September 29, 2015

Decision Analysis can be used to determine
the optimal strategies when a decision-maker
is faced with several decision alternatives and
an uncertain future events.

Possibilities to consider
 Certainty
 Uncertainty
 Risk

It is the product of the probability that the
event will occur and the amount to be
received upon such occurrence.

Let P be the probability value and X be the
amount of money.
 EV = P(X)

If an event has several possible outcomes
with probability P1, P2, ..., Pn and if X
denotes a discrete variable which can assume
the values X1, X2, ..., Xn then
 EV = P1X1 + P2X2 +...+ PnXn

A fair coin is tossed. If the coin lands heads,
Chito will receive P6, and pay P4 if it lands
tails. Find the EV.

EV = (0.50)(6) + (0.50)(-4) = P1

This means that the game is fair for Chito

Consider the following game of chance.
 Mark pays P200 and roll a fair die. Then he
receives a payment according to the following
schedule. If the event A={1,2,3} occurs, then he
will receive P100. If the event B={4,5} occurs, Mark
receives P200. If the event C = {6} occurs, then he
will receive P600. What is the average profit he
can make if he participates in this game?

If A occurs , then a profit will be
 100-200=-100 (Mark will lose P100)

If B occurs, a profit will be
 200-200=0

If C occurs, a profit will be 600-200=400

Therefore we may compute the average profit as follows:
 ave.-profit = (3/6)(-100) + (2/5)(0) + (1/6)(400) = 50/3

That is , Mark can expect to make P16.67 on the average
every time he plays this game.

The ABC construction operations manager
has to decide whether to accept a bid or not.
If the manager accepts the bid, the
construction company may gain p3.5 million
if it succeeds, or lose P2.5 million if it fails.
The probability that it will succeed is 30%.
Find the EV if the company accepts the bid.

The ABC construction operations manager has to
decide whether to accept a bid or not. If the manager
accepts the bid, the construction company may gain
p3.5 million if it succeeds, or lose P2.5 million if it fails.
The probability that it will succeed is 30%. Find the EV
if the company accepts the bid.


P1 = 30%
P2 = 70%
X1 = 3.5
X2 = -2.5


EV = -0.7
This means that the company is expected to lose.

The decision-maker is to pick the alternative
with the best payoff for the known event
 Payoff – consequence resulting from a specific combination of a decision
alternative and a state of nature

Best alternative
 Highest payoff if the payoffs are expressed in profits
 Lowest payoff if the payoffs are expressed as costs.
Consider the payoff table which illustrates a capacity planning
problem. It is helpful in selecting among alternatives because they
facilitate comparison of alternatives

Possible Future Demand
Alternative
Low
High
Small Capacity
300
370
Large Capacity
180
900
 Present values in thousand pesos


The payoffs are the present values of future revenues minus the
costs for each alternative in each event.
What is the best choice if future demand will be low?

The best choice is the one with highest
payoff.

P300,000 (leads to building small facility)

Assumption:

Managers can list the possible events but
cannot estimate their probabilities.

1.
Conditions that will be used in decision rules:
Pessimistic Approach
 Choose the alternative that is the “best of the worst.”
 It takes into account only the worst possible outcome
for each alternative.
 Maximization : maximin
 Minimization : minimax
Example: Refer to the previous table



Alternative
Small facility
Large facility
Worst Payoff
300
180
P300,000 is the worst member, the pessimist
will build a small facility.

Conditions that will be used in decision rules:
2. Optimistic
 “best of the best”
 “go for it” strategy that has high expectations
 Maximization : maximax
 Minimization : minimin
Since P900,000 is the best member, the optimistic would
build a large facility.

Conditions that will be used in decision rules:

3. Laplace
Choose the alternative with the best “weighted payoff”
Treats the state of nature as equally likely to each event



Alternative
Small facility
Large facility
Weighted Payoff
0.50(300) + 0.50(370) = 335
0.50(180) + 0.50(900)=540

Since P540,000 is the best weighted payoff, the realist would
build a large facility.
4. Minimax Regret
Choose the alternative with the best “worst regret.”
It seeks to minimize the difference between the given
payoff and the best payoff for each state of nature.
For profit: Regret Value = Highest column entry-every
column entry
For cost: Regret Value=Entry every column-lowest
column entry
Regret

Alternative
Low Demand
High Demand
Maximum
Regret
Small facility
300-300=0
900-370=530
530
Large facility
300-180=120
900-900=0
120
Pick a large facility to minimize the maximum
regret.

The manager has less information than with
decision-making under certainty but more
information than with decision-making under
uncertainty.

A widely used approach
circumstances is the EV
under
such

EV is the sum of the payoffs for an alternative
where each payoff is weighted by the
probability for the relevant state of nature.
 state of nature – possible outcomes for a chance
event

Which is the best alternative if the probability
of low demand is estimated to be 0.40 and
the probability of high demand is estimated
to be 0.60?
Possible Future Demand

Alternative
Low
High
EV
Small Facility
300
370
0.4(300)+0.6(370)=342
Large Facility
180
900
0.4(180)+0.6(900)=612
The large facility has higher EV which is 612.
 A schematic model of alternative available to
the decision maker along wit their possible
consequences
 Composed of a number of nodes that have
branches emanating from it.
 Two types of nodes
 a square
 a circle
represents a decision point
stands for a chance event.
 The branches of the tree having square nodes
represent alternatives and branches having
circular nodes represent chance events.

The manager of the company has to decide
whether to prepare a bid or not. It costs
P5,000 to prepare the bid. If the bid is
submitted, the probability that the contract
will be awarded is 60%. If the company is
awarded the contract, it may earn an income
of P60,000 if it succeeds or pay a fine of
P15,000 if it fails. The probability of success is
estimated to be 70%. Should the owner
prepare the bid?

P = 0.70

P = 0.60

contract awarded

prepare

not awarded
▪ not prepare
P = 0.40
success
60,000-5000
failure
-15,000-5,000
P = 0.30
-5,000

Compute the EV backward from position.

EV = 0.70(55,000) + 0.30(-20,000)
= 32,500



EV = 0.60(32,500) + 0.40(-5,000)
= 17,500

55,000

P=0.60


contract awarded
prepare
success P=0.70
32,500
failure
P17,500
P=0.30





not awarded
P=0.40
not prepare
-20,000
-5,000
0
Decision: The manager should therefore decide to prepare the bid.

Once a manager knows which decision to
make, the payoff increases and is now a
certainty, not a probability.

EVPI = expected payoff under certainty –
expected payoff under risk.

Compute for the expected payoff under certainty. The
best payoff for the small capacity and large capacity
are P370 and P900 respectively. Then combine by
weighing each payoff by the probability of that state
of nature and add the amounts.


The expected payoff under certainty is
0.40(370)+0.60(900) = P688

The expected payoff under risk, as computed is P612.

EVPI = P688-P612=P76

Mr. X is planning to open up a new branch of Engrande Lechon at a
new location in Pasig or expand the existing branch located in
Marikina City. Demand on the new location is expected to be 60%
high and 40% low. Fixed cost will reach the amount P150,000. If
the demand becomes high, he expects to have a revenue of
P250,000, however if the demand becomes low, he could only
expect a revenue of P200,000. Upon analyzing the situation in his
existing branch, he believes that by introducing new recipes the
sales will reach the amount P120,000 if the demand becomes high.
However, if the demand becomes low, he could only expect
P80,000 revenue. Projection on high demand in the existing
branch tends to be 55% and upon computing the fixed cost it
would reach the amount of P50,000.

If you were the consultant of Mr. X, what would you advise?

Ruth has to decide whether or not to open a
small dress shop near the U-belt, a few blocks
away from her. Her options are to open a small
shop, a medium-sized shop, or no shop at all.
The market for a dress shop can be good,
average, or bad. The probabilities are 0.20 for a
good market, 0.50 for an average, and 0.30 for a
bad market. The no profit loss for the mediumsized or small shops for the various market
conditions are given in the table. Building no
shops at all yields no loss and no gain. What do
you recommend?
Alternatives
Good Market (PhP)
Ave. Market (PhP)
Bad Market (PhP)
Small Shop
85,000
20,000
-30,000
Medium-sized shop
120,000
45,000
-70,000
No shop
0
0
0
Probabilities
0.20
0.50
0.30