09 decision theory l9
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Advanced Engineering
Projects Management
Dr. Nabil I El Sawalhi Assistant Professor of Construction
Management
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Decision theory
• Generalized approach to decision making
• Serve as basis for wide range of decision
making
• Degree of certainty about the decision is
important
• This can be from certainty to totaluncertainty which affects the way decision
taken
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Decision theory
• Two approaches for decision theory are:
• A payoff table and decision tree
• They provide structure for the organizinginformation in conductive forms to make
rational decisions.
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What is a Decision?
It is a choice from amongstalternatives
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Decision Making Criteria
• A set of goals or objectives
• A system of priorities
• Numeration of alternative actions• The outcomes associated with each
alternative
• A system of choice criteria.
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Decisions Resources
• Planning
• Organising
• Staffing• Direction
• Control
• Leadership• Communication, etc.
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Decision theory problemcharacteristics
• 1. A list of alternatives
• 2. A list of possible future state of nature
• 3. Payoffs associated with eachalternative/state of nature combination.
• 4. An assessment of the dgree of certianity
of possible future events• 5. A decision criterion.
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List of alternative
• Must be a set of mutually exclusive andcollectively exhaustive decisions that are
available to decision maker.
– For example : a real estate developer mustdecide on a plan for developing a certain
piece of property. After careful consideration
the developer has ruled out to “do nothing”
and is left with the following list of alternatives: – 1. residential proposal 2. commercial
proposal 1 3. commercial proposal 2
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State of nature
• Refers to: a set of possible futureconditions or events, beyond thecontrol of the decision maker, that will
be the primary determinant of theeventual consequence of the decision.
• Ex a real estate developer shop-center
• 1.no shopping center • 2. medium size shopping center
• 3.large shopping center AEPM L9 9
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Payoffs
• Payoffs is associated with each decision
alternative and various state of nature
• Payoffs may be:
– Profits
– Revenues
– Costs
– Or other nature of value
• Usually the measure are financially
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Payoffs
• They may be weekly, monthly, annual
• Payoffs are estimated value
• The number of payoffs depend on thenumber of alternative/state of nature
combination.
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Degree of certainty
• Three level of certainty
• 1. complete certain
• 2. complete uncertain• 3. degree of probability “risk” is between
the two extreme cases.
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Three Types of Problems
Certainty Problem
• Situations in which each course of
action is believed by the decisionmaker to result in only one outcome
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Risk Problem
• Situations in which, for each course of
action, the decision maker believes that
alternative outcomes can occur, theprobabilities of which are known or can be
estimated
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• Situations in which, for each course of
action, the decision maker does not know
which outcomes can or will occur
(ambiguous) and thus cannot assignprobabilities to the possible outcome
(variability)
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Uncertainty Problem
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Decision criterion
• The process of selecting one alternative
from a list of alternatives is governed by adecision criterion, which embodies the
decision maker‟s attitudes towered the
decision and degree of certainty.
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Decision criterion
• Some decision makers are optimistic
• Others are more pessimistic
• Some wants to maximize gains
• Some wants to reduce loss
• One example of decision criterion is “
Maximize the expected payoffs ” another is
“ Choose the alternative that has the best
possible payoffs ”
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The payoff Table
• The payoff Table is a device a decisionmaker can use to summaries and organize
information relevant to a particular
decision.• It includes”
• List of alternatives
• The possible future state of nature• The payoffs associated with each of
alternative/state of nature combination.
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• If probabilities for the state of nature are
known, these can be listed.
• There is a finite set of discrete decision
alternatives.
• The outcome of a decision is a function of
a single future event.
• Events (states of nature ) are mutually
exclusive and collectively exhaustive.
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S1 S2 S3
a1 v11 v12 v13a2 v21 v22 v23
a3 v31 v32 v33
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The payoff Table
Alternatives
State of nature
a1= the I th alternativeS j = the j th state of natureVij = the value or payoff that will be realized ifalternative I is chosen and event j occurs
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– In a Payoff table -
• The rows correspond to the possible
decision alternatives.
• The columns correspond to the
possible future events.
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Payoff or Utility Matrices
• Any problem is represented
by matrices:
• Columns: possible outcome
(O)
• Row : potential course
of action (C or S)
• Cell : represent thepayoff or utility
O2O1
U12U11S1
U22U21S2
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Payoff table for real estate
developer
• Residential
• Commercial 1
• Commercial 2
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Nocentre
Mediumcentre
Largecentre
$4 16 12
5 6 10
-1 4 15
The valuesin the tablerepresentsthe profitsor losses inhundred ofthousand if
theproposedalternativeis chosen
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Certainty
Assumptions of certainty• All information is known with certainty
• Complete Knowledge
• Stability
• No-ambiguity
• Enumeration of all strategies• Full knowledge of requirements
• Exactly one payoffs
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DMUC with a single objective
• Example 1.8• Droflas and Partners will launch one of
its heaviest campaigns to promote itssurveying services. The promotionbudget is not yet finalised, but theyknow that some £50,000 will beavailable.
• The partners want to determine howmuch they should spend for promotionalliterature, and which is the mostappropriate medium for their services.
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• They have created five „publication
strategies‟ with their projected outcomes in
terms of increased commissions.
• The decision criterion to be used in
identifying the optimal strategy is that of
maximum utility. That is the strategy that
yields the maximum utility is the optimumstrategy.
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• Utility for the purposes of this problem wasdefined as the ratio of outcome (i.e.,
increases in value of commissions) to
cost.• Shown below are the strategies and their
respective payoffs
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Strategy Cost
(£10000)
Increase in
commissions
(£10000)
Utility or Pay-off
(Ratio)
S1
1.80 1.78 0.988
S2
2.00 2.02 1.010
S3 2.25 2.42 1.075
S4
2.75 2.68 0.974
S5 3.20 3.24 1.012
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Which is the optimal strategy?
• [Answer = Strategy S3 ]
• The optimal strategy is that strategy whichyields the highest utility or pay-off.
• The pay-off is calculated by dividing thevalue of the increase in commissions by
the cost of the particular strategy.
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NOTE:
• Each strategy results in a unique pay-off;
• There is only one state of nature ;• There is a single measure of performance;
• The optimal strategy is the one that yields
the highest payoff or utility .
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Example 2DMUC with Multiple Objectives
• Droflas & Partners is developing itsannual plan in terms of three objectives:
• Increased Profits;
• Increased Market Share;• Increased Value of Commissions.
• The partners do not regard each of these
objectives with equal emphasis.• They are most interested in increased
market share, followed by commissiongrowth, and then profit.
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• The strength of this interest is currently in
the proportion of 5:3:2 for the three
objectives.
• Droflas have formulated three different
strategies for achieving the stated
objectives, each of which has a different
impact on the three outcomes underconsideration as follows:
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Measures of
Performan
ce (ofThree
Objectives)
ROI
(Profit)
% Increase
(Market
Share)
% Increase
(Commission
Growth)
Weighted or
Composite
Utility(CU)
Weights 0.2 0.5 0.3
Strategy S1 7 4 9 6.1
S2 3 6 7 5.7
S3 5 5 10 6.5
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Note:
• The profit objective could be stated in, andmeasured by, absolute money volume, orpercentage increase, or by return oninvestment (ROI);
• The market share is to be measured interms of percentage of the total market;
• Commission growth could be measured
either in money or percentage terms.• What is the optimal strategy?
• [Answer = Strategy S3]
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UNCERTAINTY
• The condition of being unsure about the possibleoutcome
• It is the variability in relation to performance
measures like cost, duration and quality
• It is associated with ambiguity
• Both of variability and ambiguity are associated
with lack of clarity
• Ambiguity is related to completeness, accuracy,meaning of information, implications.
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Uncertainty Problem
• Three criteria has been suggested for
selecting a course of action:
• MAXIMIN
– (criterion of pessimism)
MAXIMAX
– (optimism)
• MiniMax
– (criterion of regret)
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MaxiMinCriterion of pessimism
• A decision maker who isconfronted with the problemrepresented as follows
1. If (I) select S1, the minimum
gain is 12. If (I) select S2, the minimum
gain is 2
3.There, (I) will select S2because it maximize theminimum gain
O2O1
51S1
32S2
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DECISION MAKING UNDERUNCERTAINTY
• Example 1.• Having decided not to open a Warrington office
Droflas‟ managing partner is then inundatedwith commissions in the Warrington area and is
considering three „new‟ alternative strategies tocope with the work:
• S1: open a new branch office in Warrington;
• S2: merge with a competitor Warrington
practice (SMM perhaps?);• S3: takeover a competitor Warrington practice
(SMM perhaps?).
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• The managing partner has decided
that for the time being only one ofthese three strategies is economicallyfeasible.
• He has also decided that a further
alternative, staff commuting from otheroffices to execute the work, isimpractical.
• Given these options the managingpartner needs to construct aconditional payoff matrix for thisdilemma.
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• After conducting sufficient research, based
upon personal interviews and anticipating
possible reactions of competitors, the
managing partner produces the followingpayoff matrix:
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States of Nature
N1
N2
N3
Strategy S1 15 12 18
S2
9 14 10
S3
13 4 26
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CRITERION OF PESSIMISMThe optimal strategy is the strategy that yields the
„best of the worst‟ outcomes. This is also known as
MAXIMIN.
States of Nature Worst, or
Minimum
Outcome
N1 N2 N3
Strategy
S1
15 12 18 12
S2 9 14 10 9
S3 13 4 26 4
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CRITERION OF OPTIMISM
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CRITERION OF OPTIMISMThe optimal strategy is the strategy that yields the „best of
the best‟ outcomes. Also known as MAXIMAX.
States of Nature Best, or
Maximum
Outcome
N1 N2 N3
Strategy
S1
15 12 18 18
S2 9 14 10 14
S3 13 4 26 26
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COEFFICIENT OF OPTIMISM
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COEFFICIENT OF OPTIMISM Assuming that the balance between optimism and
pessimism is 60:40. This creates a coefficient of optimism
of 0.6 then S3 the weighted coefficient of optimism (0.6)solution
Best, or
Maximum
Payoff
Worst, or
Minimum
Payoff
Weighted
Payoff
Weight 0.6 0.4
Strategy S1 18 12 15.6
S2
14 9 12.0
S3 26 4 17.2
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MiniMax criterion (Regret)
1. If (I) select O1, themaximum loss is 2
2. If (I) select O2, the
maximum loss is 5
3. There, (I) select O1
because it minimize the
maximum loss.
O2O1
51S1
32S2
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Regret Criterion
1. If O1 will occur, S2 wouldbe selected
2. But If (I) selected S1 and
O1 did occur, the regret
would be 2-1=1
3. If (I) selected S2 and O1
occur, he would have no
regret (0) and so forth….
O2O1
51S1
32S2
O2O1
01S1
20S2
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CRITERION OF REGRET
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CRITERION OF REGRETThe optimal strategy is the strategy that yields the‘minimum of the maximum regret values’ outcome.
Also known as MINIMAX REGRET.The regret or opportunity-loss matrix is:
States of Nature Maximu
Regret
N1 N2 N3
Regret Or Opportunity
Loss
S1
0 2 8 8
S2 6 0 16 16
S3
2 10 0 10
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States of Nature
N1
N2
N3
S1
15 12 18
S2
9 14 10
S3 13 4 26
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Minimax = Maximin
• The point at which thisequality happened is theSaddle point
• Saddle point : is the point that
there is no higher value in itscolumn and no lower value inits row
• The corresponding strategies
for saddle point is the best forboth parties (the decisionmaker and the opponent)
O2O1
51S1
32S2
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EQUAL PROBABILITY CRITERION
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EQUAL PROBABILITY CRITERIONAlso called the LAPLACE CRITERION, or the Criterionof INSUFFICIENT REASON
States of Nature Expected
Monetary
Value
(EMV)
N1 N2 N3
Probability 1/3 1/3 1/3
Utility or Payoff
Strategy S1
15 12 18 15
S2
9 14 10 11
S3
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Minimax # Maximin
• We don‟t have a Saddlepoint
• Use Mixing strategy
• Select C1 with P1 and C2
with P2 such that
• P1(2)+ P2(3)= P1 (5)+P2(1)
O2O1
52S1
13S2
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DECISION MAKING UNDER
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DECISION MAKING UNDERCONFLICT OR COMPETITION
• Assumptions for a 2-person, zero sumgame:
• 2 rational opponents select optimal
strategies;• Both competitors know each other‟s
strategies;
• Payoff matrix is known to eachcompetitor;
• Both competitors choose theirstrategies simultaneously;
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• The loss of one competitor equals exactlythe gain of the other;
• Decision conditions remain unaltered;
• It is a repetitive decision making problem.• The lack of consistency of these
assumptions with conditions for tendering
within the construction industry should beapparent to you.
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Example 1
PURE STRATEGY• Contractor A has three potential strategies
for the execution of a project, A1, A2, A3,and player B has four potential strategies,B1, B2, B3, B4.
• If contractor A adopts strategy A1 andcontractor B adopts strategy B1,
contractor A will gain 8 units (EMV) whilstplayer B will lose 8 units.
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• If contractor A adopts strategy A1 andcontractor B adopts strategy B2,contractor A will gain 9 units whilstcontractor B will lose 9 units.
• All possible combinations of payoffs aregiven in the matrix below:
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Contractor B Minimum
of row
values
B1
B2
B3
B4
Strategy A1 8 12 7 3 3
A2 9 14 10 16 9
A3 7 4 26 5 4Maximum
of column
values
9 14 26 16
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• Applying the criterion of pessimism, the
optimal strategy for Contractor A is
identified by the MAXIMIN outcome.
• The optimal strategy for contractor B is
identified by the MINIMAX outcome.
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