Decision Making: Alternatives and Models - Chapter 7

Chapter 7: Alternatives and Models in Decision Making

• A complete alternative emerges from an interesting idea in its final state
• Alternatives should be presented for analysis whether they are likely to be feasible

Limiting and Strategic Factors

• Factors that impede the attainment of objectives are limiting factors
• Identifying and examining limiting factors is a key part of systems engineering
• Strategic factors are those that can be altered to make progress possible

Comparing Alternatives Equivalently

• Alternatives has to be converted to a common measure for equivalent comparison
• Money flow and economic optimization models are central to this conversion process

Models in System Analysis

• Models and their manipulation (simulation) are useful in systems analysis.
• A model represents a system to be brought into being or to analyze an existing one
• Science uses models in the natural world
• Engineering models are related to the human-made world

Classification of Models

• Physical models are geometric equivalents as miniatures, enlargements, or duplicates.
• Analog models are models that focus on similarity in relations
• Analogues are meaningless from a visual standpoint
• Schematic models reduce a state or event to a chart or diagram
• Schematic models may or may not look like the real world
• Mathematical models that use the language of mathematics to describe and explain a system
• Mathematical models provide a much higher degree of abstraction and precision

Models and Indirect Experimentation

• Direct experimentation involves manipulating the object, state, event, or environment
• Results are observed after direct experimentation

Indirect Experimentation or Stimulation

• When direct experimentation is impractical or expensive, models are used
• Templates or models are leveraged to represent real-world scenarios, like wind tunnel testing
• Simulation plays a crucial role in systems engineering and analysis
• Simulation allows characteristics and optimization without direct experimentation

Decision Models

• Mathematical decision models encompasses all relevant factors impacting effectiveness and cost
• Models focus on significant factors, but may lead to misconception of isolated system elements
• Ensure alignment with reality, models undergo validation through adjustments and empirical data testing

Validation Process Steps

• Postulate a model
• Test the model prediction or explanation against measurements or observations
• Modify the model to reduce the misfit

Decision Evaluation Theory

• Decision evaluation is an important part of systems engineering and analysis
• Evaluation provides a basis for choosing among alternatives from system design or operation
• Equivalence provides the common evaluation measure on which choices are based

Evaluation by Money Flow Modeling

• Economic equivalence is expressed as present (PE), annual (AE), or future equivalent (FE) amount
• Economic equivalence is also based on as the internal rate of return and the payback period
• A general equivalence function is: PE, AE, or FE = f (Ft, i, n)
  • Ft: positive or negative money flow at the end of year t
  • i: annual rate of interest
  • n: number of years

Evaluation by Economic Optimization Modeling

• Decision evaluation can require a combination of money flow modeling and economic optimization
• When investment cost, periodic costs, or project life depend on decision variables, it optimizes these
• Economic optimization requires an evaluation before figuring the economic equivalence.
• An economic optimization function links an evaluation measure (E) with controllable variables

Unconstrained form may be expresses mathematically as:

• E = f (X, Y)
  • E: Mathematical model that formally links controllable decision variable
  • X: Controllable decision variables
  • Y: System parameters, which cannot be directly controlled by the decision maker

The optimization function can be extended to both operational and design decision involving alternatives

• The extension involves identifying and isolating design/decision-dependent system parameters
• 2 can be restated in unconstrained form as E = f (X, Yd, Yi)
• Design-dependent parameters (Yd): Factors with values under the control of designers, specialize during development
• Design-independent parameters (Yi): Factors beyond designer control impacting all systems' effectiveness
• Design variables (X): Factors defining the design optimization space

Decisions Involving Multiple Criteria

• Choice is not easy when multiple criteria are present, difficulty is perpetuated by sidestepping basic concepts

Selecting Criteria

• Ensure you "Figure Out What Matters”

Basis For Decisions

• Focus on what's different

Direct Ranking Methods

• Alternatives presented to the decision maker for ranking
• Before asking alternatives to be ranked, present the important criteria and ask for these to be ranked first
• Ranking is made easier with the method of paired comparisons

Direct Ranking Example

• Consider five aspects to design office appliance: being better, cheaper, faster, repairable, and disposable

Subsequent Analysis

• Criteria are used to decide on the best mutual exclusive design

Comparisons Needed

• Need to compare N criteria when alternatives are ranked in pairs
• Paired comparisons result in "preferred to" and "equally preferred to" outcomes.

Systematic Elimination Methods

• Among the simplest approaches available for choosing from multiple alternatives
• Values must be measurable (scalar) or rank orderable (ordinal)

Systematic Elimination Limitations

• They don't consider weights
• Methods are non-compensatory and don't consider possible trade-offs

Comparing Alternatives

• Comparing alternatives can be done in two ways after the criteria are ranked

1. Select the best alternative for the most important criterion- break ties using a second criterion
2. Examine one criterion, eliminate alternatives not meeting the minimum standard

Weighting Method of Evaluation

• Weighted importance ratings can extend the ranking and elimination methods
• This extension explicitly recognize the higher importance/priority that criteria should assume

Weight-Based Analysis

• Criteria weights are applied to alternatives; an analysis of importance applied

Tabular Additive MEthod

• A structured way of combining criterion weights and ratings for each alternative
• Weights generally sum to 100%, ideal rating is 10 for all criteria
• Weighted sum indicates how close the alternative is to the ideal

Graphical Additive Method

• Data given in the Tabular Additive Method is also shown as a stacked bar chart

Decision Evaluation Display

• Differ significantly from others, where rating/eliminating are impediments to intuition/judgement
• Display is based on differences between alternatives with multiple criteria and properly exhibited

Decision Evaluation Display Elements

• Alternatives (A, B, C): Appear as vertical lines
• Equivalent Cost/Profit: Horizontal axis, represent cost/profit with cost/profit increasing left to right
• Vertical axes represent non economic criteria in nature , each with its scale relating to factor
• Threshold limiting values for non economic criteria (less than, equal to/ greater than) as horizontal lines
• Anticipated outcomes/ estimates can be entered into circles placed on, below/above threshholds making visable between outcomes

Decisions Under Risk and Uncertainty

• A decision evaluation matrix exhibits the interaction of alternatives and possible futures
• The decision evaluation matrix model shows the results that may occur for each alternative

Key Symbol Definitions

• A₁ = an alternative available for selection, where i = 1,2,..., m
• F₁ = a future not under decision maker control, where j = 1,2,..., n
• P₁ =Probability the jth future will occur, j = 1, 2, ..., n
• Eij = evaluation measure (positive or negative) associated with the ith alternative

Decisions Under Assumed Certainty

• A vector with as many evaluations, with outcomes that constitute as column
• Appears in the decision evaluation displayed with the payoffs represented by Ei, where i = 1,2,...,m.

Decision Making Under Risk

• A decision maker doesn’t suppress ignorance about the future rather assignment of probabilities

Decision Making Under Example

• Decision making is explicit thanks to the assignment of probabilities
• Probabilities are based on experimental, expert opinions, judgment, or a combination
• Computer firm bids on two contracts advertised by a municipality: a central computing facility
• The other involves the development of a distributed computing network with hardware/software
• The firm can be awarded either or both; three possible futures are possible (C1, C2, and C1+C2)

Possible Approaches

• A1: Subcontract the hardware installation, but develop the software itself
• A2: Subcontract the software development, but install the hardware itself
• A3: Handle both hardware and software tasks
• A4: Bid jointly with a firm on both hardware and software
• A5: Serve as a project manager, subcontracting all H and S tasks.

Payoff

• Next to determine payoff values and associated probabilities
• Probabilities must sum to unity

Aspiration Level Criterion

• Involves selecting a level of achievement, followed by selection of an alternative
• An alternative is selected that maximizes the stated aspiration level ( profit level set)

Criterion

• This focuses on the selection process on profit associated from future ( designated C1+C2 )
• Most probable that it will occur at 0.5%

Value Criterion

• Choices maximize profit or minimize expected loss

Decisions Under Uncertainty

• Decisions where probabilities are unavailable, more abstract environment
• Decision criteria include Laplace, Maximin/Maximax, and Hurwicz Critierons

Laplace Criterion

• The firm is unwilling and differentiate between likelihood in acquiring any contract
• One might reason that each possible state will occur
• Called the "principle of insufficient reason" based on the philosophy that nature is indifferent

Computing the average Profit

• Probability of a future state given the Laplace Principal
• Best alternative - selected/computed for each

MAXIMIN and MAXIMAX Criteria

• Two decision rules are available
• First rule is based on maximum pessimistic of an outcome of nature ( nature worst done )
• The second is the Maximax Rule, assuming best optimisic view of nature ( will do best done)

Hurwicz Criterion

• Approach by measuring what index of optimism and pessimism rule to select.
• A compromise in allowing one select select index in which one makes what is best to do.