Decision TreesDecision TreesDecision Fork and Event Fork; TerminalBranch Of A Decision Tree; IncorporatingBranch Of A Decision Tree; IncorporatingRisk Aversion Into Decision Tree Analysis;

Expected Value Of Sample Information;Expected Value Of Perfect Information

Further reading : https://www.mindtools.com/dectree.html

Why Decision Trees?

• Memiliki struktur yang efektif dan fleksibel.

• Menunjukkan gambaran yang seimbang antararesiko dan reward untuk tiap kemungkinankeputusan.

• Memungkinkan pengambil keputusan• Memungkinkan pengambil keputusanmendekomposisikan masalah keputusan yangkompleks kedalam beberapa masalah yang lebihsederhana.

• Mampu menentukan keputusan yang optimalyang melibatkan serangkaian keputusan padatitik-titik waktu yang berbeda.

How to draw it?

• Dimulai dari masa sekarang dan berakhir di masamendatang (KIRI KE KANAN)

• Nodes :– Decision nodes : keputusan harus dibuat (kotak)

– Event nodes : potensi event baru (lingkaran)– Event nodes : potensi event baru (lingkaran)

• Branch :– Decision branch

– Event branch

• Terminal : akhir– Penghitungan outcome

Nodes + Branch = FORK

Kecuali : Terminal (ends) ����

tidak memiliki fork

The Forksmutually exclusive (pemilihan hanya satu cabang)

collectively exhaustive (jumlah probability = 1, semua alternative

yang mungkin diikutsertakan)

DECISION FORK

• Titik waktu pengambilan

EVENT FORK

• Eksternal random event • Titik waktu pengambilan

keputusan

• Tiap cabang menunjukkan

decision yang mungkin

• Eksternal random event

mungkin terjadi

• Tiap cabang menunjukkan

outcome yang mungkin dan

probabilitas kejadian

Test market Chocola

Don’t test market Chocola

.60 Local success

.40 Local failure

Case (6) – ColacOColaco currently has assets of $150,000and wants to decide whether to market anew chocolate-flavored soda, Chocola.Colaco has three alternatives:Alternative 1: Test market Chocolalocally, then utilize the results of themarket study to determine whether or notto market Chocola nationally.Alternative 2: Immediately (withouttest marketing) market Chocola nationally.Alternative 3: Immediately (without

If Colaco performs a market study (at acost of $30,000), there is a 60% chancethat the study will yield favorableresults (referred to as a local success)and a 40% chance that the study willyield unfavorable results (referred toas a local failure).

If a local success is observed, there an85% chance that Chocola will be anational success. If a local failure is

test marketing) market Chocola nationally.Alternative 3: Immediately (withouttest marketing) decide not to marketChocola nationally.

In the absence of a market study, Colacobelieves that Chocola has a 55% chance ofbeing a national success and a 45%chance of being a national failure. IfChocola is a national success, Colaco’sasset position will increase by $300,000,and if Chocola is a national failure,Colaco’s asset position will decrease by$100,000.

85% chance that Chocola will be anational success. If a local failure isobserved, there is only a 10% chancethat Chocola will be a nationalsuccess. If Colaco is risk-neutral (wantsto maximize its expeceted final assetposition), what strategy should thecompany follow?

1. Gambar Decision Tree (Colaco)Untuk setiap kondisi harus dikembalikan ke kemungkinan akhir keputusan

2. Evaluate the Decision Tree (Colaco)ǁ menunjukkan alternatif dengan outcome maksimum

KANAN ke KIRI

3. Pengambilan Keputusan

• Untuk menentukan keputusan yang akanmemaksimasi expected final asset position →

evaluasi decision tree secara backward (dari kananke kiri).

– Pada tiap event fork, hitung expected final asset position– Pada tiap event fork, hitung expected final asset positiondan tulis pada Ο.

– Pada tiap decision fork, pilih keputusan (dengan simbol ll)yang memaskimasi hasil dan tulis hasil yang berasal darikeputusan tersebut pada .

– Lanjutkan kembali langkah-langkah di atas sampaimencapai titik awal decision tree.

– Urutan keputusan yang optimal diperoleh denganmengikuti jalur yang memiliki ll.

Analisis Resiko Colaco

• RISK NEUTRAL

– Strategi optimal Colaco padacontoh di atas mempunyaipeluang .45 memperoleh hasilakhir yang relatif kecil $50,000.

– Sementara strategi yang lain– Sementara strategi yang lainmempunyai peluang (.6)(.15) =.09 memperoleh hasil akhir dibawah $100,000.

• RISK ADVERSE

– Jika Colaco merupakan tiperisk-averse, strategi di atasmungkin tidak merefleksikanpreferensi perusahaan.

– Lihat grafik disamping :

Risk Aversion dalam Decision Tree

• Untuk memaksimumkan expected utility yang menjadi keputusan optimal

• Langkah :

1. Ganti tiap final asset position x0 dengan1. Ganti tiap final asset position x0 denganutility u(x0).

2. Pada tiap event fork, hitung expected utilityfinal asset position.

3. Pada tiap decision fork, pilih cabang yangmempunyai expected utility yang terbesar.

1. Hitung utility u(xo)

• Dari grafik utility

function diperoleh :

u($450) = 1 ���� most fav.

u($420) = .99u($420) = .99

u($150) = .48

u($120) = .40

u($50) = .19

u($20) = 0 ���� least fav.

2. Substitusikan ke Decision Tree

3. Evaluasi Decision Tree

Untuk Latihan di Rumah!

• Example 4 : ART DEALER

An art dealer’s client is willing to buy the painting Sunplant at $50,000. The dealer can buy the painting today for $40,000 or can wait a day and buy the painting tomorrow (if it has not been sold) for $30,000. The dealer may also wait another day and buy the painting (if it is still available) for $26,000. At the and buy the painting (if it is still available) for $26,000. At the end of the third day, the painting will no longer be available for sale. Each day, there is a .60 probability that the painting will be sold.

What strategy maximizes the dealer’s expected profit?

• Problem Group A no 7 : ERICA