Transcript Managerial Decision Modeling with Spreadsheets

INTRODUCTION TO
MANAGERIAL
DECISION
MODELING
OBJECTIVES
 Define management science
 Define and classify decision models
 List and explain steps involved in developing decision models
 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-I
(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-II
(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 are 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.
 collect accurate data to use as an input in model
STEP 1: MODEL FORMULATION (2 of 2)
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 &
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 (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 (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 (FC) - costs that remain constant regardless of
number of units produced. $’s necessary to invest in facilities
 Variable Cost (VC) - unit cost of product.
 Total variable cost (Q.VC) - function of volume (Q) and
variable per-unit cost.
 Total Cost (TC) - total fixed cost plus total variable cost.
 Profit (Z) - difference between total revenue vp (p = price) and
total cost.
BREAK-EVEN ANALYSIS (3 of 4)
Profit = Total Revenue - Total Cost
Profit = Revenue - Fixed Cost - Variable Cost
Where:
Revenue
= [Sales price ($/unit) x Number (units)]
Variable Cost = [Variable cost ($/unit) x Number (units)]
Fixed Cost
dollar
=
$ necessary to invest in facilities (buildings,
equipment, processes, etc.) = constant
value.
BREAK-EVEN ANALYSIS (4 of 4)
Z = P.Q - FC – VC.Q
Set profit equal to 0:
P.Q = FC + VC.Q
Compute the Break-Even Point:
Break-even quantity = FC/(P - VC)
EXAMPLE I: BREAK-EVEN ANALYSIS
(1 of 10)
Example: Western Clothing Company
FC = $10000
VC= $8 per pair
P = $23 per pair
Q = 666.7 pairs, break-even point
EXAMPLE I: BREAK-EVEN ANALYSIS
(2 of 10)
Graphical Solution
EXAMPLE I: BREAK-EVEN ANALYSIS
(3 of 10)
Sensitivity Analysis : Break-Even Model with a Change (Increase) in Price
EXAMPLE I: BREAK-EVEN ANALYSIS
(4 of 10)
Sensitivity Analysis : Break-Even Model with a Change (Increase) in Variable Cost
EXAMPLE I: BREAK-EVEN ANALYSIS
(5 of 10)
Sensitivity Analysis : Break-Even Model with Changes in Fixed and Variable Costs
EXAMPLE I: BREAKEVEN ANALYSIS
Excel Computer Solution
(6 of 10)
EXAMPLE I: BREAKEVEN ANALYSIS
Excel QM Computer Solution (7 of 10)
EXAMPLE I: BREAKEVEN ANALYSIS
Excel QM Computer Solution (8 of 10)
EXAMPLE I: BREAKEVEN ANALYSIS
Excel QM Computer Solution (9 of 10)
EXAMPLE I: BREAKEVEN ANALYSIS
Excel QM Computer Solution (10 of 10)
EXAMPLE II: BREAK-EVEN 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 II: BREAK-EVEN ANALYSIS (2 of 5)
Profit = $10Q - $1,000 - $5Q
Break-even quantity = FC/(P - VC)
BE = $1,000 / [$10 - $5 ] = 200 springs.
EXAMPLE II: BREAK-EVEN ANALYSIS (3 of 5)
 Breakeven point (BEP) in dollars can be computed:
BEP$ = Fixed cost + Variable cost per unit x BEP
 For Bill Pritchett's example, compute BEP$:
$1,000 + $5 x 200 = $2,000
EXAMPLE II: BREAK-EVEN ANALYSIS (4 of 5)
EXAMPLE III: USING GOAL SEEK TO FIND
THE BREAK-EVEN POINT (5 of 5)
MANAGEMENT SCIENCE MODELING
TECHNIQUES (1 of 4)
MANAGEMENT SCIENCE MODELING
TECHNIQUES (2 of 4)
 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)
 Probabilistic Techniques
a. Decision Analysis
b. Waiting Line (Queuing) Models
c. Simulation Models
d. Forecasting Models
 Network Techniques
a. Network Flow
b. Project Management Techniques (PERT/CPM)
MANAGEMENT SCIENCE MODELING
TECHNIQUES (4 of 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.