy option
Cost
Total costs of
buy option
When quality is large,
choose to make
Total costs of
make option
When quantity is
large, choose to buy
0
DSC 335
Break-even quantity
Quantity (Q)
24
(contd)
q
To find the break-even quantity, we set the two cost
functions equal and solve for Q:
Total costs to buy = Fb + cbQ
q Total cost to make = Fm + cmQ
q
Fb + cbQ = Fm + cmQ
q
The break-even quantity is
Fm Fb
Q* = cb cm
DSC 335
25
Exercise Upgrading Production Line
q
q
A sports bicycle manufacturer produces a popular 10-speed
mountain bike with a profit margin of $100 per unit. The factory
has a maximum capacity of producing 2,000 units in a year. The
manager is considering upgrade the production line to produce a
new model (with the same capacity of 2,000 units). Upgrading the
product line costs $100,000.
Assume that the manufacturer can sell all it produces. What is the
profit margin (p1) of the new model that the manufacturer should
charge to make the upgrade worthwhile?
DSC 335
26
(contd) Solution
q
The target production quantity: Q = 2,000
q
The profit margin of the old model p0 = 100
q
The total profit with the old model = p0 Q
q
Fixed cost of upgrade F = $100,000
q
The total profit with the new model = p1Q F
q
Set two revenue to be equal p0 Q = p1Q F
q
The break-even price, p1 = p0 + F/Q = $150
DSC 335
27
Outline
q
Decision making under certainty
q
q
q
Making a single decision under uncertainty
q
q
q
Single criterion: Break-even analysis
Multiple criterion: Preference matrix
When the probabilities of the possible outcomes are
unknown
When the probabilities of the possible outcomes are known
Making sequential decisions under uncertainty
q
DSC 335
Decision tree
28
Examples of Multi-criterion Decision Making
q
Buying a car
q
q
Searching for an apartment
q
q
Your criteria: cost, looking, horsepower
Your criteria: distance/time-to-school, cost, life style
How do you make your decision?
DSC 335
29
The curse of multiple criteria
q
All-the-best alternative need not exist
q
q
You trade off between the criteria
Our approach preference matrix
q
DSC 335
Observation: people give more weight to factors that are
important to them
30
Procedure for using Preference Matrix
1)
For each criterion, rate all alternatives and assign each
of them a score
q
2)
Assign a weight to each criterion
q
q
3)
The criteria can be scored on any scale as long as the same
scale is applied to all the alternatives being compared
Give more weight to a criterion, if you think it is more
important to you.
Total weights typically equal 100
The total score is the sum of the weighted scores
(weight score) for all the criteria and compared
against scores for alternatives
DSC 335
31
Example: Whom will you pick?
Leo, cool
looking
Matt, smart
Tom,
easygoing
DSC 335
32
(contd) Whom will you pick?
Weights
Tom
Leo
Matt
Looking
30
75
90
70
Charm
30
100
80
80
Intelligence
40
90
85
97
DSC 335
Weight
total
33
Exercise Students Term Grades
q
The of instructor DSC 330 will assign an A+ to the top-performer
of the class. Mike and Jenny are on the radar screen. The
following table shows the performance criteria, weights, and
scores (1 = worst, 10 = best) of Mike, a student in DSC 330.
Whats the total score of Mike?
Performance
Criterion
Mid-term exam
Weight (A) Score (B)
Weighted Score (A B)
of Mike
1600
20
80
Final exam
25
85
2125
Homework
20
70
1400
Case studies
20
75
1500
Misc.
15
80
1200
Weighted score =
DSC 335
7825
34
(contd)
q
The scores of Jenny, another student in DSC 330, is
shown in the following table. Whom should the
instructor choose to get A+?
Performance
Criterion
Mid-term exam
Weight (A) Score (B)
Weighted Score (A B)
of Jenny
2000
20
100
Final exam
25
90
2250
Homework
20
60
1200
Case studies
20
70
1400
Misc.
15
70
1050
Weighted score =
DSC 335
7900
35
(contd) Implication
q
Implication for students
q
q
Spend more time on items of higher weights
Implication for the instructor
q
DSC 335
Design the weight distribution to reflect the relative
importance of the course components
36
Exercise Car Purchasing
q
Bob owns a small business. He needs a car for both
business and personal purposes. He consider the
following criteria:
q
q
Bob considers the following four candidates
1.
2.
3.
4.
q
Cost; interior space; comfort; drivability (fun); and look.
A convertible sports car
An SUV/4x4
A comfortable family car.
A station wagon
Bob rates each car according to each criterion over a 3point scale, and gives weights to the criteria.
DSC 335
37
(contd) Bobs Rating & Weights on Factors
Factors:
Cost Space Comfort Fun Look Total
Weights:
50
20
10
10
10
Sports Car
0
0
2
3
3
SUV/4x4
1
3
2
1
1
Family Car
2
2
3
0
0
Station Wagon 2
3
3
0
1
DSC 335
100
38
Outline
q
Decision making under certainty
q
q
q
Making a single decision under uncertainty
q
q
q
Single criterion: Break-even analysis
Multiple criterion: Preference matrix
When the probabilities of the possible outcomes are
unknown
When the probabilities of the possible outcomes are known
Making sequential decisions under uncertainty
q
DSC 335
Decision tree
39
Uncertainty in Operations
q
q
q
q
q
Outcome of a football game affects sports apparel
business
Weather condition in the future affects logistics plan
Future demand for a product affects inventory level
Available production capacity in the future affects
production decision
Usable production output affects production size
DSC 335
40
Decision rules for single decision under
uncertainty
q
When the probabilities of uncertain event are unknown
q
q
q
q
MaxiMin: The best of the worst, a pessimistic approach
MaxiMax: The best of the best, an optimistic approach
MiniMax Regret: Minimizing your regret (also pessimistic)
When the probabilities are known: expectation rule
DSC 335
41
Example: Construction Project
q
A constructor has two pieces of land for its construction
project. The project takes 3 years to finish, and the value
of the project is uncertain, depending on the economy, as
in the table:
Alternatives
Location 1
$5M
$7M
Location 2
DSC 335
Value, Economy is Value,
down
Economy is up
$4.5M
$8M
42
MaxiMin Rule
q
q
Step 1. For each alternative, find the worst payoff.
Step 2. Identify the alternative that yield the highest
among all worst payoffs.
Alternatives
Location 1
$5M
$7M
Location 2
q
Value, Economy is Value,
down
Economy is up
$4.5M
$8M
Result
The best of these worse payoffs is $5M
q The pessimistic constructor will build at location 1
q
DSC 335
43
MaxiMax Rule
q
q
Step 1. For each alternative, find the best payoff.
Step 2. Identify the alternative that yield the highest
among all best payoffs.
Alternatives
Location 1
$5M
$7M
Location 2
q
Value, Economy is Value,
down
Economy is up
$4.5M
$8M
Result
The best of these best payoffs is $8M
q The optimistic constructor will build at location 2
q
DSC 335
44
MiniMax Regret Rule
q
Step 1. Calculate the regret for each alternative in each
event
1.
2.
q
q
For each possible event, identify the maximum payoff among
all alternatives.
For alternative in each possible event, the regret is the
different between the maximum payoff in that event and the
payoff of the alternative
Step 2. For each alternative, find the maximum regret
across all possible events
Step 3. choose the alternative that leads to the minimum
of the maximum regrets among all alternatives.
DSC 335
45
(contd)
q
q
When economy is down, the best payoff is $5M
When economy is up, the best payoff is $8M
Alternatives Regret if
economy is down
Max.
regret
Location 1
5-5=0
8-7=1
1
Location 2
q
Regret if
economy is up
5-4.5=0.5
8-8=0
0.5
Result: the minimum regret is 0.5. Choose location 2
DSC 335
46
Exercise
q
The manager of a company must decide whether to make Arrows,
Barrels, or Wagons. The government is about to issue a policy and
recommendation on pioneer travel that depends on whether
certain treaties are obtained. The policy will affect demand for the
products; however the probability of these policy events is
unknown. The following payoffs are available:
Payoffs (Profits)
Alternative
Land Routes
No treaty
Land Routes
Treaty
Sea Routes
Only
Arrows
$440,000
$220,000
Barrels
$470,000
$200,000
$600,000
Wagons
q
$640,000
$15,000
$950,000
- $35,000
Apply the four rules to indentify the managers decision.
DSC 335
47
q
q
Alternatives: Arrows, Barrels, or Wagons
Uncertain events: policy outcomes treaty, no treaty, sea
routes only
DSC 335
48
(contd) MaxiMin
Payoffs (Profits)
Alternative
Land Routes
No treaty
Land Routes
Treaty
Sea Routes
Only
Arrows
$640,000
$440,000
$220,000
Barrels
$470,000
$200,000
$600,000
Wagons
$15,000
$950,000
-$35,000
DSC 335
49
(contd) MaxiMax
Payoffs (Profits)
Alternative
Land Routes
No treaty
Land Routes
Treaty
Sea Routes
Only
Arrows
$640,000
$440,000
$220,000
Barrels
$470,000
$200,000
$600,000
Wagons
$15,000
$950,000
-$35,000
DSC 335
50
(contd) MiniMax Regret
Regrets
Alternative
Land Routes Land Routes
No treaty
Treaty
Arrows
0
Barrels
$130,000
Wagons
$625,000
DSC 335
Sea Routes
Only
$510,000
$380,000
$750,000
0
0
$635,000
Max regret
$510,000
$750,000
$635,000
51
When the probabilities of a random event is
know expectation
q
The expected cost (or value) of a choice =
(outcome 1)*(probability of outcome 1)
+ (outcome 2)*(probability of outcome 2)
+
q
Example: the expected values of the 2 locations, where
the probability of down is 75%
Alternatives
Location 1
$5M
$7M
Location 2
DSC 335
Value, Economy is Value,
down
Economy is up
$4.5M
$8M
52
Decision Tree Sequential Decisions under
uncertainty
q
Decision tree is a schematic model of available
alternatives along with their possible consequences
Useful with uncertain events and sequential decisions
q Example: making capacity expansion decisions with uncertain
future demand
q
q
q
Decision nodes (squares): represent alternatives
Event nodes (circles): represent random events
q
DSC 335
The probabilities of all possible events leaving a circular node
must add up to be 100%
53
Decision Tree
E1 & Probability
E2 & Probability
iv
at
rn
te
l
A
e1
1
1st Alte
rn
decision
at
i
E3 & Probability
Payoff 1
Payoff 2
Payoff 3
Alternative 3 Payoff 1
ve
2
= Event node
= Decision node
E1
&
b
ba
o
Pr
ty 2
ili
Alternative 4 Payoff 2
Possible Alternative 5 Payoff 3
2nd decision
E2 & Probability
E3 & Probability
Payoff 1
Payoff 2
Ei = Event i
P(Ei) = Probability of event i
DSC 335
54
Example: decisions in a football game
q
Your team is offending, currently at third down, 13 yards
(to the end zone), 5 yards to go for a fresh first-down.
Offence
DSC 335
55
(contd)
q
Decision 1 (at 3rd down)
kick for field goal, with the following possible outcomes
q Goal 3 points, end of offence
q Miss no points, end of offence
q Go for the 4th down, with the following possible outcomes
q Touchdown 7 points, end of offence
q Fresh first-down must choose to go for at least 3 downs
(decision 2)
q Failure no point, end of offence
q
DSC 335
56
q
The random outcomes at 3rd downs (decision 2):
Touchdown 7 points, end of offence
q Small advance Decision 3: kick or 4th down.
q
q
The outcomes of kick (Decision 3)
Goal 3 points, end of offence
q Miss no points, end of offence
q
q
The outcomes of 4th down (Decision 3)
Touchdown 7 points, end of offence
q Failure no point, end of offence
q
DSC 335
57
Decision Tree
Field goal (70%) 3
Goal (85%) 3
Kick
y
Tr
1
4th
2
e
nc
va
ad )
all 60%
Sm (
0
Try
3 downs
Miss (15%) 0
3
Try
4th down
Touchdown (45%) 7
Failure (55%) 0
wn
do
R
1s ec
t d eiv
ow e f
n res
(4 h
0%
)
Ki
ck
Miss (30%)
Touchdown (40%)
Touchdown (20%)
Failure (40%)
7
0
7
= Event node
= Decision node
DSC 335
58
How to Solve It
q
1.
2.
3.
We solve the tree by working backwards (from right to
left)
For each random event node (circle), we calculate its
event nodes expected payoff
For each decision node (square), we pick the alternative
that has the highest expected payoff
Iterate until we reach the root decision node
DSC 335
59
Decision Tree
2.1
Field goal (70%) 3
Ki
ck
Miss (30%)
3.15
e
nc
va
ad )
all 60%
Sm (
0
y
Tr
4th
w
do
R
1s ec
t d eiv
ow e f
n res
(4 h
0%
)
3.276
1
Goal (85%) 3
2.55
Kick
Try
3 downs
4.69
2
Miss (15%) 0
3
3.15
Try
4th down
Touchdown (45%) 7
Failure (55%) 0
4.69
n
Touchdown (40%)
Touchdown (20%)
3.276
Failure (40%)
7
0
7
= Event node
= Decision node
DSC 335
60