INTRODUCTION TO
MANAGERIAL DECISION
MODELING
Objectives
Define management science
Define decision model and describe its importance
Classify decision models
List and explain steps involved in developing decision
models in practice
Remind breakeven analysis with computer applications
Make a classification of management science modeling
techniques
Give examples of management science applications
Discuss possible problems in developing decision models
What is Management Science?
Management Science is the scientific approach to
executive decision making, which consists of:
1. The art of mathematical modeling of complex situations,
2. The science of the development of solution techniques
used to solve these models,
3. The ability to effectively communicate the results to the
decision maker
Management Science Approach
Management science uses a scientific approach to solving
management problems.
It is used in a variety of organizations to solve many
different types of problems.
It encompasses a logical mathematical approach to
problem solving.
It is also referred to as: Decision Modeling
QuantitativeAnalysis
Operations Research
Uses of Decision Models (1 of 2)
 They can solve complex problems.
 They provide analytical framework for evaluating modern
business problems
 They are subject to limitations
 They provide techniques applicable in many areas such as:
 Accounting, Economics, and Finance
 Logistics, Management, and Marketing
 Production, Operations, and Transportation
Uses of Decision Models (2 of 2)
They can be applied when:
designing and implementing new operations or
procedures
evaluating an ongoing set of operations or
procedures
determining and recommending corrective action for
operations and procedures that are producing
unsatisfactory results
Types of Problem Information
 Quantitative data - numeric values that indicate how
much or how many.
– Rate of return.
– Financial ratios.
– Cash flows.
 Qualitative data - labels or names used to identify an
attribute – Outcome of an upcoming election.
– New technological breakthrough.
Role of Spreadsheets in
Decision Modeling
Computers are an integral part of decision making.
Spreadsheet packages -
Are capable of handling management decision
modeling techniques.
Have built-in functions and procedures
Types of Decision Models
(by purpose of the model)
Decision
Models
Optimization
Models
Predictive
Models
Optimization Models
Optimization Models seek to maximize a quantity
(eg. profit) or minimize a quantity (eg. cost, time, etc.)
that may be restricted by a set of constraints
(limitations on the availability of capital, workers,
supplies, machines etc.)
Predictive Models
At times however, the function of a model is not to
maximize or minimize any particular quantity, but to
describe or predict events given certain conditions These
models are known as Predictive Models.
These techniques do not generate an answer or a
recommended decision. Instead they provide descriptive
results: results that describe the system being modeled.
They usually provide important input to optimization models
Types of Decision Models
(by the degree of certainty of the data)
Decision
Models
Deterministic
Models
Probabilistic
Models
Deterministic Models
 Deterministic models assume:
Complete certainty.
All information needed is available with fixed and
known values.
 Most commonly used deterministic modeling technique
is Linear Programming.
Probabilistic Models
Probabilistic models are also called stochastic models.
Probabilistic models -
– assume some of data is not known with certainty.
– take into account that information will be available
after the decision is made.
Steps Involved in Decision Modeling
(Management Science Approach)
1. Formulation.
2. Solution.
3. Interpretation.
Overview of the Steps in the
Management Science Process (1 of 3)
Observation - Identification of a problem that exists in the
system or organization.
Definition of the Problem - problem must be clearly and
consistently defined showing its boundaries and
interaction with the objectives of the organization.
Developing a clear and concise problem statement
Overview of the Steps in the
Management Science Process (2 of 3)
Developing a model – Development of the functional
mathematical relationships that describe the decision
variables, objective function and constraints of the
problem.
A management science model is an abstract
representation of an existing problem situation. It can be
in the form of a graph or chart, but most frequently a
Management Science model consists of a set of
mathematical relationships that are made up of numbers
and symbols.
Overview of the Steps in the
Management Science Process (3 of 3)
Model Solution - Models solved using management
science techniques.
Model Implementation - Actual use of the model or
its solution.
Step 1: Model Formulation (1 of 2)
Developing a model requires to:
identify the decision variables
develop the decision model by quantifying the
objective (function to be optimized-profit, cost, etc) and
constraints (restrictions on resource availability etc.), ie.
develop relevant mathematical relations for
consideration and evaluation.
Step 1: Model Formulation (2 of 2)

Acquire input data.
 Collect accurate data for use in model.
 Possible data sources are:
Official company reports.
Accounting, operating, and financial information.
 Views, and opinions from knowledgeable
individuals
Step 2: Model Solution (1 of 3)
Developing a solution may involve:
Solution of a set of mathematical expressions to arrive
at best (optimal) solution, or
Alternative trial and error iterations, or
Complete enumeration of all possibilities or
utilization of an algorithm.
Step 2: Model Solution (2 of 3)
An appropriate solution technique may be an optimization
algorithm (series of steps repeated until the best solution is
attained) or a heuristic algorithm
Most algorithms are intended to provide an optimal
solution for a model. Sometimes, however, problems can
prove to be too complex or time consuming to employ
optimization algoritms. In such cases a heuristic procedure
may be preferred
Step 2: Model Solution (3 of 3)
Prior to implementation of model solution, the solution
is tested
Testing of solution is accomplished by examining and
evaluating:
• Data utilized in the model and
• the model itself.
Step 3:Implementation & Interpretation
(1 of 2)
 Optimal solution must be implemented carefully.
 Solution implementation usually requires making
changes within the organization.
 Recommendations often require changes in data,
data handling, resource mixes, systems,
procedures, policies, and personnel.
 Managers and others may resist recommended
solutions.
Step 3: Implementation and Interpretation
(2 of 2)

Interpretation and What-if Analysis.
Analyzing the results and sensitivity analysis.
Examine changes in optimal solution as a result of
changes in input values and model parameters
Examples
Example I (1 of 2)
Information and Data:
Business firm makes and sells a steel product
Product costs $5 to produce
Product sells for $20
Product requires 4 pounds of steel to make
Firm has 100 pounds of steel
Business Problem:
Determine the number of units to produce to make the
most profit given the limited amount of steel available.
Example I (2 of 2)
Variables:
X = number of units (decision variable)
Z = total profit
Model:
Z = $20X - $5X (objective function)
4X = 100 lb of steel (resource constraint)
Parameters: $20, $5, 4 lbs, 100 lbs (known values)
Formal Specification of Model:
maximize Z = $20X - $5X
subject to 4X = 100
Break-Even Analysis
(1 of 4)
Used to determine the number of units of a product to
sell or produce (i.e. volume) that will equate total
revenue with total cost.
The volume at which total revenue equals total cost
(zero profit) is called the break-even point.
Profit at break-even point is zero.
Break-Even Analysis
(2 of 4)
Model Components:
• Fixed Costs (cf) - costs that remain constant
regardless of number of units produced. $’s necessary
to invest in facilities
• Variable Cost (cv) - unit cost of product.
• Total variable cost (vcv) - function of volume (v) and
variable per-unit cost.
• Total Cost (TC) - total fixed cost plus total variable
cost.
• Profit (Z) - difference between total revenue vp (p =
price) and total cost.
Breakeven Analysis (3 of 4)
Profit = Total Revenue - Total Cost
Profit = Revenue - Fixed Cost - Variable Cost
Where:
Revenue = [Sales price ($/unit) x Number (units)]
Variable Cost = [Variable cost ($/unit) x Number (units)]
Fixed Cost = $ necessary to invest in facilities (buildings,
equipment, processes, etc.) = constant dollar value.
Break-Even Analysis
(4 of 4)
Z = vp - cf – vcv
Set profit equal to 0:
vp = cf + vcv
Compute the Break-Even Point:
Break-even quantity = cf/(p - cv)
Example II: Break-Even Analysis
(1 of 10)
Example: Western Clothing Company
cf = $10000
cv = $8 per pair
p = $23 per pair
V = 666.7 pairs, break-even point
Example II: Break-Even Analysis
(2 of 10)
Graphical Solution
Example II: Break-Even Analysis
(3 of 10)
Sensitivity Analysis : Break-Even Model with a Change (Increase) in Price
Example II:
Break-Even Analysis (4 of 10)
Sensitivity Analysis : Break-Even Model with a Change (Increase) in Variable Cost
Example II: Break-Even Analysis
(5 of 10)
Sensitivity Analysis : Break-Even Model with Changes in Fixed and Variable Costs
Example II: Break-Even AnalysisExcel Computer Solution (6 of 10)
Example II: Break-Even AnalysisExcel QM Computer Solution (7 of 10)
Exhibit 1.2
Example II:Break-Even AnalysisExcel QM Computer Solution (8 of 10)
Exhibit 1.3
Example II: Break-Even AnalysisQM for Windows Computer Solution (9 of 10)
Example II: Break-Even AnalysisQM for Windows Computer Solution (10 of 10)
Example III: Breakeven Analysis (1 of 5)
Problem:
Bill's company, Pritchett's Precious Time Pieces,
buys, sells, and repairs old clocks and clock parts.
Bill sells rebuilt springs for unit price $10. Fixed cost
of equipment to build springs is $1,000. Variable
cost per unit is $5 for spring material.
Example III: Breakeven Analysis (2 of 5)
Profit = $10X - $1,000 - $5X
Break-even quantity = cf/(p - cv)
BE = $1,000 / [$10 - $5 ] = 200 springs.
Example III: BEP (3 of 5 )
Breakeven point (BEP) in dollars can be computed:
BEP$ = Fixed cost + Variable cost per unit x BEP
For Bill Pritchett's example, compute BEP$:
$1,000 + $5 x 200 = $2,000
Example III: Excel Solution of the Decision
Model (4 of 5)
Example III: Using Goal Seek to Find the
Breakeven Point (5 of 5)
Use of Goal Seek to find the BEP.
Management Science Modeling Techniques(1 of 4)
Management Science Modeling Techniques
(2 of 4)
1. Linear Mathematical Programming Techniques
a. Linear Programming Models
b. Transportation Models
c. Assignment Models
d. Integer Programming Models
e. Goal Programming
Management Science Modeling Techniques
(3 of 4)
2. Probabilistic Techniques
a. Decision Analysis
b. Waiting Line (Queuing) Models
c. Simulation Models
d. Forecasting Models
3. Network Techniques
a. Network Flow
b. Project Management Techniques (PERT/CPM)
Management Science Modeling Techniques
(4 of 4)
4. Other Techniques
a. Non-Linear Programming Models
b. Inventory Models
Characteristics of Modeling Techniques
• Linear Mathematical Programming - clear objective;
restrictions on resources and requirements; parameters
known with certainty.
• Probabilistic Techniques - results contain uncertainty.
• Network Techniques - model often formulated as diagram;
deterministic or probabilistic.
• Forecasting and Inventory Analysis Techniques probabilistic and deterministic methods in demand forecasting
and inventory control.
• Other Techniques - variety of deterministic and probabilistic
methods for specific types of problems.
Management Science Applications- (1 of 4)
• Some application areas:
- Project Planning
- Capital Budgeting
- Inventory Analysis
- Production Planning
- Scheduling
• Interfaces - Applications journal published by
Institute for Operations Research and Management
Sciences
Management Science Applications (2 of 4)
Linear Programming was used by Burger King to find
how to best blend cuts of meat to minimize costs.
Integer Linear Programming model was used by
American Air Lines to determine an optimal flight
schedule.
The Shortest Route Algorithm was implemented by the
Sony Corporation to develop an onboard car navigation
system aimed to give directions to car drivers.
Management Science Applications
( 3 of 4)


Project Scheduling Techniques were used by a
contractor to rebuild Interstate 10 damaged in the 1994
earthquake in the Los Angeles area.
Decision Analysis approach was the basis for the
development of a comprehensive framework for planning
environmental policy in Finland.
Management Science Applications
( 4 of 4)

Queuing models are incorporated into the overall design
plans for Disneyland and Disney World, which lead to the
development of ‘waiting line entertainment’ in order to
improve customer satisfaction.
Possible Problems in Developing
Decision Models- (1 of 2)
 Defining the Problem.
 Conflicting Viewpoints.
 Impact on Other Departments.
 Beginning Assumptions.
 Solution Outdated.
 Developing a Model.
 Fitting Textbook Models.
 Understanding the Model.
Possible Problems in Developing
Decision Models (2 of 2)
 Acquiring Input Data.
 Using Accounting Data.
 Validity of Data.
 Developing a Solution.
 Hard-to-Understand Mathematics.
 Only One Answer is Limiting.
 Testing Solution.
 Analyzing Results.
Implementation – Not Just The Final Step
 Decision models assist decision maker by providing scientific
method, model, and process which is defensible and reliable.
 Overcome sole reliance upon intuition, hunches, and
experience.
 A Swedish study found  40% of projects suggested by decision analysts were ever
implemented.
 70% of modeling projects initiated by users, and 98% of
projects suggested by top managers, were implemented.