DECISION MAKING TOOLS 1

Elements of Decision Problems 2

3 1.Objectives 2.Decisions 3.Uncertain Events 4.Consequences

4 1. Objectives Objective: A specific thing one wants to achieve: To harvest successfully – Farmer. To resolve a specific scientific problem – Scientist. To make a lot of money – Investor.

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6 Decision Context DECISION CONTEXT = The setting in which a decision occurs Decision Context activates only subset of objectives.

7 2. Decisions (to be made) At least two alternatives required Most decisions call for: The Immediate Decision Look at all possible decision alternatives: Be Creative! Decision may be of a sequential nature: Future decisions may need to be taken into account when making immediate decision

List of possible decisions is important, but more important is the order in which they occur. 8

9 3. Uncertain Events Many decisions (All?) are made under the presence of uncertainty Investment decision: Will stock of company go up or not? Camping decision: Will the weather be good or not? Mutual fund decision: Will entire stock market go up? A decisions problem becomes more complicated when the number of relevant uncertain events increases

The time sequence of uncertain events related to the sequence of decision is important. Why? Tells you what information becomes known before a decision has to be made Uncertain events may be unknown at the time of the immediate decision, but may be known by subsequent decisions

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12 4. Consequences Evaluation of outcomes: Profit – Measured in # Dollars Casualties – Measured in # Deaths Environmental Damage – Measured in # Polluted Soil Health Risk – Measured in # Infected People Trade off between has to be made in almost any decision problem

Planning Horizon = Time when decision maker finds out the results 13

Larkin Oil 15m 14

What is the immediate decisions? Is this a sequential decision problem? What is an appropriate planning horizon for Larkin? A graphical representation? 15

Structuring Decisions 16

17 Steps Suppose elements of Decision Problem (DP) are available, i.e.: Objectives that apply to the decision context Immediate Decision and subsequent decision(s) Alternatives for each decision Uncertain elements (events) Consequences How does one proceed with structuring the DP?

18 STEP 1: Filter & Operationalize the Objectives STEP 2: Structure the elements in a logical framework STEP 3: Fill in the Details

STEP 1: Filter & Operationalize the Objectives  Getting the Decision Context right  Enlarging Decision Context may increase the number of objectives that are relevant.  Decreasing the Decision Context may cause current relevant objectives to become irrelevant.  Classify how to measure objectives 19

STEP 2: Structure the elements in a logical framework 20 Structure Logic and time sequence between decisions Structure Logic (dependence) between the uncertain events Structure time sequence of uncertain events related to the sequence of decisions Represent Logic by using Influence Diagrams or Decision Trees

STEP 3: Fill in the Details 21 e.g.; Give precise definitions of decisions & uncertain events Specify probability distributions for the uncertain events through a combination of data analysis & expert judgment. Specify precisely how consequences are measured and formalize trade off between objectives

Influence Diagrams 22

23 About An influence diagram (or decision diagram) is a graphical model used to represent the structure of a decision problem and the relationships among its different elements (uncertainties, decisions, and consequences). The diagram is built based on the decision maker ’ s current state of knowledge about the situation. different elements (uncertainties, decisions, and consequences).

24 An influence diagram captures current state of knowledge An influence diagram should NEVER contain cycles Interpreting an influence diagram is generally easy Creating influence diagrams is difficult

25 Basic Elements A node is the basic element in an influence diagram. Each node corresponds to a specific distinction or variable, including uncertainties, decisions, and consequences. Decision Chance/ Uncertainty Deterministic Consequence/ Value/ Objective

26 An arc is a line with an arrowhead pointing from one node to another node in an influence diagram. We refer to the sending node as a parent and the receiving node as a child. If the child node is a decision node, then the arc is informational, and indicates that the parent node ’ s value will be known to the decision maker at the time the decision will be chosen. Otherwise, the arc is conditional, and indicates that we will be assessing a (probability) distribution for the child conditioned on its parents.

Logical relationships 27

28 Basic Influence Diagrams Basic Risk Decision

Imperfect Information 29

Sequential Decisions 30

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Intermediate Calculations (deterministic nodes) 32

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A Lease/Buy Problem  The Amiable Insurance Company needs additional copying capacity.  They are currently negotiating with Sharp Image (SI), manufacturer of the X100 copier.  Lease or buy the X100 from SI? 35

36  Facts:  effective life of three years (length of planning horizon).  SI will sell an X100 copier to Amiable for $10,000.  SI will lease Amiable an X100 copier for a yearly fee of $1,500 plus a usage fee of 7¢per copy.  maintenance fees (if purchased): $800 annually.  X100 will have a salvage value of $1,000 at the end of three years.  expect to make 50,000 copies on the X100 per year.  interest rate for discounting purposes is 20%.

 Amiable’s objective: minimize the total discounted costs associated with the X100 copier that are generated over the three year planning horizon.  Should they lease or buy the X100? 37

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Enriching Determination of Salvage Value  Salvage value now depends upon:  the purchase price (P);  the length of the planning horizon (N); and,  the usage per year (U). Specified as kP/(N × U), where k is a given constant. 39

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41 Example: Toxic Chemicals and the EPA 15m

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