MANAJEMEN SAINS

“TEORI KEPUTUSAN”

Dr. Siti Aisjah, SE., MS

PPS MAGISTER MANAJEMEN

FAKULTAS EKONOMI UNIVERSITAS BRAWIJAYA

MALANG

TEORI KEPUTUSAN

Suatu proses untuk memilih tindakan yang terbaik dari sejumlah alternatif yang ada.

Pengambilan keputusan

1. sasaran dan tujuan

2. alternatif tindakan

3. resiko atau perolehan

Ada 4 ModelPengambilan Keputusan

1. Model keputusan dalam Kondisi Pasti model deterministik.

Asumsi: yad pasti dan tidak menyimpang

2. Model keputusan dalam Kondisi Resiko Setiap alternatif keputusan memiliki

kemungkinan kejadian yang lebih dari satu. Untuk bisa dikatagorikan sebagai model

keputusan dengan resiko besarnya probabilitas kemungkinan kejadian dari satu alternatif keputusan harus diketahui.

3. Model keputusan dalam Kondisi Tidak Pasti setiap alternatif keputusan memiliki

kemungkinan kejadian lebih dari satu.

besarnya probabilitas kejadian tidak diketahui.

4. Model keputusan dengan Kondisi Konflik model pengambilan keputusan dimana pengambil keputusan lebih dari satu.

ModelPengambilan Keputusan

Model Keputusan Dalam Kondisi Ketidakpastian

Model Keputusan Tanpa Probabilitas.

Contoh:

Keputusan

(untuk membeli)

Apartemen

Bangunan Kantor

Gudang

Kondisi Dasar

Kondisi Ekonomi Baik Ekonomi Krisis

$ 50.000 $ 30.000

$ 100.000 $ - 40.000

$ 30.000 $ 10.000

Kriteria pengambilan keputusan dalam kondsi ketidakpastian

Maximax nilai paling maksimum dari hasil-hasil yang maksimum.

Maximin nilai paling maksimum dari hasil-hasil yang minimum

Hurwich mencari kompromi antara kriteria Maximax dan Maximin keputusan dikalikan dengan Koefisien Optimisme

Minimak regretKriteria Penyesalan, Equal Likilihood Kriteria Bobot yang Sama

Decision AnalysisComponents of Decision Making

• A state of nature is an actual event that may occur in the future.

• A payoff table is a means of organizing a decision situation, presenting the payoffs from different decisions given the various states of nature.

Table 12.1 Payoff Table

Decision AnalysisDecision Making without Probabilities

Decision situation:

Decision-Making Criteria:

maximax, maximin, minimax, minimax regret, Hurwicz, equal likelihood

Table 12.2Payoff Table for the Real Estate Investments

Decision Making without ProbabilitiesThe Maximax Criterion

- In the maximax criterion the decision maker selects the decision that will result in the maximum of maximum payoffs; an optimistic criterion.

Table 12.3Payoff Table Illustrating a Maximax Decision

Decision Making without ProbabilitiesThe Maximin Criterion

- In the maximin criterion the decision maker selects the decision that will reflect the maximum of the minimum payoffs; a pessimistic criterion.

Table 12.4Payoff Table Illustrating a Maximin Decision

Decision Making without ProbabilitiesThe Minimax Regret Criterion

- Regret is the difference between the payoff from the best decision and all other decision payoffs.

- The decision maker attempts to avoid regret by selecting the decision alternative that minimizes the maximum regret.

Table 12.6 Regret Table Illustrating the Minimax Regret Decision

Decision Making without Probabilities

The Hurwicz Criterion

- The Hurwicz criterion is a compromise between the maximax and maximin criterion.

- A coefficient of optimism, , is a measure of the decision maker’s optimism.

- The Hurwicz criterion multiplies the best payoff by and the worst payoff by 1- ., for each decision, and the best result is selected.

Decision Values

Apartment building $50,000(.4) + 30,000(.6) = 38,000

Office building $100,000(.4) - 40,000(.6) = 16,000

Warehouse $30,000(.4) + 10,000(.6) = 18,000

Decision Making without Probabilities

The Equal Likelihood Criterion

- The equal likelihood ( or Laplace) criterion multiplies the decision payoff for each state of nature by an equal weight, thus assuming that the states of nature are equally likely to occur.

Decision Values

Apartment building $50,000(.5) + 30,000(.5) = 40,000

Office building $100,000(.5) - 40,000(.5) = 30,000

Warehouse $30,000(.5) + 10,000(.5) = 20,000

Decision Making without ProbabilitiesThe Maximin Criterion

- In the maximin criterion the decision maker selects the decision that will reflect the maximum of the minimum payoffs; a pessimistic criterion.

Table 12.4Payoff Table Illustrating a Maximin Decision

Decision Making without ProbabilitiesThe Minimax Regret Criterion

- Regret is the difference between the payoff from the best decision and all other decision payoffs.

- The decision maker attempts to avoid regret by selecting the decision alternative that minimizes the maximum regret.

Table 12.6 Regret Table Illustrating the Minimax Regret Decision

Decision Making without Probabilities

The Hurwicz Criterion

- The Hurwicz criterion is a compromise between the maximax and maximin criterion.

- A coefficient of optimism, , is a measure of the decision maker’s optimism.

- The Hurwicz criterion multiplies the best payoff by and the worst payoff by 1- ., for each decision, and the best result is selected.

Decision Values

Apartment building $50,000(.4) + 30,000(.6) = 38,000

Office building $100,000(.4) - 40,000(.6) = 16,000

Warehouse $30,000(.4) + 10,000(.6) = 18,000

Decision Making without Probabilities

The Equal Likelihood Criterion

- The equal likelihood ( or Laplace) criterion multiplies the decision payoff for each state of nature by an equal weight, thus assuming that the states of nature are equally likely to occur.

Decision Values

Apartment building $50,000(.5) + 30,000(.5) = 40,000

Office building $100,000(.5) - 40,000(.5) = 30,000

Warehouse $30,000(.5) + 10,000(.5) = 20,000

Decision Making without Probabilities

Summary of Criteria Results

- A dominant decision is one that has a better payoff than another decision under each state of nature.

- The appropriate criterion is dependent on the “risk” personality and philosophy of the decision maker.

Criterion Decision (Purchase)

Maximax Office building

Maximin Apartment building

Minimax regret Apartment building

Hurwicz Apartment building

Equal liklihood Apartment building

Decision Making without ProbabilitiesSolutions with QM for Windows (1 of 2)

Exhibit 12.1

Decision Making without ProbabilitiesSolutions with QM for Windows (2 of 2)

Exhibit 12.2

Exhibit 12.3

Decision Making with ProbabilitiesExpected Value

-Expected value is computed by multiplying each decision outcome under each state of nature by the probability of its occurance.

EV(Apartment) = $50,000(.6) + 30,000(.4) = 42,000

EV(Office) = $100,000(.6) - 40,000(.4) = 44,000

EV(Warehouse) = $30,000(.6) + 10,000(.4) = 22,000

Table 12.7 Payoff table with Probabilities for States of Nature

Decision Making with ProbabilitiesExpected Opportunity Loss

- The expected opportunity loss is the expected value of the regret for each decision.

- The expected value and expected opportunity loss criterion result in the same decision.

EOL(Apartment) = $50,000(.6) + 0(.4) = 30,000

EOL(Office) = $0(.6) + 70,000(.4) = 28,000

EOL(Warehouse) = $70,000(.6) + 20,000(.4) = 50,000

Table 12.8 Regret (Opportunity Loss) Table with Probabilities for States of Nature

Decision Making with ProbabilitiesSolution of Expected Value Problems with QM for

Windows

Exhibit 12.4

Decision Making with ProbabilitiesSolution of Expected Value Problems with Excel and Excel

QM(1 of 2)

Exhibit 12.5

Decision Making with ProbabilitiesSolution of Expected Value Problems with Excel and Excel QM

(2 of 2)

Exhibit 12.6

Decision Making with Probabilities

Expected Value of Perfect Information

• The expected value of perfect information (EVPI) is the maximum amount a decision maker would pay for additional information.

• EVPI equals the expected value given perfect information minus the expected value without perfect information.

• EVPI equals the expected opportunity loss (EOL) for the best decision.

Decision Making with ProbabilitiesEVPI Example

Decision with perfect information: $100,000(.60) + 30,000(.40) = $72,000 Decision without perfect information: EV(office) = $100,000(.60) - 40,000(.40) = $44,000 EVPI = $72,000 - 44,000 = $28,000 EOL(office) = $0(.60) + 70,000(.4) = $28,000

Table 12.9 Payoff Table with Decisions, Given Perfect Information

Decision Making with ProbabilitiesEVPI with QM for Windows

Exhibit 12.7

Decision Making with ProbabilitiesDecision Trees (1 of 2)

- A decision tree is a diagram consisting of decision nodes (represented as squares), probability nodes (circles), and decision alternatives (branches).

Table 12.10Payoff Table for Real Estate Investment Example

Figure 12.1Decision tree for

real estate investment example

Decision Making with ProbabilitiesDecision Trees (2 of 2)

- The expected value is computed at each probability node:

EV(node 2) = .60($50,000) + .40(30,000) = $42,000

EV(node 3) = .60($100,000) + .40(-40,000) = $44,000

EV(node 4) = .60($30,000) + .40(10,000) = $22,000

- Branches with the greartest expected value are selected :

Figure 12.2Decision tree with expected value at probability nodes

Decision Making with ProbabilitiesDecision Trees with QM for Windows

Exhibit 12.8

Decision Making with ProbabilitiesDecision Trees with Excel and TreePlan

(1 of 4)

Exhibit 12.9

Decision Making with ProbabilitiesDecision Trees with Excel and TreePlan

(2 of 4)

Exhibit 12.10

Decision Making with ProbabilitiesDecision Trees with Excel and TreePlan

(3 of 4)

Exhibit 12.11

Decision Making with ProbabilitiesDecision Trees with Excel and TreePlan

(4 of 4)

Exhibit 12.12

Decision Making with ProbabilitiesSequential Decision Trees

(1 of 2)- A sequential decision tree is used to illustrate a situation requiring a series of decisions.

- Used where a payoff table, limited to a single decision, cannot be used.

- Real estate investment example modified to encompass a ten-year period in which several decisions must be made:

Figure 12.3Sequential decision tree

Decision Making with ProbabilitiesSequential Decision Trees

(2 of 2)- Decision is to purchase land; highest net expected value ($1,160,000).

- Payoff of the decision is $1,160,000.

Figure 12.4Sequential decision tree with nodal expected values

Sequential Decision Tree Analysis with QM for Windows

Exhibit 12.13

Sequential Decision Tree Analysis with Excel and TreePlan

Exhibit 12.14

Decision Analysis with Additional InformationBayesian Analysis

(1 of 3)- Bayesian analysis uses additional information to alter the marginal probability of the

occurence of an event.

- In real estate investment example, using expected value criterion, best decision was to purchase office building with expected value of $444,000, and EVPI of $28,000.

Table 12.11 Payoff Table for the Real Estate Investment Example

Decision Analysis with Additional InformationBayesian Analysis

(2 of 3)

- A conditional probability is the probability that an event will occur given that another event has already occurred.

- Economic analyst provides additional information for real estate investment decision, forming conditional probabilities:

g = good economic conditions

p = poor economic conditions

P = positive economic report

N = negative economic report

P(Pg) = .80

P(Ng) = .20

P(Pp) = .10

P(Np) = .90

Decision Analysis with Additional InformationBayesian Analysis

(3 of 3)

- A posteria probability is the altered marginal probability of an event based on additional information.

-Prior probabilities for good or poor economic conditions in real estate decision:

P(g) = .60; P(p) = .40

- Posteria probabilities by Bayes’s rule:

P(gP) = P(PG)P(g)/[P(Pg)P(g) + P(Pp)P(p)] = (.80)(.60)/[(.80)(.60) + (.10)(.40)] = .923

- Posteria (revised) probabilities for decision:

P(gN) = .250

P(pP) = .077

P(pN) = .750

Decision Analysis with Additional Information Decision Trees with Posterior Probabilities

(1 of 2)- Decision tree below differs from earlier versions in that :

1. Two new branches at beginning of tree represent report outcomes;

2. Probabilities of each state of nature are posterior probabilities from Bayes’s rule.

Figure 12.5Decision tree with posterior

probabilities

Decision Analysis with Additional Information Decision Trees with Posterior Probabilities

(2 of 2)- EV (apartment building) = $50,000(.923) + 30,000(.077) = $48,460

- EV (strategy) = $89,220(.52) + 35,000(.48) = $63,194

Figure 12.6Decision tree analysis

Decision Analysis with Additional Information Computing Posterior Probabilities with Tables

Table 12.12Computation of Posterior Probabilities

Decision Analysis with Additional Information

The Expected Value of Sample Information

• The expected value of sample information (EVSI) is the difference between the expected value with and without information.:

For example problem, EVSI = $63,194 - 44,000 = $19,194

• The efficiency of sample information is the ratio of the expected value of sample information to the expected value of perfect information:

efficiency = EVSI /EVPI = $19,194/ 28,000 = .68

Decision Analysis with Additional Information Utility

Expected Cost (insurance) = .992($500) + .008(500) = $500

Expected Cost (no insurance) = .992($0) + .008(10,000) = $80

- Decision should be do not purchase insurance, but people almost always do purchase insurance.

- Utility is a measure of personal satisfaction derived from money.

- Utiles are units of subjective measures of utility.

- Risk averters forgo a high expected value to avoid a low-probability disaster.

- Risk takers take a chance for a bonanza on a very low-probability event in lieu of a sure thing.

Table 12.13 Payoff Table for Auto Insurance Example

Example Problem Solution(1 of 7)

a. Determine the best decision without probabilities using the 5 criteria of the chapter.

b. Determine best decision with probabilites assuming .70 probability of good conditions, .30 of poor conditions. Use expected value and expected opportunity loss criteria.

c. Compute expected value of perfect information.

d. Develp a decision tree with expected value at the nodes.

e. Given following, P(Pg) = .70, P(Ng) = .30, P(Pp) = 20, P(Np) = .80, determine posteria probabilities using Bayes’s rule.

f. Perform a decision tree analysis using the posterior probability obtained in part e.

States of Nature

DecisionGood ForeignCompetitiveConditions

Poor ForeignCompetitiveConditions

ExpandMaintain Status QuoSell now

$800,0001,300,000320,000

$500,000-150,000320,000

Example Problem Solution(2 of 7)

Step 1 (part a): Determine Decisions Without Probabilities

Maximax Decision: Maintain status quo

Decisions Maximum Payoffs

Expand $800,000

Status quo 1,300,000 (maximum)

Sell 320,000

Maximin Decision: Expand

Decisions Minimum Payoffs

Expand $500,000 (maximum)

Status quo -150,000

Sell 320,000

Example Problem Solution(3 of 7)

Minimax Regret Decision: Expand

Decisions Maximum Regrets

Expand $500,000 (minimum)

Status quo 650,000

Sell 980,000

Hurwicz ( = .3) Decision: Expand

Expand $800,000(.3) + 500,000(.7) = $590,000

Status quo $1,300,000(.3) - 150,000(.7) = $285,000

Sell $320,000(.3) + 320,000(.7) = $320,000

Example Problem Solution(4 of 7)

Equal Liklihood Decision: Expand

Expand $800,000(.5) + 500,000(.5) = $650,000

Status quo $1,300,000(.5) - 150,000(.5) = $575,000

Sell $320,000(.5) + 320,000(.5) = $320,000

Step 2 (part b): Determine Decisions with EV and EOL

Expected value decision: Maintain status quo

Expand $800,000(.7) + 500,000(.3) = $710,000

Status quo $1,300,000(.7) - 150,000(.3) = $865,000

Sell $320,000(.7) + 320,000(.3) = $320,000

Example Problem Solution(5 of 7)

Expected opportunity loss decision: Maintain status quo

Expand $500,000(.7) + 0(.3) = $350,000

Status quo 0(.7) + 650,000(.3) = $195,000

Sell $980,000(.7) + 180,000(.3) = $740,000

Step 3 (part c): Compute EVPI

EV given perfect information = 1,300,000(.7) + 500,000(.3) = $1,060,000

EV without perfect information = $1,300,000(.7) - 150,000(.3) = $865,000

EVPI = $1.060,000 - 865,000 = $195,000

Example Problem Solution(6 of 7)

Step 4 (part d): Develop a Decision Tree

Example Problem Solution(7 of 7)

Step 5 (part e): Determine Posterior Probabilities

P(gP) = P(Pg)P(g)/[P(Pg)P(g) + P(Pp)P(p)] = (.70)(.70)/[(.70)(.70) + (.20)(.30)] = .891 P(p P) = .109P(gN) = P(Ng)P(g)/[P(Ng)P(g) + P(Np)P(p)] = (.30)(.70)/[(.30)(.70) + (.80)(.30)] = .467 P(pN) = .533 Step 6 (part f): Perform Decision tree Analysis with Posterior Probabilities