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ELEMENT OF DECISION
PROBLEMS
TI-Unand, 2014
Larkin Oil
Bill Mills shuffled his feet. The Spill Oil
Contingency Plan Committee was supposed
to come up with a concrete proposal for the
top management of Larkin Oil, Inc.
The committee members had lots of time;
the CEO had asked for recommendations
within three months. This was their first
meeting.
Over the past hour, Peter Wilton and Bob Brown had argued about exactly what level of resources should be committed to planning for a major oil spill in the company’s main shipping terminal bay.
Look, said Peter. We’ve been over this so many times. When, and if, an oil spill actually occurs, we will have to move fast to clean up the oil. To do that, we have to have equipment ready to go.
But having equipment on standby like that means tying up a lot of capital, Bob replied. As a member of the financial staff, Bob was sensitive to committing capital for capital that would be idle all the time and might actually have to be replaced before it was ever used.
We’d better off keeping extensive records, maybe just a long list of equipment that would be useful in a major cleanup. We need to know where it is, what it’s capable of, what its condition is, and how to transport it.
Come to think of it, our list will also have to include information on transportation equipment and strategies, Leslie Taylor added.
Bill finally stirred himself. You know what bother me? We’re talking about these alternatives, and the fact that we need to do thus and so in order to accomplish such and such. We’re getting the cart before the horse. We just don’t have our hands on the problem yet. I say we go back to basics. First, how could an oil spill happen?
Easy, said Peter. Most likely something would happen at the pipeline terminal.
Something goes wrong with a coupling, or
someone just doesn’t pay attention with loading oil on the ship. The other possibility
is that a tanker’s hull fails for some reason, probably from running aground because of
weather.
Weather or not be the problem, suggested Leslie. What about incompetence? What if the pilot gets drunk?
Tom Kelso always was able to imagine
unusual scenarios. And what about the possibility of sabotage? What if a terrorist
decides to wreak environmental havoc?
Okay, said Bill. In terms of the actual cleanup, the more likely terminal spill would require a different kind of response than the less likely event of a hull failure.
In a planning for a terminal accident, we need to think about having some equipment at the terminal. Given the higher possibility of such an accident, we should probably spend money on cleanup equipment that would be right there and available.
I supposed so, conceded Bob. At least we would be spending our money on the right kind of thing.
You know, there’s another problem that we’re not really thinking about, Leslie offered. An oil spill at the terminal can be easily contained with relatively little environmental damage. On the other hand, if we ever have a hull failure, we have to act fast. If we don’t, and mind you, we may not be able to because of weather, Larkin Oil will have terrible time trying to clean up the public relations as well as the beaches. And think about the difference in the PR problem if the spill is due to incompetence on the part of a pilot rather than weather or sabotage.
Even if we act fast, a huge spill could still be nearly impossible to contain. Bill point out. So what’s the upshot? Sounds to me like we need someone who could make a decision immediately about how to respond. We need to recover as much oil as possible, minimize environmental damage, and manage the public relations problem.
And do this all efficiently, growled Bob Brown. We still have to do it without having tied up all
the company’s assets for years waiting for something to happen.
Decision Making Process
Identify the
problem
Identify objectives
and alternatives
Decompose and
model the problem
Choose the best
alternative
Sensitivity Analysis
Implement the
chosen Alternative
Is further analysis
needed?
A
A
Y
N
How should decision making
process begin? Given a complicated problem, how should
one begin?
A critical first step is that of identifying the
elements of the situation.
Elements of the problem
Decision to make
Uncertain events
The value of specific outcomes
Decision to make
Imagine a farmer whose trees are laden with
fruit that is not ripe yet
If the weather forecasts:
mild weather there is nothing to worry about
freezing weather it might be appropriate to spend money on protective measures that will
save the crop.
In such situation, the problem has: a decision to make: whether or not to take
protective action
A decision: at least two alternatives
There may be a wide variety of alternatives
He may have several strategies for saving the crop
For example: wait and obtain more information But, there may be not enough time to take action. The later the decision, the worse outcome might be obtained.
Another possibility: Taking out insurance.
And also: Taking no action
Sequential decisions
In many cases, there simply is no single
decision to make, but several sequential
decision.
The orchard example: Suppose that several
weeks of the growing season remain.
Each day the farmer will get a new weather
forecast, and each time there is a forecast of
adverse weather it will be necessary to decide once again whether to protect the crops.
When a decision situation is complicated by
sequential decisions, a decision maker
generally will want to consider them when
making the immediate decision.
Furthermore, the future decision may depend
on exactly what happened before.
Sequential decisions
The decision maker must consider decisions
to be made now and later
First
Decision
Second
Decision
Third
Decision Last
Decision
TIME LINE
Now
Uncertain events
In the previous discussion:
the decision problem can be complicated because
of uncertainty about what the future holds
Many important decisions must be made without
knowing exactly:
what will be happen in the future or
what the ultimate outcome will be from a decision
made today.
Example: In a stock market, one investor will buy some
stock, but in what company?
Some share prices will go up and others down
Moreover, the market as a whole may move up or down, depending economic forces.
The best thing to do: the investor have to think carefully about the
chances associated with each security’s price as well as the market as a whole
Uncertain Events and Sequential Decision
First
Decision
Second
Decision
Third
Decision Last
Decision
TIME LINE
Now
Uncertain
Events
Resolved
before second
decision
Resolved
before third
decision
Resolved
before last
decision
Resolved after
last decision
Outcomes and values
After the last decision has been made and the last uncertain event has been resolved, the decision maker’s fate is finally determined.
It may be a matter of profit or loss as in the case of farmer.
It may be a matter of increase in the investor’s portfolio value.
In some case the final outcome may be a net value figure that account for both cash outflows and inflows during the time sequence of the decisions.
Including the outcomes
First
Decision
Second
Decision
Last
Decision
TIME LINE
Now
Uncertain
Events
Resolved
before second
decision
Resolved
before last
decision
Resolved after
last decision
Outcomes
Planning
Horizon
The time value of money: A special
kind of trade-off
One of the most common outcomes in personal and business decision is a stream of cash flows.
One investor may spend money on a project (an initial cash outflows) to obtain revenue in the future (cash inflows) over a period of years.
There is a special kind of trade-off: spending dollars today to obtain dollars tomorrow. If a dollar today were worth the same tomorrow, there
would be no problem.
In general, we talk about the present value of an amount x that will be received at the end of n time periods
Larkin Oil’s Problem
Policy
Decision
Action
Management Decision
TIME LINE
Now
Outcomes
Location
Accident
Cause
Weather
Weather for
clean up
Environmental
damage
Cost
•Cost
•Environmental
damage
•PR damage
TI_Unand, 2012
Persoalan Texaco vs Penzoil Awal Tahun 1984, Penzoil dan Getty Oil setuju untuk
merger. Tetapi sebelum dokumen formal ditandatangani, Texaco menawarkan kepada Getty Oil harga yang lebih baik. Pimpinan Getty setuju dengan penawaran Texaco.
Penzoil yang merasa dirugikan, ingin menuntut Texaco ke pengadilan.
Namun Texaco bersedia membayar ganti rugi $ 2 juta
Apa keputusan yang harus diambil oleh Penzoil? Terima tawaran $ 2 juta tersebut atau tetap lanjutkan ke pengadilan dengan keputusan final yang belum diketahui?
Accept $2 Billion
Counter over
$5Billion
Texaco Accept $5 Billion
Texaco Refuses
Counterover
Accept $3 Billion
Refuse
Final Court
Decision
Final Court
Decision
Payoff ($ Billion)
2
5
10.3
5
0
10.3
5
0
3
Texaco
Counterover
$3 Billion
Accept $2 Billion
Counter over
$5Billion
Texaco Accept $5 Billion
Texaco Refuses
Counterover
Texaco
Counterover
$3 Billion
Accept $3 Billion
Refuse
Final Court
Decision
Final Court
Decision
Payoff ($ Billion)
2
5
10.3
5
0
10.3
5
0
3
(0.17)
(0.50)
(0.33)
(0.2)
(0.5)
(0.3)
(0.2)
(0.5)
(0.3)
Decision Tree and EMV
Trade Ticket
Keep Ticket
Win 25
Win 10
Lose
Lose
24
-1
0
10
(0.20)
(0.80)
(0.45)
(0.55)
Trade Ticket With Friend or Keep It
EMV (Keep Ticket) = 0.45*10 + 0.55*0 = $4.5
EMV (Trade Ticket) = 0.20*24 + 0.80*(-1) = $4
Trade
Ticket
Keep
Ticket $4.5
$4
Texaco vs Pennzoil EMV (Court Decision) =
[P(Award=10.3)x10.3] + [P(Award=5)x5]+ [P(Award=0)x0]
EMV (Court Decision) = 0.2x10.3+0.5x5+0.3x0 = 4.56
Accept $2 Billion
Counter offer
$5Billion
Texaco Accept $5 Billion
Texaco Refuses
Counteroffer
Texaco
Counteroffer
$3 Billion
Accept $3 Billion
Refuse
Expected Value
2
5
4.56
4.56
3
(0.17)
(0.50)
(0.33)
Texaco vs Pennzoil
Accept $2 Billion
Counter offer
$5Billion
Texaco Accept $5 Billion
Texaco Refuses Counteroffer
Texaco Counteroffer $3 Billion
Expected Value
2
5
4.56
4.56
(0.17)
(0.50)
(0.33)
Texaco vs Pennzoil
EMV (Counteroffer $5 Billion) =
[P(Texaco Accepts)x5] + [P(Texaco Refuses)x4.56]+ [P(Texaco Counteroffer $3 Billion)x4.56]
EMV (Counteroffer $ 5 Billion) =
0.17x5 + 0.5x4.56 + 0.33x4.56 = 4.63
Accept $2 Billion
Counteroffer $5 Billion 4.63
2 Expected Value
Accept $2 Billion
Counter over
$5Billion
Texaco Accept $5 Billion
Texaco Refuses
Counterover
Texaco
Counterover
$3 Billion
Accept $3 Billion
Refuse
Final Court
Decision
Final Court
Decision
Payoff ($ Billion)
2
5
10.3
5
0
10.3
5
0
3
(0.17)
(0.50)
(0.33)
(0.2)
(0.5)
(0.3)
(0.2)
(0.5)
(0.3)
Texaco vs Pennzoil
4.56
4.56
4.56
4.63
TI Unand, 2014
Pendahuluan Mengapa pengambilan keputusan penting
Contoh persoalan keputusan
Tujuan Pembelajaran:
Mahasiswa mampu memodelkan struktur persoalan keputusan (1 kriteria) agar dapat diambil keputusan yang secara empiris lebih baik
Mahasiswa dapat menggunakan beberapa konsep pengambilan keputusan multikriteria
Contoh Persoalan Persoalan Texaco vs Penzoil
Awal Tahun 1984, Penzoil dan Getty Oil setuju untuk merger. Tetapi sebelum dokumen formal ditandatangani, Texaco menawarkan kepada Getty Oil harga yang lebih baik. Pimpinan Getty setuju dengan penawaran Texaco.
Penzoil yang merasa dirugikan, ingin menuntut Texaco ke pengadilan.
Namun Texaco bersedia membayar ganti rugi $ 2 juta
Apa keputusan yang harus diambil oleh Penzoil? Terima tawaran $ 2 juta tersebut atau tetap lanjutkan ke pengadilan dengan keputusan final yang belum diketahui?
Pemilihan lokasi pabrik
Ingin ditentukan di mana lokasi pabrik tertentu akan didirikan.
Terdapat 4 alternatif lokasi yang mungkin untuk dipilih.
Terima $ 2 juta
Texaco Setuju $ 5 juta
Texaco Menolak
$ 5 juta
Texaco Menawar
$ 3 juta
Terima $ 3 juta
Tolak
$ 3 juta
Putusan Final
Pengadilan
Putusan Final
Pengadilan
10.3
5
0
5
3
10.3
5
0
5
Minta
$ 5 juta
Hasil ($ juta)
Pemilihan Lokasi Pabrik
Alternatif Bahan Baku Pasar Tenaga Kerja Infrastruktur
Lokasi 1 5 2 3 3
Lokasi 2 4 3 5 1
Lokasi 3 3 4 4 2
Lokasi 4 2 5 3 4
Langkah Pengambilan
Keputusan
1. Identifikasi Permasalahan
2. Identifikasi obyektif dan
alternatif
3. Dekomposisi dan modelkan
persoalan
4. Pemilihan Alternatif
5. Analisis Sensitivitas
6. Implementasi alternatif terpilih
1. Model struktur persoalan
2. Model ketidakpastian
3. Model preferensi
Pembelajaran Ming-
gu Materi
Ming-
gu Materi
1 Pengantar 9 Kreativitas dalam
Pengambilan Keputusan
2 Pemodelan Keputusan:
Unsur-unsur dalam
Pengambilan Keputusan
10 Perilaku Resiko dalam
Pengambilan Keputusan
3 Penstrukturan
Keputusan
11 Obyektif yang bertentangan:
Konsep Dasar
4 Penetapan Pilihan 12 Model Multi Atribut
5 Analisis Sensitivitas 13 AHP
6 Presentasi I 14 Presentasi II
7 Presentasi I (lanjutan) 15 Presentasi II (lanjutan)
8 UTS 16 UAS
Evaluasi:
1. Tugas
2. Aktivitas dalam pembelajaran
3. Presentasi
4. UTS
5. UAS Referensi:
Clement, R.T. 1992. Making Hard Decision. PWS-Kent Publishing Company, Boston
Kesepakatan:
Kehadiran: 80%
Toleransi Keterlambatan: 15 menit (minggu 2 dan 3)
Pakaian-rambut:
No T-shirt
No trousers for women
No long hair for men
Ketua Kelas: Sandi Kurnia (082382011562)
SENSITIVITY ANALYSIS
TI-Unand, 2014
Eagle Airlines
Dick Carothers, President of Eagle Airlines, have been considering his operation, and now the opportunity was available. An acquaintance had put him in contact with the president of a small airline in the Midwest that was selling an airplane. Many aspects of the situation needed to be thought about, however, and Carothers was having a hard time sorting them out.
Eagle Airline owned and operated three-twin engine aircraft. With this equipment, Eagle provided both charter flights and scheduled commuter service among several communities in the eastern United States.
Scheduled flights continued approximately 40% of Eagle’s flights, averaging only 90 minutes of flying time and a distance of some 300 miles. The remaining 60% of flights were chartered.
The mixture of charter flights and short scheduled flights had provide profitable, and Charoters felt that he had found a niche for his company. He was aching to increase the level of service, especially in the area of charter flights, but this was impossible without more aircraft.
A Piper Seneca was for sale at a price of $95,000, and Carothers figured that he could buy it for between $85,000 and $90,000. This twin-engine airplane had been maintained according to FAA regulations. In particular, the engines were almost new, with only 150 hours of operation since a major overhaul.
Furthermore, having been used by another small commercial charter service, the Seneca contained all of the navigation and communication equipment that Eagle required. There were seats for five passengers and the pilot, plus room for baggage. Typical airspeed was approximately 175 nautical miles per hour (knots), or 200 statute miles per hour (mph).
Operating cost was approximately $245 per hour, including fuel, maintenance, and pilot salary. Annual fixed costs include insurance ($20,000) and finance charges.
Carothers figured that he would have to borrow some 40% of the money required, and he knew that the interest rate would be two percentage points above the prime rate (currently 9.5% but subject to change).
Based on his experience at Eagle, Carothers knew, that he could arrange charters for $300 to $550 per hour or charge a rate of approximately $100 per person per hour on a scheduled flights. He could expect on average that the scheduled flights would be half full.
He hoped to be able to fly the plane for up to 1000 hours per year, but realized that 800 might be more realistic. In the past, his business had been approximately 50% charter flights but he wanted to increase that percentage if possible.
The owner of the Seneca had told Carothers that he would either sell the airplane outright or sell Carothers to purchase it within a year at a specific price. (The current owner would continue to operate the plane during the year).
Although the two had not agreed on a price for this option, the discussion had led Carothers to believe that the option would cost between $2500 and $4000. Of course, he could always invest his cash in the money market and expect to earn about 8%.
As Carothers pondered this information, he realized that many of the numbers that he was using were estimates. Furthermore, some were within his control (for example, the amount financed and prices charged) while others, such as the cost of insurance or operating cost, were not. Was it worth considering?
Last, but not least, did he really want to expand the fleet? Or was there something else that he should consider?
Identify
The Decision to Make
Uncertain Event
The Outcomes
Model the Eagle Decision Problem!
Influence Diagram
Purchase
Seneca?
Charter
Price
Ticket
Price
Proportion
Financial
Revenue Total
Cost
Financial
Cost
PROFIT
Interest
Rate
Price
Insurance
Operating
Cost Capacity of
Scheduled
Flight Ratio
Charter/
Scheduled
Hours
Flown
Input Variables and Ranges of Possible
Values
Variable Base Value Lower Bound Upper Bound
Hours Flown 800 500 1000
Charter Price/Hour $325 $500 $550
Ticket Price/Hour $100 $95 $108
Capacity on
Scheduled Flights
50% 40% 60%
Ratio of Charter to
Scheduled Flights
50% 45% 70%
Operating
Cost/Hour
$245 $230 260
Insurance $20,000 $18,000 $25,000
Proportion
Financed
0.40 0.30 0.50
Interest Rate 11.5% 10.5% 13%
Purchase Price $87,500 $85,000 $90,000
Tornado Diagram
-15000 -10000 -5000 0 5000 10000 15000 20000 25000 30000 35000
Purchase Price
Interest Rate
Proportion Financed
Insurance
Ticket Price/Hour
Ratio of Charter to Scheduled Flights
Charter Price/Hour
Hours Flown
Operating Cost/Hour
Capacity on Scheduled Flights
Expected Profit
Two-way Sensitivity Analysis
0.4
0.45
0.5
0.55
0.6
230 235 240 245 250 255 260
Ca
pa
city
of
Sch
ed
ule
d F
lig
hts
Operating Cost ($)
Profit >4200
Profit <4200
Base
value.
Operating Cost
Do Not Purchase Earn 8% of $52,500
Purchase Piper Seneca
Capacity of Scheduled Flights
$253 (p)
Payoff ($)
-9,725
-4,225
6,525
Hours Flown
$237 (1-p)
45% (q)
55% (1-q)
45% (q)
55% (1-q)
650 (s)
900 (1-s)
650 (r)
900 (1-r)
650 (s)
900 (1-s)
650 (r)
900 (1-r)
18,275
675
10,175
16,925
32,675
4,200
SENSITIVITY TO
PROBABILITIES
Operating
Cost
Do Not Purchase
Earn 8% of $52,500
Purchase Piper Seneca
Capacity of
Scheduled Flights
$253
(0.5)
Payoff ($)
-9,725
-4,225
6,525
Hours
Flown
$237
(0.5)
45%
(q)
55%
(1-q)
45%
(q)
55%
(1-q)
650 (0.8r)
900 (1-0.8r)
650 (r)
900 (1-r)
650 (0.8r)
900 (1-0.8r)
650 (r)
900 (1-r)
18,275
675
10,175
16,925
32,675
4,200
STRATEGY
REGIONS
Strategy Region Graph
00.10.20.30.40.50.60.70.80.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
q
r
Invest in Money Market
Purchase Seneca
TI-Unand, 2014
Objective:
To show the roles of influence diagrams and
decision trees in the decision structuring process
Having identified the elements of a decision
problem, how should one begin the modeling
process?
Two approaches for structuring problems:
Influence diagram
Decision trees
An influence diagram provides a simple
representation of a decision problem.
The element of a decision problem:
The decision to make
Uncertain event
The value of outcomes
•Show up in different shapes
•Linked with arrows to show
the relationship among the
elements:
Elements Representation
Decision Decision
nodes
Chance event Chance nodes
Value Value nodes
•Nodes are put together in a graph, connected by arrows (arcs)
•Node at the beginning of an arc: Predecessor
•Node at the end of an arc: Successor
A venture capitalist’s problem in deciding whether to invest in a small business.
In fact, the entrepreneur will be able to obtain
financial backing from some source.
The only problem is that the proposed is
extremely risky, more so than most new ventures.
The venture capitalist must decide whether to
invest in this highly risky undertaking.
If she invests,
she may be able to get in on the ground floor of a
highly successful business.
On the other hand, the operation may fail
altogether.
The capitalist’s dilemma is whether the chance of getting in on the ground
floor of something big is worth the risk of losing
her investment entirely.
If she does not invest, she may leave her
capital in the stock market or invests in other
less risky venture.
Invest? Value
Venture
Succeeds or
Fail
A B
C D
E F
G H
The outcome of A is relevant
for assessing the chances
associated with Event B
The decision maker knows
the outcome of Event E
when making Decision F
Decision C is relevant for
assessing the chances
associated with Event D
The decision G is made
before Decision H
Choices:
Savings
Stocks
Outcome
Market Up
Market Down
Choice:
Stock
market
outcome Payoff
Savings Up 200
Down 200
Stocks Up 500
Down -400
Payoff
Market
Activity
Investment
choice
Problem of defective products
A manufacturing plant manager’s faces a string of defective products and must decide
what action to take.
He has dispatched his maintenance engineer
to a preliminary inspection of machine 3
which is suggested to be the source of the
problem.
Possible Reports:
I think, 3 needs fixing
I think, 3 is OK
Choices:
Change Products
Replace 3
Outcome
3 OK
3 Not OK
Choice: Outcome Payoff
Change
Products
3 OK Behind schedule
3 Not OK
Replace 3 3 OK Behind schedule, costly
3 Not OK On schedule, costly
Payoff
Machine 3
OK?
Manager’s Decision
Engineer’s Report
Possible Forecast:
Will hit Miami
Will miss Miami
Choices:
Evacuate
Stay
Outcome
Hits Miami
Misses Miami
Choice: Outcome Payoff
Evacuate Hits Miami Safety, high cost
Misses Miami
Stay Hits Miami Danger, low cost
Misses Miami Safety, low cost
Payoff
Hurricane
Path
Decision
Forecast
Introduce
Product? Profit
Cost Revenue
Introduce
Product? Profit
Fixed Cost
Units
Sold Variable
Cost Price
Introduce
Product? Profit
Cost Revenue
Fixed
Cost
Units
Sold Variable
Cost Price
Bomb-detection
System Choice
Overall
satisfaction
Detection
effectiveness
Time to
implement
Passenger
Acceptance Cost
Protect
Day 1?
Total
Payoff
Weather
Day n
Protect
Day 2? Protect
Day n?
Payoff
Day 1
Payoff
Day 2
Payoff
Day n
Weather
Day 2
Forecast
Day 2
Weather
Day 1
Forecast
Day 1
Forecast
Day n
The Environmental Protection Agency (EPA) often must decide whether to permit the use of an economically beneficial chemical that may be carcinogenic (cancer-causing).
Furthermore, the decision often must be made without perfect information about either the long-term benefits or health hazards.
Alternative courses are to permit the use of the chemical,
restrict its use, or
ban it altogether.
Usage
Decision
Net
Value
Economic
Value
Cancer
Cost
Tests can be run to learn something about the carcinogenic potential of the material, and survey data can indicate the extent of exposure when people use the chemical.
These pieces of information are both important in making the decision.
For example,
if the chemical is only mildly toxic and human exposure is minimal, then restricted use may be reasonable.
On the other hand, if the chemical is only mildly toxic, but people are widely exposed, then banning its use may be imperative.
Usage
Decision
Net
Value
Economic
Value
Cancer
Cost Cancer
Risk
Human
Exposure
Carcinogenic
Potential
Invest
Do not Invest
Venture succeed
Venture fails
Large investment return
Fund lost
Less risky investment
Typical Return
Run for Reelection
Run for
Senate
Win
Lose
US Representative
(Intermediate)
US Senator
(Best)
Lawyer
(Worst)
Basic Risky Decision
Double-Risk Decision
Run for
Reelection
Run for Senate
Win
Win
Lose
Lose
US Representative
Small-time lawyer
Big-time lawyer
US Senator
Range of Risk Decision
Accept settlement
Reject
settlement
Highest
Lowest
Known Amount
Amount of court award
Imperfect Information
Forecast: Will
Hit Miami
Forecast: Will
Miss Miami
Danger, Low cost
Safety, Low cost
Safety, High cost
Danger, Low cost
Safety, Low cost
Safety, High cost Evacuate
Evacuate
Stay
Stay
Hurricane
Hits Miami
Hurricane
Misses Miami
Hurricane
Hits Miami
Hurricane
Misses Miami
Multiple Objective and Trade-offs
Job Offer 2 Chicago, Illinois:
High Salary
Madison, Wisconsin:
Low Salary
Job Offer 1
Sequential Decision
…Total Payoff
Forecast
Day 1
Forecast
Day 2
Weather
Day 1 Weather
Day 2
Decision
Day 2
Decision
Day 1