ELEMENT OF DECISION PROBLEMS.pdf

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