Instructor: Vincent Duffy, Ph.D. Instructor: Vincent Duffy, Ph.D. Associate Professor of IE Associate Professor of IE Lab 2 Tutorial – Uncertainty in Lab 2 Tutorial – Uncertainty in Decision Making Decision Making Fri. Feb. 2, 2006 Fri. Feb. 2, 2006 IE 486 Work Analysis & Design II IE 486 Work Analysis & Design II
24
Embed
Instructor: Vincent Duffy, Ph.D. Associate Professor of IE Lab 2 Tutorial – Uncertainty in Decision Making Fri. Feb. 2, 2006 IE 486 Work Analysis & Design.
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Instructor: Vincent Duffy, Ph.D.Instructor: Vincent Duffy, Ph.D.
Associate Professor of IE Associate Professor of IE
Lab 2 Tutorial – Uncertainty in Decision MakingLab 2 Tutorial – Uncertainty in Decision Making
Fri. Feb. 2, 2006Fri. Feb. 2, 2006
IE 486 Work Analysis & Design IIIE 486 Work Analysis & Design II
Discussion on uncertainty in decision making – Discussion on uncertainty in decision making – related to economic decision making and related to economic decision making and material from ch.7 in Wickens on Decision material from ch.7 in Wickens on Decision making in the context of human factors and making in the context of human factors and ergonomics.ergonomics.
In lab exercise: In lab exercise: Suppose the range of outcomes is known, but Suppose the range of outcomes is known, but the probability distribution is the probability distribution is unknownunknown (uncertain). Use a sheet of (uncertain). Use a sheet of paper to illustrate the selection of alternative A, B or C based on paper to illustrate the selection of alternative A, B or C based on four different analytical criteria known as Maxi-min, Maxi-max, Mini-four different analytical criteria known as Maxi-min, Maxi-max, Mini-max regret, and equal likelihood. Write the payoff matrix on your max regret, and equal likelihood. Write the payoff matrix on your sheet of paper and re-calculate to decide based on each of the four sheet of paper and re-calculate to decide based on each of the four criteria.criteria.
Lab 2 Exercise: Decision Making & Uncertainty. Lab 2 Exercise: Decision Making & Uncertainty. Suppose the range of outcomes is known, but the probability distribution is Suppose the range of outcomes is known, but the probability distribution is
unknownunknown (uncertain). Use a sheet of paper to illustrate the selection of (uncertain). Use a sheet of paper to illustrate the selection of alternative A, B or C based on four different analytical criteria known as Maxi-alternative A, B or C based on four different analytical criteria known as Maxi-
min, Maxi-max, Mini-max regret, and equal likelihood. Write the payoff matrix on min, Maxi-max, Mini-max regret, and equal likelihood. Write the payoff matrix on your sheet of paper and re-calculate to decide based on each of the four criteria.your sheet of paper and re-calculate to decide based on each of the four criteria.
Observed outcomes of four trials are shown in the payoff matrix below. Observed outcomes of four trials are shown in the payoff matrix below. For each method, determine the expected outcomes before making your For each method, determine the expected outcomes before making your decision. decision. What is illustrated by the use of the different analytical techniques?What is illustrated by the use of the different analytical techniques?
observed outcome observed outcome expectedexpectedalternativealternative______11______22______33______4____ outcome4____ outcome ______ ______ A 6 0 1 3 A 6 0 1 3 B 2 4 4 1B 2 4 4 1 C 0 1 3 8 C 0 1 3 8
1. 1. MaxiMaxi--minmin criteria - pessimistic view criteria - pessimistic viewtry to maximize the minimum outcometry to maximize the minimum outcomea. for any given alternative (eg. A,B, or C), assume the a. for any given alternative (eg. A,B, or C), assume the worstworst possible outcome. possible outcome.b. choose the best (of those previously chosen).b. choose the best (of those previously chosen).
2. 2. MaxiMaxi--maxmax criteria - optimistic view criteria - optimistic viewtry to maximize the maximum outcometry to maximize the maximum outcomea. for any given alternative (eg. A,B, or C), assume the a. for any given alternative (eg. A,B, or C), assume the bestbest possible outcome. possible outcome.b. choose the best (of those previously chosen).b. choose the best (of those previously chosen).
3. 3. MiniMini--maxmax regretregret criteria criteria – Mini-max Regret: minimize the maximum possible regret.Mini-max Regret: minimize the maximum possible regret.– regret: difference between regret: difference between observedobserved and and bestbest payoff. payoff. 4. 4. EqualEqual--likelihoodlikelihood criteria criteria
a. for any given alternative (eg. A,B, or C), assume all outcomes are equally likely.a. for any given alternative (eg. A,B, or C), assume all outcomes are equally likely.b. maximize the b. maximize the expectedexpected value. value.
from Chapter 4 in Babcock in Managing Engineering and from Chapter 4 in Babcock in Managing Engineering and Technology (Babcock, 1991).Technology (Babcock, 1991).– especially...especially...
Decision making under uncertainty. p. 74-75 (today) Decision making under uncertainty. p. 74-75 (today) – In Babcock, D.L. 1991. Managing engineering and technology: an In Babcock, D.L. 1991. Managing engineering and technology: an
introduction to management for engineers, Prentice-Hall: Englewood introduction to management for engineers, Prentice-Hall: Englewood Cliffs, NJ.Cliffs, NJ.
You may consider ‘economic’ decision making (related to You may consider ‘economic’ decision making (related to decisions made on investment alternatives) somewhat decisions made on investment alternatives) somewhat different from ‘cognitive’ considerations in decision making different from ‘cognitive’ considerations in decision making (related to decisions made during a task) from the Wickens (related to decisions made during a task) from the Wickens text. text.
However, this material may be considered to help bridge the However, this material may be considered to help bridge the material without considering ‘time value of money’ yet.material without considering ‘time value of money’ yet.
Analytical tools for decision making Analytical tools for decision making under uncertaintyunder uncertainty
Uncertainty - example 1 Uncertainty - example 1
In a discussion of forecasting, and decision making In a discussion of forecasting, and decision making – Suppose the range of outcomes is known, but the Suppose the range of outcomes is known, but the
probability distribution is probability distribution is unknownunknown (uncertain). (uncertain).
1. 1. MaxiMaxi--minmin criteria - pessimistic view criteria - pessimistic view– try to maximize the minimum outcometry to maximize the minimum outcome– a. for any given alternative (eg. A,B, or C), assume the a. for any given alternative (eg. A,B, or C), assume the worstworst possible possible
outcome.outcome.– b. choose the best (of those previously chosen).b. choose the best (of those previously chosen).
Uncertainty - example 1 Uncertainty - example 1
In a discussion of forecasting, and decision making In a discussion of forecasting, and decision making
Suppose the range of outcomes is known, but the probability distribution is Suppose the range of outcomes is known, but the probability distribution is unknownunknown (uncertain). (uncertain).
1. 1. MaxiMaxi--minmin criteria - pessimistic view criteria - pessimistic viewtry to maximize the minimum outcometry to maximize the minimum outcome
a. for any given alternative (eg. A,B, or C), assume the a. for any given alternative (eg. A,B, or C), assume the worstworst possible outcome. possible outcome.
b. choose the best (of those previously chosen).b. choose the best (of those previously chosen).
Example 1) Suppose we have the following payoff matrix Example 1) Suppose we have the following payoff matrix
In a discussion of forecasting, and decision making In a discussion of forecasting, and decision making
Suppose the range of outcomes is known, but the probability distribution is Suppose the range of outcomes is known, but the probability distribution is unknownunknown (uncertain). (uncertain).
1. 1. MaxiMaxi--minmin criteria - pessimistic view criteria - pessimistic viewtry to maximize the minimum outcometry to maximize the minimum outcome
a. for any given alternative (eg. A,B, or C), assume the a. for any given alternative (eg. A,B, or C), assume the worstworst possible outcome. possible outcome.
b. choose the best (of those previously chosen).b. choose the best (of those previously chosen).
Example 1) Suppose we have the following payoff matrix Example 1) Suppose we have the following payoff matrix
1. 1. MaxiMaxi--minmin criteria - pessimistic view criteria - pessimistic viewtry to maximize the minimum outcometry to maximize the minimum outcome
a. for any given alternative (eg. A,B, or C), assume the a. for any given alternative (eg. A,B, or C), assume the worstworst possible outcome.possible outcome.
b. choose the best (of those previously chosen).b. choose the best (of those previously chosen).
Example 1) Suppose we have the following payoff matrix Example 1) Suppose we have the following payoff matrix
1. 1. MaxiMaxi--minmin criteria - pessimistic view criteria - pessimistic viewtry to maximize the minimum outcometry to maximize the minimum outcome
a. for any given alternative (eg. A,B, or C), assume the a. for any given alternative (eg. A,B, or C), assume the worstworst possible possible outcome.outcome.
b. choose the best (of those previously chosen).b. choose the best (of those previously chosen).
Example 1) Suppose we have the following payoff matrix Example 1) Suppose we have the following payoff matrix
try to maximize the maximum outcometry to maximize the maximum outcome
a. for any given alternative (eg. A,B, or C), assume a. for any given alternative (eg. A,B, or C), assume the the bestbest possible outcome. possible outcome.
b. choose the best (of those previously chosen).b. choose the best (of those previously chosen).
Uncertainty - example 2 Uncertainty - example 2
2. 2. MaxiMaxi--maxmax criteria - optimistic view criteria - optimistic viewtry to maximize the maximum outcometry to maximize the maximum outcome
a. for any given alternative (eg. A,B, or C), assume the a. for any given alternative (eg. A,B, or C), assume the bestbest possible outcome. possible outcome.
b. choose the best (of those previously chosen).b. choose the best (of those previously chosen).
Example 2) Suppose we have the following payoff matrix Example 2) Suppose we have the following payoff matrix
2. 2. MaxiMaxi--maxmax criteria - optimistic view criteria - optimistic viewtry to maximize the maximum outcometry to maximize the maximum outcome
a. for any given alternative (eg. A,B, or C), assume the a. for any given alternative (eg. A,B, or C), assume the bestbest possible outcome. possible outcome.
b. choose the best (of those previously chosen).b. choose the best (of those previously chosen).
Example 2) Suppose we have the following payoff matrix Example 2) Suppose we have the following payoff matrix
Uncertainty - example 2 Uncertainty - example 2 2. 2. MaxiMaxi--maxmax criteria - optimistic view criteria - optimistic view
try to maximize the maximum outcometry to maximize the maximum outcome
a. for any given alternative (eg. A,B, or C), assume the a. for any given alternative (eg. A,B, or C), assume the bestbest possible outcome. possible outcome.
b. choose the best (of those previously chosen).b. choose the best (of those previously chosen).
Example 2) Suppose we have the following payoff matrix Example 2) Suppose we have the following payoff matrix
Uncertainty - example 2 Uncertainty - example 2 2. 2. MaxiMaxi--maxmax criteria - optimistic view criteria - optimistic view
try to maximize the maximum outcometry to maximize the maximum outcome
a. for any given alternative (eg. A,B, or C), assume the a. for any given alternative (eg. A,B, or C), assume the bestbest possible outcome. possible outcome.
b. choose the best (of those previously chosen).b. choose the best (of those previously chosen).
Example 2) Suppose we have the following payoff matrix Example 2) Suppose we have the following payoff matrix
for maxi-max criteria: choose Cfor maxi-max criteria: choose C
Uncertainty - example 3Uncertainty - example 33. 3. MiniMini--maxmax regretregret criteria criteria – Mini-max Regret: minimize the maximum possible Mini-max Regret: minimize the maximum possible
regret.regret.– regret: difference between regret: difference between observedobserved and and bestbest payoff. payoff.
eg. suppose we chose eg. suppose we chose BB, but in outcome 1, if we had , but in outcome 1, if we had chosen chosen AA we could have had we could have had 66 (from (from AA) instead of ) instead of 22 (from (from BB). ).
So we have So we have regretregret…if only we had chosen …if only we had chosen AA, we could , we could
have had have had 44 more! more!
Uncertainty - example 3Uncertainty - example 33. 3. MiniMini--maxmax regretregret criteria criteria
Mini-max Regret: minimize the maximum possible regret.Mini-max Regret: minimize the maximum possible regret.
regret: difference between regret: difference between observedobserved and and bestbest payoff. payoff.
Example 3) Suppose we have a payoff matrix (payoff) Example 3) Suppose we have a payoff matrix (payoff) observed outcome (regret matrix) observed outcomeobserved outcome (regret matrix) observed outcome
for mini-max regret criteria: *choose Afor mini-max regret criteria: *choose A
Uncertainty - example 3Uncertainty - example 33. 3. MiniMini--maxmax regretregret criteria criteria
eg. suppose we chose eg. suppose we chose BB, but in outcome 1, if we had chosen , but in outcome 1, if we had chosen AA we could have had we could have had 66 (from (from AA) instead of ) instead of 22 (from (from BB). So we ). So we have have regretregret…if only we had chosen …if only we had chosen AA, we could have had , we could have had 44 more! more!
Example 3) Suppose we have a payoff matrix (payoff) Example 3) Suppose we have a payoff matrix (payoff) observed outcome (regret matrix) observed outcomeobserved outcome (regret matrix) observed outcome
Uncertainty - example 3Uncertainty - example 33. 3. MiniMini--maxmax regretregret criteria criteria
eg. suppose we chose eg. suppose we chose BB, but in outcome 1, if we had chosen , but in outcome 1, if we had chosen AA we could have had we could have had 66 (from (from AA) instead of ) instead of 22 (from (from BB). So we ). So we have have regretregret…if only we had chosen …if only we had chosen AA, we could have had , we could have had 44 more! more!
Example 3) Suppose we have a payoff matrix (payoff) Example 3) Suppose we have a payoff matrix (payoff) observed outcome (regret matrix) observed outcomeobserved outcome (regret matrix) observed outcome
Uncertainty - example 3Uncertainty - example 33. 3. MiniMini--maxmax regretregret criteria criteria
Example 3) Suppose we have a payoff matrix (payoff) Example 3) Suppose we have a payoff matrix (payoff) observed outcome (regret matrix) observed outcomeobserved outcome (regret matrix) observed outcome
Uncertainty - example 3Uncertainty - example 33. 3. MiniMini--maxmax regretregret criteria criteria
Example 3) Suppose we have a payoff matrix (payoff) Example 3) Suppose we have a payoff matrix (payoff) observed outcome (regret matrix) observed outcomeobserved outcome (regret matrix) observed outcome
Uncertainty - example 3Uncertainty - example 33. 3. MiniMini--maxmax regretregret criteria criteria Example 3) Suppose we have a payoff matrix (payoff) Example 3) Suppose we have a payoff matrix (payoff)
BB 2 4 4 1 2 4 4 1 B 4 0 0 7 7 B 4 0 0 7 7 C 0 1 3 8 C 6 3 1 0 C 0 1 3 8 C 6 3 1 0
66
for mini-max regret criteria: choose Afor mini-max regret criteria: choose A
Uncertainty - example 4Uncertainty - example 44. 4. EqualEqual--likelihoodlikelihood criteria criteria – this looks more like a ‘risk’ problem because you this looks more like a ‘risk’ problem because you
do use ‘assumed’ probabilitiesdo use ‘assumed’ probabilities
a. for any given alternative (eg. A,B, or C), a. for any given alternative (eg. A,B, or C), assume all outcomes are equally likely.assume all outcomes are equally likely.
b. maximize the b. maximize the expectedexpected value. value.
Uncertainty - example 4Uncertainty - example 44. 4. EqualEqual--likelihoodlikelihood criteria criteria
a. for any given alternative (eg. A,B, or C), assume all a. for any given alternative (eg. A,B, or C), assume all outcomes are equally likely.outcomes are equally likely.
b. maximize the b. maximize the expectedexpected value. value.
Example 4) Suppose we have the following payoff matrix Example 4) Suppose we have the following payoff matrix
Uncertainty - example 4Uncertainty - example 44. 4. EqualEqual--likelihoodlikelihood criteria criteria Example 4) Suppose we have the following payoff matrix Example 4) Suppose we have the following payoff matrix