02. EMS-02 Quantitative Analysis

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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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02. EMS-02 Quantitative Analysis