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Introduction to the
Quantitative Analysis
Instructor: Md. Aftab Anwar
Lecture 3 & 4
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Body of Knowledge
Problem Solving and Decision Making
Quantitative Analysis and Decision Making Quantitative Analysis
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Management science, an approach to decision makingbased on the scientific method, makes extensive use ofquantitative analysis.
Today, many use the terms management science,operations research, and decision scienceinterchangeably.
The scientific management revolution of the early1900s, initiated by Frederic W. Taylor, provided thefoundation for the use of quantitative methods inmanagement.
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It had its early roots in World War II and isflourishing in business and industry due, in part, to:
numerous methodological developments (e.g.simplex method for solving linear programmingproblems)
a virtual explosion in computing power
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Definition:
Problem solving can be defined as the process
of identifying a difference between the actualand the desiredstate of affairs and thentaking action to resolve the difference.
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7 Steps of Problem Solving(First 5 steps are the process of decision making)
1. Identify and define the problem.
2. Determine the set of alternative solutions.
3. Determine the criteria for evaluating alternatives.
4. Evaluate the alternatives.
5. Choose an alternative (make a decision).
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6. Implement the selected alternative.
7. Evaluate the results.
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Suppose Mr. Andy currently unemployed and wouldlike a position that will lead to a satisfying career.
Suppose that your job search has resulted in offersfrom companies in
Rochester, New York;
Dallas, Texas;
Greensboro, North Carolina; andPittsburgh, Pennsylvania.
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Thus, the alternatives for your decision problem can bestated as follows:
1. Accept the position in Rochester.
2. Accept the position in Dallas.
3. Accept the position in Greensboro.4. Accept the position in Pittsburgh.
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Quantitative Analysis and Decision Making
Definethe
Problem
Identifythe
Alternatives
Determinethe
Criteria
Identifythe
Alternatives
Choosean
Alternative
Structuring the Problem Analyzing the Problem
Decision-Making Process
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THE ROLE OF QUALITATIVE AND QUANTITATIVE ANALYSIS
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Qualitative Analysis
based largely on themanagersjudgment and
experience includes the managersintuitive feel for theproblem
is more of an artthan ascience
Quantitative Analysis and Decision Making
Quantitative Analysis concentrate on the
quantitative facts or dataassociated with the problem
develop mathematicalexpressions that describe theobjectives, constraints, andother relationships that existin the problem
use one or more quantitativemethods to make arecommendation
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Potential Reasons for a Quantitative AnalysisApproach to Decision Making The problem is complex.
The problem is very important.
The problem is new.
The problem is repetitive.
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Quantitative Analysis Process
Model Development
Data PreparationModel Solution
Report Generation
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Generally, experimenting with models (compared toexperimenting with the real situation): requires less time
is less expensive involves less risk
The more closely the model represents the realsituation, the accurate the conclusions and
predictions will be.
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Objective Function a mathematical expressionthat describes the problems objective, such asmaximizing profit or minimizing cost
Constraints a set of restrictions or limitations,such as production capacities
Uncontrollable Inputs environmental factorsthat are not under the control of the decision
maker Decision Variables controllable inputs; decision
alternatives specified by the decision maker, suchas the number of units of Product X to produce
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Mathematical Models
Deterministic Model if all uncontrollableinputs to the model are known and cannot vary.(e.g. Tax rate)
Stochastic (or Probabilistic) Model if anyuncontrollable are uncertain and subject tovariation. (e.g. demand for the product)
Stochastic models are often more difficult toanalyze.
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Mathematical Models
Cost/benefit considerations must be made inselecting an appropriate mathematical model.
Frequently a less complicated (and perhaps lessprecise) model is more appropriate than a morecomplex and accurate one due to cost and easeof solution considerations.
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Uncontrollable Inputs(Environmental Factors)
ControllableInputs
(Decision
Variables)
Output(Projected
Results)
MathematicalModel
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For Example: Each unit profit = $ 10 Profit equation: P = 10x (x= unit of product) Objective function of a firm is to maximize profit Constraints: 5 hrs to produce each unit and
maximum 40 hrs are available per week, Thus the production time constraints
5x 40 ------------------------- (1) So, how many units of the product should be
scheduled each week to maximize profit?P = 10x Objective function
5x 40 ConstraintsX 0 Constraints
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FLOWCHART FOR THE PRODUCTION MODEL
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Data preparation is not a trivial step, due tothe time required and the possibility of datacollection errors.
A model with 50 decision variables and 25constraints could have over 1300 dataelements!
Often, a fairly large data base is needed.
Information systems specialists might beneeded.
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The analyst attempts to identify the alternative(the set of decision variable values) that provides thebest output for the model.
The best output is the optimal solution.
If the alternative does not satisfy all of the modelconstraints, it is rejected as being infeasible,regardless of the objective function value.
If the alternative satisfies all of the modelconstraints, it is feasibleand a candidate for thebest solution.
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Production Projected Total Hours Feasible
Quantity Profit of Production Solution
0 0 0 Yes
2 20 10 Yes4 40 20 Yes
6 60 30 Yes
10 100 50 No12 120 60 No
Model Solution
Trial-and-Error Solution for Production Problem
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One solution approach is trial-and-error. Might not provide the best solution Inefficient (numerous calculations
required) Special solution procedures have been
developed for specific mathematical models. Some small models/problems can be
solved by hand calculations Most practical applications require using a
computer
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A variety of software packages are availablefor solving mathematical models.
Microsoft Excel The Management Scientist
LINGO
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Often, goodness/accuracy of a model cannot be
assessed until solutions are generated.
Small test problems having known, or at leastexpected, solutions can be used for model testingand validation.
If the model generates expected solutions, use themodel on the full-scale problem.
If inaccuracies or potential shortcomings inherent
in the model are identified, take corrective actionsuch as: Collection of more-accurate input data
Modification of the model
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A managerial report, based on the results of themodel, should be prepared.
The report should be easily understood by the
decision maker. The report should include:
the recommended decision
other pertinent information about the results(for example, how sensitive the modelsolution is to the assumptions and data usedin the model)
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Successful implementation of model resultsis of critical importance.
Secure as much user involvement as possiblethroughout the modeling process.
Continue to monitor the contribution of themodel.
It might be necessary to refine or expand themodel.
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Recall the production model from previous slide:
Suppose the firm in this example considers a secondproduct that has a unit profit of $5 and requires 2hours of production time for each unit produced. Use
y as the number of units of product 2 produced.
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a. Show the mathematical model when bothproducts are considered simultaneously.
b. Identify the controllable and uncontrollableinputs for this model.
c. Draw the flowchart of the input-output processfor this model (see Figure ).
d. What are the optimal solution values ofx and y?
e. Is the model developed in part (a) a deterministicor a stochastic model? Explain.
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Identify an organizational problem, Justify the problem from its financial and operational
perspective,
Describe it by following all the steps of Problem
solving Justify your answer (Not more than 10 pages)
Use your own opinion and recommendation.
Individual submission
Typed (hardcopy)
Date of submission: 8thOctober, 2013
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Chapter 01 and 02
Date: 10thOctober, 2013Duration: 30 Minutes
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