1. Purpose 2. Introduction 3. Decision Rules 4. References 5. Related Links 6. Bibliography PPT presentation

Decisions Under Uncertainty

ENME 808s Product & System Cost Analysis  End of Semester Class Project Authors: Brian Reynolds, Brian Schaeffer Professor: Dr. Peter Sandborn

1. Purpose: Explains the purpose and use of this tutorial. 2. Introduction: An introduction to "decisions under uncertainty". 3. Decision Rules:  Defines and explains the different decision rules commonly used for decisions under uncertainty and illustrates their use in a hypothetical decision problem. 4. References: References to information used in this tutorial. 5. Related Links: WWW links relevant to this topic. 6. Bibliography: Extended bibliography of sources relevant to this topic.

1. Purpose:  The purpose of this project is to give a tutorial level summary of "decisions under uncertainty" and its application to product and system cost analysis.  Included will be the summary of the topic, a list of relevant sources with links, and an extended bibliography.  The depth and breadth of coverage should be equivalent to one class lecture.

2. Introduction:

Typically, personal and professional decisions can be made with little difficulty.  Either the best course of action is clear or the ramifications of the decision are not significant enough to require a great amount of attention.  On occasion, decisions arise where the path is not clear and it is necessary to take substantial time and effort in devising a systematic method of analyzing the various courses of action. [2,3]

When a decision maker must choose one among a number of possible actions, the ultimate consequences of some if not all of these actions will generally depend on uncertain events and future actions extending indefinitely far into the future.  With decisions under uncertainty, the decision maker must:

1. Take an inventory of all viable options available for gathering information, for experimentation, and for action; 2. List all events that may occur;

3. Arrange all pertinent information and choices/assumptions made; 4. Rank the consequences resulting from the various courses of action; 5. Determine the probability of an uncertain event occurring. [2,3]

Upon systematically describing the problem and recording all necessary data, judgments, and preferences, the decision maker must synthesize the information set before him/her using the most appropriate decision rules.  Decision rules prescribe how an individual faced with a decision under uncertainty should go about choosing a course of action consistent with the individual’s basic judgments and preferences.  This website will describe five such decision rules commonly used in industry [2,3]: 

Hurwicz criterion;  Laplace insufficient reason criterion;  Maximax criterion;  Maximin criterion;  Savage minimax regret criterion.

3. Decision Rules:

A tool commonly used to display information needed for the decision process is a payoff matrix or decision table.  The table shown below is an example of a payoff matrix.  The A's stand for the alternative actions available to the decision maker.  These actions represent the controllable variables in the system.  The uncertain events or states of nature are represented by the S's.  Each S has an associated probability of its occurance, denoted P.  (However, the only decsion rule that makes use of the probabilities is the Laplace criterion.)  The payoff is the numerical value associated with an action and a particular state of nature.  This numerical value can represent monetary value, utility, or both.  This type of table will be used to illustrate each type of decision rule.   

Actions\States S1 (P=.25) S2 (P=.25) S3 (P=.25) S4 (P=.25)

A1 20 60 -60 20

A2 0 20 -20 20

A3 50 -20 -80 20Table 1: General Payoff Matrix style from Chankong [4].  This generic/hypothetical example illustrates 3 different actions that can be taken, and 4 different possible, uncertain states of

nature with their respective payoffs.

i.  Hurwicz criterion.

This approach attempts to strike a balance between the maximax and maximin criteria.  It suggests that the minimum and maximum of each strategy should be averaged using a and 1 - a as weights. a represents the index of pessimism and the

alternative with the highest average is selected.  The index a reflects the decision maker’s attitude towards risk taking.  A cautious decision maker will set a = 1 which reduces the Hurwicz criterion to the maximin criterion.  An adventurous decision maker will set a = 0 which reduces the Hurwicz criterion to the maximax criterion. [1]  A decision table illustrating the application of this criterion (with a = .5) to a decision situation is shown below.  

Actions\States S1 S2 S3 S4 a = .5

A1 20 60 -60 20 0

A2 0 20 -20 20 0

A3 50 -20 -80 20 -15Table 2: Hurwicz criterion illustration (a = .5); Here the probability of each state is not

considered; results in a tie between the first two alternatives.

ii. Laplace insufficient reason criterion.

The Laplace insufficient reason criterion postulates that if no information is available about the probabilities of the various outcomes, it is reasonable to assume that they are equally likely.  Therefore, if there are n outcomes, the probability of each is 1/n.  This approach also suggests that the decision maker calculate the expected payoff for each alternative and select the alternative with the largest value.  The use of expected values distinguishes this approach from the criteria that use only extreme payoffs.  This characteristic makes the approach similar to decision making under risk. A table illustrates this criterion below. [1]   

Actions\States S1 (P=.25) S2 (P=.25) S3 (P=.25) S4 (P=.25) Expected Payoff:

A1 20 60 -60 20 0

A2 0 20 -20 20 5

A3 50 -20 -80 20 -7.5Table 3: Laplace insufficiency illustration; Second alternative wins when expected payoff is

calculated between equiprobable states.

iii. Maximax criterion.

The maximax criterion is an optimistic approach.  It suggests that the decision maker examine the maximum payoffs of alternatives and choose the alternative whose outcome is the best.  This criterion appeals to the adventurous decision maker who is attracted by high payoffs.  This approach may also appeal to a decision maker who likes to gamble and who is in the position to withstand any losses without substantial inconvenience. See the table below for an illustration of this criterion. [1]   

Actions\States S1 S2 S3 S4 Max Payoff

A1 20 60 -60 20 60

A2 0 20 -20 20 20

A3 50 -20 -80 20 50Table 4: Maximax illustration; First alternative wins.

iv. Maximin criterion.

The maximin criterion is a pessimistic approach.  It suggests that the decision maker examine only the minimum payoffs of alternatives and choose the alternative whose outcome is the least bad.  This criterion appeals to the cautious decision maker who seeks to ensure that in the event of an unfavorable outcome, there is at least a known minimum payoff.  This approach may be justified because the minimum payoffs may have a higher probability of occurrence or the lowest payoff may lead to an extremely unfavorable outcome. This criterion is illustrated in the table below. [1]   

Actions\States S1 S2 S3 S4 Min payoff

A1 20 60 -60 20 -60

A2 0 20 -20 20 -20

A3 50 -20 -80 20 -80Table 5: Maximin illustration. Second alternative wins.

v. Savage minimax regret criterion.

The Savage minimax regret criterion examines the regret, opportunity cost or loss resulting when a particular situation occurs and the payoff of the selected alternative is smaller than the payoff that could have been attained with that particular situation.  The regret corresponding to a particular payoff Xij is defined as Rij = Xj(max) – Xij where Xj(max) is the maximum payoff attainable under the situation Sj.  This definition of regret allows the decision maker to transform the payoff matrix into a regret matrix.  The minimax criterion suggests that the decision maker look at the maximum regret of each strategy and select the one with the smallest value.  This approach appeals to cautious decision makers who want to ensure that the selected alternative does well when compared to other alternatives regardless of what situation arises.  It is particularly attractive to a decision maker who knows that several competitors face identical or similar circumstances and who is aware that the decision maker’s performance will be evaluated in relation to the competitors. This criterion is applied to the same decision situation and transforms the payoff matrix into a regret matrix.  This is shown below. [1]    

Actions\States R1 R2 R3 R4 Max Regret

A1 30 0 40 0 40

A2 50 40 0 0 50

A3 0 80 60 0 80Table 5: Minimax illustration. First alternative wins.

4. Related Links:

http://www.csi.uottawa.ca/ordal/papers/fishburn/node8.html -- "Decision Under Risk and Uncertainty": webpage giving an introduction to the topic (mathematical basis).

http://www.aae.wisc.edu/aae705/notes/a06prisk.htm -- introduction to production decisions under risk.

http://www.palisade.com/html/decision_making.html -- a recent book covering the subject Decision making under uncertainty.

http://www.eng.uts.edu.au/~ronm/syseng/SLIDES/06_ALTMO/ index.htm -- "Alternative models in decision making" slide show.

http://vislab-www.nps.navy.mil/~me/calvano/asnesem/index.htm -- "A Survey of Systems Engineering in a Ship Design Environment".  Addresses Decisions under uncertainty in the context of systems engineering.

http://web.nps.navy.mil/~me/calvano/asnesem/sld098.htm -- Slide on decisions under uncertainty.

http://www.iot.ntnu.no/iok_html/users/sww/sto-pro.htm -- Stochastic Programming.

Other Links: http://www.research.microsoft.com/~horvitz/reflect.htm   http://www.bus.ed.ac.uk/courses/honours/dmu.html   http://www.york.ac.uk/inst/cee/hey.htm   http://www.csi.uottawa.ca/ordal/papers/fishburn/node8.html   http://www.aae.wisc.edu/aae705/notes/a06prisk.htm   http://informs.org/Conf/NO95/TALKS/WA17.4.html  

5. References:

[1]  Z.W. Kmietowicz, and A.D. Pearman. Decision Theory and Incomplete Knowledge. p. 7-9. Gower Publishing Company Limited:  Aldershot, Hampshire, England. 1981.

[2] Raiffa, Howard. Decision Analysis: Introductory Lectures on Choices Under Uncertainty. p. ix. Addison-Wesley Publishing Company: Reading, Massachusetts. 1970.

[3] Schlaifer, Robert. Analysis of Decisions Under Uncertainty. p. 65-68. Robert E. Krieger Publishing Company: Huntington, New York.

1978.

[4] Vira Chankong, Yacov Y. Haimes, Multiobjective Decision Making: Theory and methodology, (North Holland series in system science and engineering; 8). p. 32-38. Elsevier Science Publishing Co., Inc. New York, NY, 1983.http://terpconnect.umd.edu/~sandborn/courses/808S_projects/reynolds.html#purpose

1. Pay Off Matrix :– The main characteristics of the pay off matrix can be summarized as the follows –a. Very commonly used method.b. Acts as a very good quantitative technique.c. Helps in summarizing the various interactions of the various alternative actions and the various events.d. Explains about the probability in a very good manner.e. The probability is expressed in terms of the percentages.f. The probability can also be expressed in terms of the number of the times the particular event is appropriate to occur in a hundred trials.g. With the help of the probability, the pay off matrix can be prepared.h. The pay off matrix helps the decision maker a lot as it provides him with the quantitative measures of the pay off for each of the possible consequences and also each for the alternatives, which are under the consideration this is generally referred to as the Expected Value (E.V).

But the pay off matrix also has some weaknesses and these can be summarized as the follows – a. The pay off matrix is very largely dependent on the decision maker’s judgment about the possible outcomes for each of the alternative and also the values, which are assigned by the Decision Maker to each of them.b. The decision maker is forced by the pay off matrix to make a firm judgment about what he thinks may happen and the worth to him to those outcomes.c. The pay off matrix doesnot make a decision but instead it forces the Decision maker to be more realistic about the various outcomes that are possible.

2. Decision Treea. This technique is also referred to as the Decision Tables.b. Is a very simple technique.c. Helps in the representation of the sequential multistage logic of a decision problem.d. Shows the various decision paths that may be taken in – to account rather than the criteria used for the selection of a given path.e. The main concept of the technique is actually based on the extension of the probability theory.f. Decision Tree technique generally mathematically factors the degree of the risk into a business decision.g. Very helpful in representing the various probabilities for the outcomes.

h. Helps the decision maker in working out the various options and along with this also helps a lot in taking care of the different types of the odds and further helps in making a reasonably precise comparison among the various alternative courses of the action.i. Helps in the presentation of the analysis, when the decision maker has to make a sequence of the decisions and this is referred to as the Decision Node.j. Then after this movement takes place on to the various options emanating points and this is referred to as the Chance Nodes.k. The various steps that are to be followed in the process of this technique can be summarized as the follows –A. First of all, the tree has to be made with the help of the various types of the decision points.B. After this, the branches are to be added mainly for the external states of the events, which have the possibility of occurring.C. Then the probability of each of the state has to be included and then followed by the assignment of a value for each of the unique branches.D. Then one has to work in the backward direction as this step helps a great deal in analyzing the various consequences at each node of the tree.

3. Decision Rules – a. The decision rules and the decision tables find their use together in the process of the decision – making.b. Are generally used for the programmable or the routine / operating decisions.c. With the help of the Decision Rules, one is able to make the various decisions very economically and also in a very much efficient manner.d. Also the decisions taken are more accurate and also faster in the nature.e. The decision rules are documented in the nature.

4. Decision Table – a. Is very much precise and also very compact in the nature.b. Is very critical for the analyst as it helps the analyst to take in to account the various options, conditions, variables and the alternatives.c. Documents the rules that are used for the selection of one or more actions based on one or more conditions from a set of the various conditions that are possible.d. Can include both the qualitative and the quantitative bases for the decision making.e. Decision Tables are in the form of “IF” LISTINGS and “THEN” LISTINGS.f. The “IF” listings stipulate the required conditions.g. The “THEN” listings offer the actions that are needed to be taken if the suitable conditions are present.h. The “IF” LISTINGS form the ‘CONDITION STUB’ and the “THEN” LISTINGS form the ‘ACTION STUB’.i. But this technique can only be used in the conjunction with the other techniques.

http://www.mbaofficial.com/mba-courses/principles-of-management/explain-various-decision-making-tools/

What skills and experience do you possess and how do they relate to this position:

I believe my experiences in Credit Administration and RBWM are well enough to facilitate businesses/ functions in the development of products to ensure compliance; coordinate development and maintenance of supporting policies, procedures, agreement and contract. As I am responsible for preparing GDC and flash report of retail credit operations for HTS reporting, local and group reporting related to compliance will be easier tasks for me. I feel confident to provide support and deliver training whenever required since I have excellent communication and interpersonal skills. My understanding of managing BB audit team and having a strong view of subordinating personal interest to organizational interest will undoubtedly assist me to identify and report potential and significant compliance breaches to concern parties. Moreover, I am proficient at building rapport with customers from different backgrounds as I understand customer relationship management very well.