decision making

Decision MakingDecision Making

Sales – Price Relationship AnalysisSales – Price Relationship Analysis

A workshop making lampshades finds that the number it can sell varies

depending on selling price.

It can sell 10 per week if the price is set at Rs. 80, but 50 per week if the

price is reduced to Rs. 40. The cost of production is Rs. 20 for each

lampshade and there are overheads of Rs. 60 per week.

Assume linear relationship between price and sales.

What should be the price to maximize his profit.

Sales – Price Relationship AnalysisSales – Price Relationship Analysis

0

500

1000

1500

2000

2500

0 20 40 60 80

Sales

Ru

pe

es

Revenue Cost Profit

Inverse CostsInverse Costs

Maintenance department of a foundry wants to plan its annual expenditure on

equipment maintenance.

Currently it has a crew of 10 people. It costs the company Rs. 20000 per

month per crew member.

If department increases its crew size, it can make maintenance operations

more efficient. As a result breakdown costs will come down.

Data analysis showed that size of maintenance crew and breakdown loss

have a inverse relation as follows.


Crew size 10 11 12 13 14 15

Ependiture 2400000 2640000 2880000 3120000 3360000 3600000

Breakdown loss 12000000 6000000 4000000 3000000 2400000 2000000

Total cost 14400000 8640000 6880000 6120000 5760000 5600000

Crew size 16 17 18 19 20

Ependiture 3840000 4080000 4320000 4560000 4800000

Breakdown loss 1900000 1800000 1700000 1600000 1500000

Total cost 5740000 5880000 6020000 6160000 6300000


0

2000000

4000000

6000000

8000000

10000000

12000000

14000000

16000000

8 9 10 11 12 13 14 15 16 17 18 19 20 21

Crew size

Co

st

Expenditure Breakdown loss Total cost

Inventory CostsInventory Costs

An

nu

al c

os

tA

nn

ual

co

st

Lot Size (Lot Size (QQ))

Holding cost (Holding cost (HCHC))

Ordering cost (Ordering cost (OCOC))

Total cost = Total cost = HCHC + + OCOC

Replacement DecisionsReplacement Decisions

DepreciationDepreciation

Any equipment we use at work reduces in value year by year,

which is called as depreciation.

Calculation of depreciation is needed for many decision making

situations and one of them is replacement analysis.

There are two basic methods of depreciation calculation.

1. Straight line analysis

2. Declining Balance method

Depreciation and Replacement Depreciation and Replacement AnalysisAnalysis

A machine tool costs Rs. 300,000 when new.

Lets calculate the written down value after 1,2 and 3 years using

1. Straight line method with annual depreciation of Rs. 50,000

2. By declining Balance method with annual depreciation of 20 %

Approach 1: Straight line method

Capital cost = 3,00,000

Annual depreciation = 50,000

Value after 1st year = 2,50,000

Value after 2nd year = 2,00,000

Value after 3rd year = 1,50,000

Depreciation and Replacement Depreciation and Replacement AnalysisAnalysis

A machine tool costs Rs. 300,000 when new.

Lets calculate the written down value after 1,2 and 3 years using

1. Straight line method with annual depreciation of Rs. 50,000

2. By declining Balance method with annual depreciation of 20 %

Approach 2: Declining balance method

Capital cost = 3,00,000

Annual depreciation = 20%

Value after 1st year = 30,00,000 - 0.2 x 3,00,000 = 2,40,000

Value after 2nd year = 2,40,000 – 0.2 x 2,40,000 = 1,92,000

Value after 3rd year = 1,92,000 – 0.2 x 1,92,000 = 1,53,600

Equipment Replacement DecisionsEquipment Replacement Decisions

Suppose a factory has a permanent need for an equipment, that wears

out over a period of several years. In the initial period of use, the

depreciation is likely to be high but maintenance costs will be low.

Towards the end of its useful life, the rate of depreciation may be slow

but maintenance costs will be high.

When will it be better to sell off the existing equipment and purchase a

new one ?


When will it be better to sell off the existing equipment and purchase a new one ?

Year Depreciationmaintenance

Cost1 50000 60002 45000 75003 40000 120004 35000 200005 30000 340006 25000 500007 20000 700008 15000 90000


0

20000

40000

60000

80000

100000

120000

0 2 4 6 8 10Year

Ru

pe

es

Depreciation Maintenence Total Cost

Decision making Under UncertaintyDecision making Under Uncertainty

A set of quantitative decision-making techniques for decision situations

where uncertainty exists

States of nature

events that may occur in the future

decision maker is uncertain which state of nature will occur

decision maker has no control over the states of nature

Decision making Under UncertaintyDecision making Under Uncertainty

Payoff TablePayoff Table

A method of organizing & illustrating the payoffs from different decisions

given various states of nature

A payoff is the outcome of the decision

Payoff TablePayoff Table

States Of Nature

Decision a b

1 Payoff 1a Payoff 1b

2 Payoff 2a Payoff 2b

Decision making CriteriaDecision making Criteria

Maximax criterion (optimistic)

choose decision with the maximum of the maximum payoffs

Maximin criterion (Pessimist)

choose decision with the maximum of the minimum payoffs

Minimax regret criterion

choose decision with the minimum of the maximum regrets for

each alternative

Hurwicz criterion

choose decision in which decision payoffs are weighted by a

coefficient of optimism,

coefficient of optimism () is a measure of a decision maker’s

optimism, from 0 (completely pessimistic) to 1 (completely optimistic)

Equal likelihood (Laplace) criterion

choose decision in which each state of nature is weighted equally

Decision making CriteriaDecision making Criteria

A B C DX 8 0 -10 6Y -4 12 18 -2Z 14 6 0 8

Pay-Offs in Thousands of rupeesAlternative

X -10 8Y -4 18Z 0 14

Alternative Minimum Pay-off Maximum Pay-off

Decision Making ExampleDecision Making Example

A B C DX 8 0 -10 6Y -4 12 18 -2Z 14 6 0 8

Pay-Offs in Thousands of rupeesAlternative

X -10 8Y -4 18Z 0 14

Alternative Minimum Pay-off Maximum Pay-off

Maximin Maximax

Decision Making ExampleDecision Making Example

Minimax Regret ExampleMinimax Regret Example

A B C

S1 700 300 150S2 500 450 200S3 300 300 100

Events and Pay-offsStrategic Altenatives

A B C

S1 0 150 50S2 200 0 0S3 400 150 100

Strategic Altenatives

Events and Regrets

Minimax Regret ExampleMinimax Regret Example

A B C

S1 700 300 150S2 500 450 200S3 300 300 100

Events and Pay-offsStrategic Altenatives

A B C

S1 0 150 50 150S2 200 0 0 200S3 400 150 100 400

Maximum Regret

Strategic Altenatives

Events and Regrets

Hurwicz CriterionHurwicz Criterion

Step 1: Choose alfa and (1-alfa)

Step 2: Determine for each alternative,

h = (alfa) (max pay off) + (1-alfa) (minimum pay off)

Step 3: Select the alternative with maximum value of ‘h’

‘alfa’ is the coefficient of optimism. It is a measure of a decision maker’s optimism, from 0 to 1 (completely optimistic)

(1-alfa) is the degree of pessimism

Hurwicz Criterion ExampleHurwicz Criterion Example

Take degree of optimism as 0.6

A B CS1 8000 4500 2000S2 3500 4500 5000S3 5000 5000 4000

Strategic Altenativ

Events and Pay-offs

For alternative S1, h = 0.6(8000)+0.4(2000) = 5600



A B CS1 8000 4500 2000 5600S2 3500 4500 5000 4400S3 5000 5000 4000 4600

Strategic Altenative

Events and Pay-offsh



A B CS1 8000 4500 2000 5600S2 3500 4500 5000 4400S3 5000 5000 4000 4600

Strategic Altenativ

Events and Pay-offsh

Laplace Criterion ExampleLaplace Criterion Example

In this method we each state of nature is weighted equally.

In other words, probability of occurrence of events is considered to be equal.

Step 1: Assign equal weights to each pay off of an alternative or strategy.

Step 2: Estimate the expected pay off for each alternative

Step 3: Select the alternative which has the maximum expected pay off


A B C D

1 4 0 -5 32 -2 6 9 13 7 3 2 4

Events and Pay offsAlternative

Expected Pay off for Alternative 1:

0.25 (4) + 0.25 (0) +0.25 (-5) + 0.25 (3) = 0.5


A B C D

1 4 0 -5 3 0.52 -2 6 9 1 3.53 7 3 2 4 4.0

Events and Pay offsAlternative

Expected Pay off

Expected Pay off for Alternative 1:

0.25 (4) + 0.25 (0) +0.25 (-5) + 0.25 (3) = 0.5

Decision making With ProbabilitiesDecision making With Probabilities

Decision making With ProbabilitiesDecision making With Probabilities

Probabilities need to be assigned to events

Expected value is a weighted average of decision outcomes.

EV x p ix ixi

n

where

ix outcome i

p ix probability of outco

( )

1

me i

Expected Monetary Value CriterionExpected Monetary Value Criterion

A store keeper stocks a perishable item. Shelf life of this item is one month. Store keeper wants to determine the number of items he should stock at the beginning of the month.

He buys the item for Rs. 30 and sells at Rs. 50.

He analyzes the trend for last two years i.e. 24 months. The following table gives the sales during last 24 months.

Sales 10 11 12 13

Frequency 3 5 10 6


Sales 10 11 12 13

Frequency 3 5 10 6

Probability 0.125 0.208 0.417 0.250


10 11 12 13

10 200 170 140 11011 200 220 190 16012 200 220 240 21013 200 220 240 260

StockDemand


10 11 12 13

10 25.00 21.25 17.50 13.7511 41.67 45.83 39.58 33.3312 83.33 91.67 100.00 87.5013 50.00 55.00 60.00 65.00

EMV 200.00 213.75 217.08 199.58

Stock and conditional pay offDemand

Expected Regret CriterionExpected Regret Criterion

10 11 12 13

10 0 30 60 9011 20 0 30 6012 40 20 0 3013 60 40 20 0

Stock and RegretDemand

10 11 12 13

10 0.00 3.75 7.50 11.2511 4.17 0.00 6.25 12.5012 16.67 8.33 0.00 12.5013 15.00 10.00 5.00 0.00ER 35.83 22.08 18.75 36.25

Stock and Conditional RegretDemand

Decision TreesDecision Trees


Bharat Oil Company (BOC) owns a land that may contain oil.

Geologist report shows a 25% chance of oil

Another company is offering to buy the land for Rs. 90 Cr

If BOC decides to drill, it will earn a profit of Rs. 700 Cr if oil is found.

However, it will incur a loss of Rs. 100 Cr if oil is not found.

Should BOC drill or sell ?


Oil

Oil

Dry

Dry

(0.25)

(0.25)

(0.75)

(0.75)

700 Cr

-100 Cr

90 Cr

90 Cr

Drill

Sell

decision

Expected pay off is 100 Cr

Expected pay off is

90 Cr

Value of Perfect InformationValue of Perfect Information

In many decision making exercises it is possible to get more or extra information about the events or state of nature.

But it will cost extra money.

Question : Is additional information worth the cost ?


Continuing with the previous example,

A sesmic survey can tell whether the land is fairly likely or fairly unlikely to have oil.

Cost of the survey is Rs. 30 Cr

Should BOC do the survey ?


Expected pay off with perfect information is

= 0.25 (700) + 0.75 (90) = 242.5 Cr

Expected value of perfect information is

= Expected pay off with perfect information - Expected pay off without perfect information

= 242.5 – 100 = 142.5 Cr.

If EVPI is less than the cost of survey, then don’t do the survey. It’s not worth it.

In this case, 142.5 Cr. >> 30 Cr.

It is worthwhile doing the survey.


A firm is adding a new product line and must build a new plant. Demand will

either be favourable or unfavourable, with probabilities of 0.6 and 0.4,

respectively. If a large plant is built and demand is favourable the pay off is

estimated to be Rs. 1520 Cr. If the demand is unfavourable, the loss with larger

plant will be Rs. 20 Cr

If a medium sized plant is built and demand is unfavourable, the pay off is Rs.

760 Cr. If the demand proves to be favourable, the firm can maintain the medium

sized facility or expand it. Maintaining medium sized facility will result in to a pay

off of Rs. 950 Cr and expanding it will give a pay off of Rs 570 Cr.

Draw a decision tree for this problem

What should the management do to achieve the highest expected pay off ?


Fav

Un Fav

(0.6)

(0.6)

(0.4)

(0.4)

1520 Cr

-20 Cr

760 Cr

Large

Small

decision Fav

Un Fav

Expand

Continue

570 Cr

950 Cr

0.6 (1520) – 0.4 (20) = 904 Cr

0.6 (950) + 0.4 (760) = 874 Cr

Build a large Plant

decision making

Documents

annual depreciation

value year

calculation of depreciation

cost of production

hc oc annual cost

size of maintenance

annual expenditure

overheads of rs