QIT3023 Information Systems and Decision Making

Mohd. Noor abdul hamid

mohdnoor@uum.edu.my

1

CHAPTER 7: MODELS IN DECISION SUPPORT SYSTEMS

7.1 DECISION MODELS:

• used to make a prediction what would happen in the real world if certain

choices were made.

• Enable decision maker to evaluate each alternatives without trying them

out

7.1.1 Model Types:

• Basic types of system models include:

a) Graphical model – eg: DFD, map

b) Narrative model – describe a system in a natural language

c) Physical model – smaller or idealized representation of the real system.

d) Symbolic model / Information-Based model

- represent reality by data

- Types of data:

i. True/False or Yes/No (Boolean Variables)

ii. Character String

iii. Numerical Value

Which model often become a part of DSS??

• models incorporate procedures and formulas to manipulate their data

elements – derive new data element values from values of other data

elements in the model.

Figure 1 : “Family tree” of Model Types

Models

Descriptive

(system)

Prescriptive

(process)

Static Dynamic

Static system Dynamic system Continuous Discrete-event QIT3023 Information Systems and Decision Making

Mohd. Noor abdul hamid

mohdnoor@uum.edu.my

2

• A useful characteristic of most model Æ the model remains valid when the

data change

7.1.2 Model Types Used in DSS

A DSS can incorporate several mathematical models :

a. System vs Process Models :

• What are we modeling?

• system model – models the system that we wish to study

• process model (prescriptive models) – models the process that

humans follow in making a decision about a system.

• process model can be normative or descriptive.

b. Static vs Dynamic Models : Cause and effect over time

Static Models: Dynamic models:

• Static models show the values

that system attributes take

when the system is in balance

- ignore time-based

variances

• Dynamic models follow the

changes overtime that result

from system activities – data

values change over time.

• Passage of time does not

play a part

• Involve less data – easier to

analyze & provide results

more quickly

• Passage of time, with cause –

and effect relationships

connecting one time period to

the next, is essential to system

behavior

• The variables used in the

computations are averages

• A dynamic model constantly

recomputes its equations as time

changes

• Eg: A model that traffic flow in

the intersection used to

minimized delays by adjusting

the signal timing

• To apply static model to

dynamic system – that system

must be in equilibrium (in

balance)– steady state

• Dynamic models can only be

applied to dynamic system. QIT3023 Information Systems and Decision Making

Mohd. Noor abdul hamid

mohdnoor@uum.edu.my

3

c. Continuous vs Discrete-event models : how do quantities vary in the

system??

• Dynamic system model can be divided into two categories:

d. Deterministic vs Stochastic Models

• Statistical uncertainty

• Most models have elements of certainty and uncertainty

Deterministic Stochastic

Model is deterministic if its outputs

are fixed for a given set of inputs

Model is stochastic if they reflect an

element of uncertainty

Eg: 3 step assembly process might

indicate that each step takes

exactly one hour – entire process

= three hour

Each time the model is run, the

results are always three hours.

Eg: The same 3 steps assembly

process might have the duration of

each step vary around the one-hour

average, with normal distribution

having standard deviation of ten

minutes.

Running this model many times will

resulted many different answers,

clustered around three hours.

Corresponds closely to the

accounting model category DSS

Representational model category

DSS

• How to deal with uncertainty??

Continuous-system models Discrete-event models

• Describe physical or economic

processes, in which the numbers,

that describe the system, vary

continuously.

• Deal with systems in which

individual events, occur at

identifiable points in time, and

change the state of the system

instantaneously from one value

to a different one

• Eg: Blood pressure varies

continuously over time - there are

processes that cause it to rise or

fall at given rates .

• Eg: parts being assemble - the

individual entities (parts) are

assembled based on events

(receipt or anticipation of

orders).

• Other examples: Arrival of a new

order, customers calling, etc.

• In continuous models, values

change based directly on

changes in time - the time line for

a continuous model is evenly

spaced.

• The time between events in a

discrete event model is seldom

uniform. QIT3023 Information Systems and Decision Making

Mohd. Noor abdul hamid

mohdnoor@uum.edu.my

4

7.2 PROBABILITY

• All decision contain elements of uncertainty

• Those uncertainty must be quantified in some manner to make a good decision.

• Properly applied – probability can be invaluable in structuring, resolution and

choice selection of a given problem context

• improperly applied – lead to decisions that are perfect in all respects except for

their outcome

• three requirements of probability

− all probabilities must lie within the range of 0 to 1.

− the probabilities of all individual outcomes of an event must add up to

the probability of their union (assuming all outcome is mutually

exclusive

− the total probability of a complete set of outcomes must be equal to 1.

7.2.1 Type of Probability:

a) Long run frequency

− Law of large numbers

− States that if an event or an experiment is repeated a large number of

times, the observed frequency of a particular outcome of that event

will be a good estimate of the true probability of that outcome

− Example : flip of a coin

− Often referred as a ‘frequentists’ – the estimation of probability through

experimentation and repetitions

− Sometimes it is impractical or untenable

b) Subjective probability

− Require a perspective that is different from the classical long-run

frequency approach.

− Views probability as the “degree of belief” an individual has that a

particular outcome will occur

− To adopt this approach is more than just allowing for probability

estimations that are “acts of faith”

− Implicit in its acceptance is a set of underlying assumptions that, if

satisfied, infer a set of number that can describe our degree of belief.

c) Logical Probability

− Suggest that even though a probability may be derivable, its accuracy

may not be acceptable under any circumstances.

− Situations where logical probability is applicable usually manifest

themselves in a manner that suggests that a probability estimation of

less than 100 percent is the same as zero. QIT3023 Information Systems and Decision Making

Mohd. Noor abdul hamid

mohdnoor@uum.edu.my

5

7.3 TECHNIQUE FOR FORECASTING PROBABILITIES

7.3.1 Direct Probability Forecasting

• the simplest technique for eliciting subjective probabilities

• Decision maker or expert is simply asked to estimate the probability of an

outcome for a particular event

• Depend on how skill and experience to obtain the accurate estimation

• Properly obtained direct estimates can be useful and efficient methods of

assigning numerical values to subjective probabilities

7.3.2 Odds Forecasting

• another method of expressing the subjective probability

• Focus on gambling perspective - to find specific amount of money to win or lose

such that the decision maker is willing to accept either side of the bet

• once these amount determined, they can be transformed into odds and from

there into estimates of probabilities

• Eg: Amount of money to win = X, amount of money to lose = Y,

7.3.3 Comparison Forecasting

• sometimes referred to as the lottery forecast

• present the decision maker with a choice between the participating in one of

two lottery-like games:

- uncertain event: winning a big prize, lose a small amount of money

- reference game (with a known probability of winning): structured in the form

of partially shaded wheel of fortune – shaded represents a winner and the

unshaded represents a loser.

The probability of winning is repeatedly adjusted slightly upward or downward

until the decision maker is indifferent as to which game to play.

• The assumption is that, if the decision maker is indifferent, it is his/her subjective

probability estimation of winning the uncertain game that creates this

indifference.

Subjective Probability:

P(win) = Y .

[X+Y] QIT3023 Information Systems and Decision Making

Mohd. Noor abdul hamid

mohdnoor@uum.edu.my

6

7.4 CALIBRATION AND SENSITIVITY

7.4.1 Calibration

• In most situations – don’t really need to know the exact probability for a

particular outcome or event – it is still just a probability

• A probability is just a specialized way of specifying an average.

• Although averages are useful descriptors, they can also be misleading.

• We need more information than simply a probability estimation if we are to

make an informed decision.

• A well calibrate source requires years of experience and feedback to develop.

7.4.2 Sensitivity Analysis (a.k.a what-if analysis)

• Method use to determine the degree to which the alteration of an underlying

assumption has a material effect on the results obtained from the model

• Performing sensitivity analysis on a model or model set can accomplish a

number of useful objectives

• Variable highly sensitive or significant – small change in the variable of interest

causes a measurable change in the outcome

• Insensitive or insignificant – varying a particular variable over its expected range

produces only a minor change in the outcome

7.5 DISCRETE-EVENT SIMULATION MODEL

• Simulation Model??

• Model : the description of the system (normally in a form of computer program)

– a thing

• Simulation : the process of using this model to study a system – a process

• simulation can’t exist without suitable model

• allow us to predict the behavior of a business system by modeling the expected

behaviors and interactions of its components over time

• Characteristics of Simulation Model :

- a dynamic model

- a stochastic model

- a discrete-event model QIT3023 Information Systems and Decision Making

Mohd. Noor abdul hamid

mohdnoor@uum.edu.my

7

7.5.1 Concept of Discrete-Event Simulation (DES)

• Model represents the states of the system by the values of data elements

(variables) in the computer – these variables change as events occur in the

system.

• Must know how often different types of events occur – can know how the

variables changes – reflect what would happen to the system in the real world.

• Simulation program are usually designed to gather helpful information about

system behavior

• Most of DES are stochastic or probabilistic

• The accuracy of the decisions depends on the accuracy of the model

• Key to understand how DES work is : the future events queue – list of events that

are scheduled to take place in the system, together with the time that each will

occur.

7.5.2 Designing a DES Model

• Process of designing DES:

− Determine the objective of the model

− Define the system itself

− Define the state of the system in terms of a set of state variables (or

uncontrollable) variables.

− Define the events that can affect the state of the system and the

impact of each event on each state variable.

− Choose the time units which the simulations will use.

− Define statistically, the rate at which each event occurs.

− Determine the statistics you would like to obtain from your simulation

and what data you need in order to obtain them.

− Define the initial (starting) state of the system.

• Describe the model to a computer in a form of program – reflect all the events

that can take place in the system, their occurrence statistics and their impact

on the state variables

7.6 RANDOM NUMBERS, PSEUDO-RANDOM NUMBER AND STATISTICAL DISTRIBUTIONS

• The behavior of a simulation model depends on the number (random) that

determine when each event occurs.

• many ways to generate random numbers

− rolling a dice

− opening a phone book or table of random numbers with close eyes &

choose a number using your finger computer

− computer : physical random number generator

• disadvantage of using truly random number is that their sequence is not

repeatable.

• so pseudo-random numbers is used in simulation model– generate by a

repeatable formula, which behave statistically as if they truly random