Week 1 Chapter 1 Taylor9_01

1Chapter 1- Management Science

Introduction to Management Science9th Edition

by Bernard W. Taylor III

Chapter 1Management Science

© 2007 Pearson Education


Chapter TopicsChapter Topics

The Management Science Approach to Problem SolvingThe Management Science Approach to Problem Solving Model Building : Break-Even AnalysisModel Building : Break-Even Analysis Computer SolutionComputer Solution Management Science Modeling TechniquesManagement Science Modeling Techniques Business Usage of Management Science TechniquesBusiness Usage of Management Science Techniques Management Science Models in Decision Support Management Science Models in Decision Support

SystemsSystems


The Management Science ApproachThe Management Science Approach

Management science uses a scientific approach to Management science uses a scientific approach to solving management problems.solving management problems.

It is used in a variety of organizations to solve many It is used in a variety of organizations to solve many different types of problems.different types of problems.

It encompasses a logical mathematical approach to It encompasses a logical mathematical approach to problem solving.problem solving.

Management Science, also known as Operations Management Science, also known as Operations Research, Decision Sciences, etc., involves a philosophy Research, Decision Sciences, etc., involves a philosophy of problem solving in a logical manner.of problem solving in a logical manner.


Figure 1.1 The Management Science Process

The Management Science ProcessThe Management Science Process


Steps in the Management Science Process

Observation - Identification of a problem that exists (or may occur soon) in a system or organization.

Definition of the Problem - problem must be clearly and consistently defined, showing its boundaries and interactions with the objectives of the organization.

Model Construction - Development of the functional mathematical relationships that describe the decision variables, objective function and constraints of the problem.

Model Solution - Models solved using management science techniques.

Model Implementation - Actual use of the model or its solution.


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 of Model Construction (1 of 3)


Variables: X = number of units to produce (decision variable)

Z = total profit (in $)

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




Consider the constraint equation:

4x = 100 or x = 25 units

Substitute this value into the profit function:

Z = $20x - $5x = (20)(25) – (5)(25)

= $375

(Produce 25 units, to yield a profit of $375)

Model Solution


Model Building:Break-Even Analysis (1 of 8)

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 is called the break-even point.

Profit at break-even point is zero.


Model ComponentsModel Components Fixed Costs (cFixed Costs (cff)) - costs that remain constant regardless of - costs that remain constant regardless of

number of units produced.number of units produced. Variable Cost (cVariable Cost (cvv)) - unit production cost of product. - unit production cost of product. Total variable cost (vcTotal variable cost (vcvv)) - function of volume (v) and unit - function of volume (v) and unit

variable cost. variable cost. Total Cost (TC)Total Cost (TC) - total fixed cost plus total variable cost. - total fixed cost plus total variable cost. Profit (Z)Profit (Z) - difference between total revenue vp (p = unit - difference between total revenue vp (p = unit

price) and total cost, i.e.price) and total cost, i.e.Z = vp - cZ = vp - cff - vc - vcvv




Computing the Break-Even PointComputing the Break-Even Point

The break-even point is that volume at which total revenue The break-even point is that volume at which total revenue equals total cost and profit is zero:equals total cost and profit is zero:

vp - cvp - cff – vc – vcv v == 00

or v = cor v = cff/(p - c/(p - cvv))

(Break-Even Point)(Break-Even Point)



Example:Example: Western Clothing CompanyWestern Clothing Company Fixed Costs: cFixed Costs: cff = $10000 = $10000 Variable Costs: cVariable Costs: cvv = $8 per pair = $8 per pair Price : p = $23 per pairPrice : p = $23 per pair

The Break-Even Point is:The Break-Even Point is:

v = (10,000)/(23 -8)v = (10,000)/(23 -8) = 666.7 pairs= 666.7 pairs


Model Building: Break-Even Analysis (5 of 8)

Graphical Solution

Figure 1.2 Break-Even Model



Figure 1.3 Sensitivity Analysis - Break-even Model with a Change in Price


Figure 1.4Sensitivity Analysis - Break-Even Model with a Change in Variable Cost



Figure 1.5Sensitivity Analysis - Break-Even Model with a Change in Fixed Cost



Break-Even Analysis: Excel Solution (1 of 5)

Exhibit 1.1


Exhibit 1.2

Break-Even Analysis: Excel QM Solution (2 of 5)


Break-Even Analysis: Excel QM Solution (3 of 5)

Exhibit 1.3


Break-Even Analysis: QM Solution (4 of 5)

Exhibit 1.4


Break-Even Analysis: QM Solution (5 of 5)

Exhibit 1.5


Figure 1.6 Modeling Techniques

Classification of Management Science Techniques


Linear Mathematical ProgrammingLinear Mathematical Programming -- clear objective; clear objective; restrictions on resources and requirements; parameters restrictions on resources and requirements; parameters known with certainty.known with certainty.

Probabilistic TechniquesProbabilistic Techniques -- results contain uncertainty.results contain uncertainty. Network TechniquesNetwork Techniques - model often formulated as diagram; - model often formulated as diagram;

deterministic or probabilistic.deterministic or probabilistic. Forecasting and Inventory Analysis TechniquesForecasting and Inventory Analysis Techniques - -

probabilistic and deterministic methods in demand probabilistic and deterministic methods in demand forecasting and inventory control.forecasting and inventory control.

Other TechniquesOther Techniques - variety of deterministic and - variety of deterministic and probabilistic methods for specific types of problems.probabilistic methods for specific types of problems.

Characteristics of Modeling TechniquesCharacteristics of Modeling Techniques


Some application areasSome application areas:: - Project Planning- Project Planning - Capital Budgeting- Capital Budgeting - Inventory Analysis - Inventory Analysis - Production Planning- Production Planning - Scheduling- Scheduling InterfacesInterfaces - - Applications journal published by Institute Applications journal published by Institute

for Operations Research and Management Sciencesfor Operations Research and Management Sciences (INFORMS)(INFORMS)

Business Use of Management ScienceBusiness Use of Management Science


A A decision support system (DSS)decision support system (DSS) is a computer-based is a computer-based system that helps decision makers address complex system that helps decision makers address complex problems that cut across different parts of an organization problems that cut across different parts of an organization and operations.and operations.

A DSS is normally A DSS is normally interactiveinteractive, combining various , combining various databases and different management science models and databases and different management science models and solution techniques with a user interface that enables the solution techniques with a user interface that enables the decision maker to ask questions and receive answers.decision maker to ask questions and receive answers.

Online analytical processing system (OLAP)Online analytical processing system (OLAP),, thethe analytical hierarchy process (AHP)analytical hierarchy process (AHP), and , and enterprise enterprise resource planning (ERP)resource planning (ERP) are types of decision support are types of decision support systems.systems.

Decision support systems are most useful in answering Decision support systems are most useful in answering “what-if?” questions and performing sensitivity analysis.“what-if?” questions and performing sensitivity analysis.

Management Science ModelsDecision Support Systems (1 of 2)


Figure 1.7 A Decision Support System

Management Science ModelsDecision Support Systems (2 of 2)


End of Chapter

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Week 1 Chapter 1 Taylor9_01