Decision Support System

Chapter 4: Modeling and Analysis

Current modeling issues• Problems exist in identifying correct measures that lead to

overall goal success.• Objectives to indicate model’s objective function/measure(s)

must be properly and accurately determined.• Issues include:– Identification of the problem and environmental analysis.– Variable indentification– Forecasting (Predictive Analytics)– Multiple models– Model categories– Model management– Knoweldge-based modeling

Problem Identification & Env. analysis• First phase in Simon’s decision phases.• Environmental scanning and analysis is part of analysis.• BI/BA help in identifying problems.• The problem must be well understood and everyone involved

should share the same frame of understanding because the problem will ultimately be presented by the model in one form or another.

Variable identification• Identification of a model variable (decision, result,

uncontrollable) is critical as the relationships of the variables.– Tools: influnce diagrams, cognitive maps.

Forecasting (Predictive Analytics)• Forecasting: predicting the feature.• Is essential for construction and manipulating models because

when a decision is implemented, the results usually occur in the future. Whereas DSS are typically designed to determine what will be.

• Tradition MIS report what is or what was, there is no point in running a what-if(sensitivity) analysis on the past.

• CRM & RMS [Cox Communication application case 4.2]

Multiple models• DSS can include several models, each representing different

part of the decision-making problem.• AHP: Analytic hierarchical Process is used in such situations.

Model categories

Model management & Knowledge-base Modeling

• Model management :models like data must be managed.• Knowledge-based modelling :• DSS uses mostly quantitative models whereas expert systems

qualitative , knowledge based models. • Trend toward transparency– Multidimensional modeling exhibits as spreadsheet

Static and Dynamic modelsSTATIC ANALYSIS:• Single photograph of situation• Single interval• Time can be rolled forward , but it is nonetheless static.• Decision-making situations usually repeat with the identical

condition• Example:• Process simulation begins with Steady state which models a

static representation of a plant to find its Optimal operating parameters.– assumption: flow of material will be Continuous and

unvarying– Primary tool for process design

Static and Dynamic modelsDYNAMIC ANALYSIS:• Represent scenarios that change over time .• Example:5-years profit- and-loss projection in which input

data(cost , prices,….) change from year to year. • Time dependent• Varying conditions• Generate and use trends and patterns over time.• Occurrence may not repeat• Static model can be expanded to be dynamic.• Dynamic simulation ,in contrast to steady-state(variation in

materials flow)

Certainty, Uncertainty and Risk• Decision situations are often classified on the basis of what the decision

maker knows about the forecasted results.• This knowledge classified into three categoriesranging from complete knowledge to total ignorance• These categories are:• Certainty• Uncertainty• risk

Complete knowledge Risk Ignorance, total certainty uncertainty

Increasing knowledge

decreasing knowledge

• Certainty– Assume complete knowledge (deterministic environment)– Example: U.S. Treasury bill investment(complete information about

the future of ROI).

– All potential outcomes known(assumed only one for each course of action).

– Easy to develop , solve model ,and yield optimal solution.• Typically for structured problems with short time horizons.• Sometimes DSS approach is needed for certainty situations.

Decision making under certainty

• Uncertainty– Situations in which several outcomes are possible for each

course of action.– BUT the decision maker does not know, or cannot

estimate, the probability of occurrence of the possible outcomes.

– More difficult - insufficient information– Managers attempt to avoid uncertainty as much as

possible. – Modeling involves assessing the decision maker's (and/or

the organizational) attitude toward risk.

Decision making under uncertainty

• (Probabilistic or stochastic decision situation) • Decision maker must consider several possible outcomes for each

alternative, each with a given probability of occurrence• Long-run probabilities of the occurrences of the given outcomes are

assumed known or can be estimated– Decision maker can assess the degree of risk associated with each

alternative (calculated risk)

– Risk analysis• Calculate value of each alternative• Select best expected value

Decision making under risk

• Flexible and easy to use• Popular end-user modeling tool (financial , mathematical ,

statistical ,….. Functions)• Allows linear programming and regression analysis(add-ins

solver)• transparent data analysis tools• Features what-if analysis, data management, macros.• Incorporates both static and dynamic models

Modeling with Spreadsheets

Static model example

Modeling with Spreadsheets

Modeling with Spreadsheets

• Decision analysis is used to model a decision situations that have a finite number of alternatives.

• Single goal situation can be modeled with decision tables or decision trees.

• Multiple goals can be modeled by another techniques(described later).

Decision analysis of few alternatives (decision tables & decision trees)

• Example : an investment company want to investing in three alternatives : 1. Bonds,2. Stocks,3. Or certificates of deposit(CDs). • Goal :maximize profit• The yield depends on state of economy : solid growth , stagnation, or

inflation .• If solid growth then annual yields are 12%,15%,or 6.5% for bonds,

stocks ,CDs respectively.• If stagnation then annual yields are 6%,3%,6.5%• for bonds ,stocks ,CDs respectively.• If inflation then annual yields are 3%,-2%,6.5%• for bonds ,stocks ,CDs respectively.

Decision tables

Alternative Solid growth % Stagnation % Inflation %

bonds 12.0 6.0 3.0

stocks 15.0 3.0 -2.0

CDs 6.5 6.5 6.5

State of nature (uncontrollable variables)

• If a decision making problem under certainty , then we would know what the economy will be and could easily choose the best investment • If a decision making problem under uncertainty:Two approaches can be used :

1. Optimistic approach : Select the best from the best (stocks)2. Pessimistic approach: Select the best from the worst(CDs)

Decision tables

• Treating risk : with risk analysis, select the alternative with the greatest expected value .

• If experts estimate the chance of solid growth at 50%, stagnation at 30%,and that inflation at 20%

• Expected value of bonds =12(.5)+ 6(.3)+3(.2)=8.4%

alternative Solid growth 50%

Stagnation 30%

Inflation 20% Expected values %

bonds 12.0 6.0 3.0 8.4

stocks 15.0 3.0 -2.0 8.0

CDs 6.5 6.5 6.5 6.5

Decision tables

• This approach may sometimes be a dangerous strategy because the utility of each potential outcome may be different from the value. Even if there is an infinitesimals chance of catastrophic loss.

• Example: A financial advisor presents you with an “almost sure” investment of 1,000$ that can double your money in one day (2000$), and then the advisor says “well, there is a 0.9999 probability that you will double your money, but unfortunately there is a 0.0001 probability that you will be liable for $500,000 out-of-pocket loss”, the expected value of this investment is as follows:

0.9999 * ($2000 - $1000) + 0.0001* (-$500,000 - $1000) = $999.90 -$50.10 = $449.80

Clearly, the potential loss could be catastrophic for any investor who is not a billionaire. Depending on the investor’s ability to cover the loss, an investment has different expected utilities, remember that the investor makes the decision only once.

Decision tables

• Graphical representation of relationships• Multiple criteria approach• Demonstrates complex relationships• Cumbersome, if many alternatives• Consult Application case 4.3: Johnson &

Johnson Decides About New Pharmaceuticals by Using Trees.

Decision Tree

• Components of MSS mathematical models:• Decision variables, uncontrollable variables, parameters, and

result variables– Decision variables: describe alternative choices.– Uncontrollable variables :are outside decision-maker’s

control.– Fixed factors are parameters. – Intermediate outcomes: produce intermediate result

variables.– Result variables :are dependent on chosen solution and

uncontrollable variables.– Reflect the effectiveness of the system.

MSS Mathematical Models

General Structure of Quantitative Model

Intermediate Variables

Examples of components of Models

• Mathematical expressions (e.g., equations or inequalities) connect the components

• Example:• Present-value model

P = F / (1+i)n

P:present value , F: a future single payment in$, i: interest rate% ,n: no of years

• Calculate the present value of a payment of 100.000$to be made of 5 years from today at 10% interest rate ?

P=100.000/ (1+0.1) 5 =$62.092

The Structure of Quantitative Models

• Linear programming (LP) is best known technique in a family of optimization tools called mathematical programming

• LP is used extensively in DSS.• Mathematical Programming: is a family of tools designed to

help solve managerial problem in which the decision maker must allocate scarce resources among activities to optimize a measurable goal.

• Example : distribution of machine time(resource) among various products(activities).

Mathematical programming optimization

LP characteristics:• A limited quantity of resources is

available of allocation.• Resources used in the production

of products or services.• There are two or more ways in

which the resources can be used.• Each activity (product or service)

in which the resources are used yields a return in terms of the stated goal.

• The allocations usually restricted by several limitations and requirements called constraints.

LP assumptions• Returns from different allocations

can be compared (measured by a common unit) (ex: dollar or utility)

• The return of any allocation is independent of other allocations

• The total return is the sum of the returns yielded by the different activities.

• All data are known with certainty .• The resources are to be used in

the most economical manner

Linear Programming

• LP Consists of :1- Decision variables (whose values are known and searched for).2- Objective function (linear mathematical function) .3- Object functions coefficients (unit profit or cost coefficients indicating the

contribution to the objective of one unit of a decision variable)4- Constraints (expressed in the form of linear inequalities or equalities that limit

resource and/or requirements, theses relate the variables through linear relationships).

5- Capacities (which describe the upper and sometimes lower limits on the constraints and variables)

5- Input/output(technology) coefficients (which indicate resource utilization for a decision variable).

Example :Z=4x1+5x2 where:

1x1+1x2<=300 and 3x1+0x2<=100

Mathematical Programming

• MBI Corporation • Decision: How many computers to build next

month?• Two types of computers• Labor limit• Materials limit• Marketing lower limits

Constraint CC7 CC8 Rel LimitLabor (days) 300 500 <= 200,000 / moMaterials $ 10,000 15,000 <= 8,000,000/moUnits 1 >= 100Units 1 >= 200Profit $ 8,000 12,000 Max

Objective: Maximize Total Profit / Month

Assignment: The Product-Mix Linear Programming Model

• solve problem by using add-in solver in Excel

Assignment: The Product-Mix Linear Programming Model