Decision Analysis. Chapter 13. Introduction to Decision Analysis. Used to develop an optimal strategy, when decision maker is faced with several alternatives And An uncertain/ risk filed pattern of future events Examples
Select the best decision - influenced by chance events concerning the demand for the condominiums, known as States of Nature. For PDC these are:
The Consequence is PDC’s profit
Evaluates each decision in terms of the best payoff
Evaluates each decision alternative in terms of the worst payoff that can occur
Profit is $8million. However would have been $20 if gone with large complex, & demand is strong
Thus opportunity lost or regret associated with decision alternative is 20-8= $12million
Rij = | Vj* - Vij|
Rij = regret associated with decision alternative di & state of nature sj
Vj* = payoff value corresponding to best decision for state of nature sj
Vij = payoff corresponding to decision alternative di & state of nature sj
Remember: trying to quantify the options open to management & help come to a decision, where options have values e.g. profit / contribution etc., as well as probabilities, the concept of expected value (EV) is often used.
N = the number of state of nature or Outcomes
P(sj)= probability of the state of nature sj or outcome of an event
P(sj) ≥ 0 for all states of nature / outcomes
∑ P(sj) = P(s1) +P(s2) +P(s3) + ………. + P(sN) = 1
EV= expected number of times that this outcome will occur in ‘N’ events = N x p.
or EV (di) = ∑ P(sj) Vij
EV = its probability times the outcome or value of the event over a series of trials. It is a weighted average based on probabilities.
Units Probability EV .
1,000 0.2 200
2,000 0.3 600
3,000 0.4 1200
4,000 0.1 400 .
1.0 2,400 = EV of daily sales
Step 1 Calculate the EV of the project(s), which in the long run should approximate actual average of the event many times over.
In example 1 we do not expect the sales on any one day to be 2,400 units, but in the long run, over a large number of days, the average sales would be equal to 2,400 units per day.
Advantages of expected value:
Project AProject B
Probability Profit EVProbability Profit EV___
0.8 5,000 4000 0.1 (2,000) (200)
0.2 6000 1200 0.25000 1000
£5,200 0.6 7000 4200
0.1 8000 800
Project B has a higher EV of profit. This means that on balance of probabilities it could offer a better return than A and is so arguably a better choice. On the other hand the minimum return from project A would be £5000. In addition with project B there is a small chance of making a loss.
NOTES: Although it appears to be widely used for the purpose , the concept of EV is not particularly well suited to one off decisions. EV can strictly only be interpreted as the value that would be obtained if a large number of similar decisions were taken with the same ranges of outcomes and associated probabilities.
A distributor buys perishable articles for £2 per item and sells them at £5. Demand per day is uncertain and items unsold at the end of the day represent a write off because of perishiability. If he under stocks he loses profit he could have made.
Daily Demand (units) No. of Days p
10 30 0.1
11 60 0.2
12 120 0.4
What stock level should be held from day to day?
Conditional Profit calculation , CP = (10 x £5) - (10 x £2) = £24
(CP = £3 per unit) units demanded units bought
Expected profit, EP = CP x probability of the demand
IF PDC knew for certain that the state of nature S1 (strong demand) would occur then the best alternative would be d3, with a payoff of $20million
If S1, select d3 and receive a payoff of $20 million
If S2, select d1 and receive a payoff of $8 million
EVPI = |EVwPI – EVwoPI |
Note: to stock 12 units per dayregardless of whether the decision analysis involves maximisation or minimisation, the minimum expected opportunity loss always provides the best decision alternativeIn addition, the minimum expected opportunity loss is always equal to the EVPI