Maximin benefit criterion
- The max of the mins - find minimum of each row and get maximum
- PESSIMISTIC AND RISK AVERSE
Minimax regret criterion
- Find maximum value of each column, calculate maximum regret - redraw table. Find maximum of each row. The minimum of the maximums regrets.
- PESSIMISTIC AND RISK AVERSE
- would try to avoid missing opportunity if using this criterion
Maximax benefit
- Maximum benefit, choose action with max benefit
- OPTIMISTIC AND RISK TAKING
Hurwicz criterion
- degree of optimism
- each row take optimism level x best outcome + pessimistic level x worst outcome =
- choose max value
- takes into account the level of optimism / but assume that the DM is honest
Laplace criterion
- equal likelihood
- choose max option
Lexicographic approach
- Requires the DM to rank the attributes, and compare the alternatives one attribute at a time according to their importance
- logical and simple but does not allow tradeoffs among the three criteria
Sensitivity analysis
Sensitivity analysis is carried out to investigate whether the results are robust or if they are sensitive to changes in aspects of the model. We do so by changing slightly the probabilities/weights to see if the outcome changes.
How many conditions were discussed in this
course, on which the additive value function approach can be used?
- Satisfaction of preferential independence among any groups of attributes
- Satisfaction of corresponding trade-off, or Thomsen condition
- Interval scale property for constructing marginal value function
- Weights of attributes need to be assessed as scaling constants (trade-offs), not necessarily relative importance
- Linear & complete compensation among criteria without any limit
Simon’s satisficing level model
Set a satisfactory level of performance for the most important criterion, e.g. 7 for TC
Eliminate unsatisfied alternatives, e.g. Candidates C and D
Set a satisfactory level of performance for the next most important criterion, e.g. 0.7 for PE
Eliminate unsatisfied alternatives, e.g. Candidates B and E
After the above two rounds, Candidate A is chosen as the most preferred solution
Simon’s model is based on bounded rationality and is not a prescriptive model,
it is good for solving routine MCDM problems but it is not easy to set satisfacing levels
- Can backtrack if levels seem to strict or too lenient
2 stage transition in markov chains formula
S2 = S1 x P ( = S0 x P1)
Explain whether and why this markov chain has a steady state or not
- Unichain: There is a single recurrent class made by three recurrent states that communicate with each other.
- Aperiodic: for each state it is possible to return to itself with a positive probability (p_ii > 0, forall i=1,2,3).
- So, the process is completely ergodic, meaning that the market share does have a steady state.
Utility definition
Quantification of the DM’s preferences towards an outcome under risk
Difference between lexicographic methods and utility ranking
Candidate E is the best compromised or balanced choice on all the three criteria
5’Os for problem structuring
- Ideas generated from brainstorming should be grouped and clustered
- Useful ‘checklists’ for grouping and clustering e.g. 5 O’s
- Owners: DM, stakeholders
- Objectives: criteria, values
- Options: alternatives
- Occasion: context, constraints, environment
- Odds: uncertainties
How many Von Neumann & Morgenstern axioms are there? What are they?
- These axioms prove that if the DM’s preferences satisfy the following axioms, then he should choose between lotteries by using the expected utility criterion
- 5 axioms
- AXIOM 1: complete orderly axiom
- For any two rewards r1 & r2 either
- r1 .> r2 or r2 > r1 or r1 - r2
- and if r1 > r2 and r2 > r3 then r1 > r3
- AXIOM 2: Continuity axiom
- AXIOM 3: Independence axiom
- AXIOM 4:Unequal probability axiom
- AXIOM 5: Compound lottery axiom
Local scale and global scale for value assessment in MCDA
Local scale: A best alternative on a criterion listed in the decision matrix is assigned a score of 1 (100%) and the worst assigned a score of 0 (0%). This is a “lazy” approach”.
– Global scale: The end point defined by the ideal and worst conceivable performance on the particular criterion, or by the best and worst performance which could realistically occur. A global scale can be set before consideration of specific alternatives, so
weights can be assigned before consideration of alternatives.
Issues to consider when identifying criteria
- Value relevance
- Understandability
- Measurability
- Avoiding redundancy
- Value and preferential independence
- Balancing completeness and conciseness
- Operationality - not unduly demanding, data available
- Keep it simple
Risk averse
Of any lottery of the form (A,0.5,B) - where A and B are specific monetary values, their CME x is less than the EMV of the lottery, that is
x < 0.5 (A+B) - (CME < EMV)
p(x) = 0.5 (p(A)+p(B))
Concave curve
Risk taking
Of any lottery of the form (A,0.5,B) - where A and B are specific monetary values, their CME x is less than the EMV of the lottery, that is
x > 0.5 (A+B) - (CME > EMV)
p(x) =0.5 (p(A)+p(B))
Convex curve
Risk neutral
x = 0.5 (A+B)
p(x) =0.5 (p(A)+p(B))
Straight line / indifferent curve
Baye’s equation
p (dj , fi ) = p (fi l dj) x p (dj)
p (fi) = p(di,fi) + p(d2,fi)
p (dj/fi) = p(dj,fi)/p(fi)
Expected value of the perfect information
SUM (MAX VALUE OF EACH COLUMN x PROBABILITY)
- MAX VALUE OF TREE
- FEE
WORTHWHILE?
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Industrial Action - Readings17
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Industrial Action - Lecture10
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Employment status30
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Decision Making22
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The “Object of Control” Frame Work - Merchant and Van der Stede57
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Performance Measurement and Management I: Behavioural implications of performance measurement systems25
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Levers of control0
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Inter-organisational Relations: Transaction costs economics, bureaucracies & management control52
