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DECISION MODELS IN
MANAGEMENT
PGDM-I TERM III
by
PROF. R.N.VENKATESWARAN
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Reference Books
An Introduction to Management Science:Quantitative Approaches to Decision Making, by:
Anderson Sweeney, Williams, Thomson South-
Western, 10e
Principles of Operations Research for
Management (2e) - by Budnick; McLeavey, and
Mojena AITB,Delhi edition
Operations Research by Taha, HA (6e), Prenhall Principles of Operations Research with
applications to Managerial Decisions, (2e), by
Wagner, Prenhall, India
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DECISION MODELS
Various names given to body of knowledge which use
Quantitative Methods in Decision Making:Management Science (MS)
Operations Research (OR)
Decision Science
Modern management requires executive-generalists
who are trained and effectively operate in business,
industry, government, hospitals, armed forces, educational
institutions, service industries etc., They could coordinate
the contributions of all of the specialists of an organization.Their task requires the ability to employ structure before
content in coping with the extreme diversity of information
produced by the organization.
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DECISION MODELScontd
Modern Management differs from Taylors scientific
management:
It views efficiency as secondary achievement, which
should follow adequate planning. Both good and poor
decisions can be implemented in an efficient way. A
company can manufacture a high-quality product at a
minimum cost, but the product itself might not be the bestchoice to meet the companys objectives.
Modern management attempts to establish relationship
between organizations objectives and its resources.
It cuts across traditional areas of management andemphasizes inter-disciplinary approach. People with
diverse specialties - e.g. mathematicians, engineers,
behavioural scientists, accountants etc., join together to
solve an organizational problem
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Problem Solving & Decision Making
Problem Solving is the process of identifying a difference
between the actual and the desired state of affairs and then
taking action to resolve the difference.
Decision Making is associated with management process
of planning, organizing, coordinating, controlling etc.,
Managementas defined by Websters Dictionary, is thejudicious use of means to accomplish an end.
Doing and Deciding are both managerial/executive
functions. Routine operations require doing. Exceptions
require deciding.
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Problem Solving & Decision Making Executive is a word derived from a Latin word meaning
to do; the Oxford Dictionary defines it as the action of
carrying out or carrying into effect. This does not suggestthat the main responsibility and function of the executive is
to make decisions.The executive is rewarded and evaluated
in terms of his success at making decisions while
managing his function.
Organization structure is set up to help executives do
decision making
Managerial PROBLEM SOLVING would involve both
doing - with the organization structure and deciding
using various management tools and techniques. The
manager has to form a partnership between those who
perceive they have a problem (users) and those who have
the specialized knowledge or skills in problem-solving
techniques (specialists)
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TAXONOMY OF OR MODELS
Search Methods
Classical Methods
Non-linear Optimization
GOAL
Programming
Transportation& Assignment
Linear Programming
Linear Optimization
Deterministic
MarkovProcesses
Queuing
Models
DecisionAnalysis
Stochastic
Simulation
InventoryModels
Dynamic
Programming
PERT/CPM
HYBRID
ORMODELS
C S O O S
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DECISION MODELS
TOPICS & SESSIONS
Decision Theory & Modeling 2
Linear Programming 7
Multi-Criteria (Goal Programming). 3
Simulation 3
Transportation Models 4 Assignment Problems 3
Game Theory 2
Queuing (Waiting-line) Models 4
(with simulation application) Markov Processes 2
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Evaluation Pedagogy
End-Term Exam ... 50%
Attendance ... 5%
Quizzes ... 20%
Cases/Problems(2 Sessions)... 25%
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Decision-Making Process Role of Quantitative Analysis in the Decision-Making
Process:
Problem
ExperienceSubjective
Analysis
Quantitative
AnalysisOpinion
Decision Inputs
P bl l i P
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Need
Recognition
Problem
Formulation
Model
Construction
Modeling
Real System
Data
Collection
Model
Solution
Model
Validation &
Sensitivity
Analysis
Interpretation
of Results
Implement-
ation &
Control
System of
Interest
Problem-solving Process
Schematic
Diagram ofProblem Solving
Process
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Stages of Problem-Solving Process
Green, Lee and Newsom classify problem-solving process into
three major stages:
Pre-modeling function
Modeling function
Implementation (Post-modeling)function
These stages can be further mapped onto an eight-step process:Pre-modeling:
Recognition of Need
Problem Formulation
Systems Approach Controllable & Uncontrollable variables
Parameters
Constraints
Objective Function
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Objectives,Criteria and Surrogates
Objective: The ultimate desired goal. In DMM we use the
term objective function. Surrogates: To say the company has to perform better is a
qualitative criterion or objective. But it has to be broken
into measurable surrogates - Market Share; Profit after
Tax, ROR etc.,
To say the standard of living of an individual is to be
improved is a qualitative criterion. It is to be broken to
surrogates such as: Income; growth in income; amount of
spending; amount of savings etc.,
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Stages of Problem-Solving Processcontd.
Modeling
Model Construction - Mathematical Models Data Collection - MIS; Databases; Decision-
Support systems
Model Solution(Have alternatives)- OR Models
Model Validation and Sensitivity Analysis(Optimizing/Satisficing)
Post-Modeling
Interpretation of Results and Implication- Selling yourideas
Implementation, and Control - HRD Issues
Doing
Decision making
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MODEL BUILDING A MODEL is a representation of reality intended to
explain the behaviour of some aspect of it.
Taxonomy of Models: Normative & Descriptive
Normative models tend to prescribe what oughtto be:
Physicians possess a normative model of health
Civil Engineers possess a normative model of a building
Philosophers have a code of conduct for ethics
Descriptive Models describe facts and relationships:
Physician conducting tests and analyzing the results to determine
the ailment
A civil engineer analyzing the soil conditions and other parameters
to decide on the type of structure
Constructing a physical scale model to give the projected view
of the final structure/equipment/device.
Analyzing what-if situations in a management problem solving.
In DMM we are concerned with descriptive models.
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MODEL BUILDING SIMULATION MODELS
SIMULATION is one of the key techniques of DMM. It
involves construction of a mathematical model of theproblem; and imitate (simulate) the operation of the
system.(System modeling & simulation is an elective
course in VI term)
E.g: Simulation of an airplane flight in a wind tunnel
Simulation of the traffic in traffic junction
Simulation of customer servicing in a service counters
Simulation of production - in a manufacturing situation.
Simulation modeling process helps to understand andanalyze the various alternatives, over pre-determined time
periods, without physically operating or modifying the
system.(we will learn more about it under simulation)
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PROBLEM SOLVING FRAMEWORK
1. Verbal Statement of the Problem
2. Decisions:
* Verbal Statement
* Mathematical Definition
3. Criteria
* Verbal Statement
* Mathematical Definition
4. Constraining Conditions
* Verbal Statement
* Mathematical Definition
5. Mathematical Model
6. Model Outcomes
7. Interpretation of the Results
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CLASSICAL DETERMINISTIC
MODELS
Decision Models for Management
E f U i P bl S l i F k
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E.g. of Using Problem Solving FrameworkIn-house Computer -vs.- Service Bureau Decision
A large poly-clinic has 30 full-time and visiting doctors.Currently all billing is done manually by clerks. Due to
the heavy volume of billing, the hospital managementwishes to computerise the billing operation. It has 2options: (1) To buy a computer and carry-out the billing byitself (the make/own option). Or (2) To contract with anagency that would do the operations (the buy/lease option)
Cost Data: The company can lease a small p.c. and therequired software at Rs. 15000 per year. The variable costof doing the billing in this manner is 0.65 paise per bill.
Alternatively, the company can sub-contract the operation
to an outside agency, who would charge Rs. 3000 fixedcharges per year and 0.95 paise per bill processed.
The company would like to know the critical patient volume tomake a decision on make-or buy. (this is also a deterministic
decision making problem)
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Mathematical Representation of Relationships
Assumptions:
Criteria are used to make decisionsThey are quantifiable and can be represented by
mathematical functions
Such mathematical problems are solved by using Algebra,
Simultaneous Equations; Differential Calculus etc.,Functional Notation: A functionis a mathematical
relationship for which the value of a particular variable is
determined from the values of one or more other variables.
Y = f(x) is a general representationY = 5x is a specific case.
Similarly Y = f(x1,x2,x3) is general and
Y = 3x1 + 2x2 + 6x3 is specific.
A l i h F k
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Applying the Framework
1. Verbal Statement of the Problem:
Determine the number of patient-bills, (contrast with no. ofpatients) beyond which the make option is less costly.
2. Decisions:
a. Verbal Statement: Number of patient bills per year
b. Mathematical Definition: Let x = no. of patient bills/yr.
3. Criteria: There are no optimizing criteria. Find out thatnumber of patient bills at which the annual costs of makeor buy are equal.
4. Constraining Conditions:
The critical point beyond which the lease option is lesscostly is known as break-even pointfor the two options
A l i h F k
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Applying the Framework
a. Verbal Statement: The annual cost of agency equalsannual cost of in-house operation
b. Mathematical statement: To find a value for x such thatOwn Cost: 15000 + 0.65 x
Sub-contract: 3000 + 0.95 x
5. Model: Solve for x, where :
3000 + 0.95x = 15000 + 0.65x6. Model Outcomes:
the value of x = 40000
7. Interpretation of the results:
If the break-even number of patient bills = 40000. Hence,if the number is expected to be more than 40000, doingbilling on our own is cheaper. If the bills number is lessthan 40000, it is cheaper to sub-contract the operation.
Are both equal
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Single Product Pricing Problem (Deterministic
Problem; Using problem solving framework)
The Massachusetts Bay Transit Authority (MBTA) wishes
to smooth its demand for subway services. The system
operates to full capacity during the early morning and later
afternoon rush hours. The MBTA wants to stimulate
greater demand during off-peak hours and to encourage
riders who do not need to travel during peak hours to travelat other times.
Currently the normal fares are 75 during normal hours
and 30 during off-peak hours. The demand function is
estimated from data gathered with demand at differentfares. p = off-peak fare; q = off-peak demand (000s of
passengers)
p = 70 65 60 55 50
q = 10.0 12.6 14.9 17.4 20.1
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Single Product Pricing Problem contd
Initial attempt was to fit a least-squares regression line:
q = 45 - ()p or p = -2q + 90
If the objective is to maximize demand for off-peak hours,
this would suggest eliminating such fares, and demand
would be 45,000 passengers.
But if we derive that the revenue is TR = q * p, then
TR = f(p) = 45p - p2/2
This would yield maximum revenue when p = 45.
And the revenue for this is: 1012.5, and substituting this in
the regression formula:q = 45 - ()45 = 22.5 or 22500 passengers.