Management Science

Chapter 1 1-1

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Chapter Topics

The Management Science Approach to Problem Solving

Model Building: Break-Even Analysis

Computer Solution

Management Science Modeling Techniques

Business Usage of Management Science Techniques

Management Science Models in Decision Support

Systems

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The 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.

Management science, also known as operations

research, quantitative methods, etc., involves a

philosophy of problem solving in a logical manner.

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The Management Science Process

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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.

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Example of Model Construction (1 of 3)

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.

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Example of Model Construction (2 of 3)

Variables: X = # 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

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Example of Model Construction (3 of 3)

Model Solution:

Solve the constraint equation:

4x = 100

(4x)/4 = (100)/4

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)

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Model Building:

Break-Even Analysis (1 of 9)

■ Used to determine the number of units of a product to sell

or produce 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.

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Model Building:

Break-Even Analysis (2 of 9)

Model Components

Fixed Cost (cf) - costs that remain constant regardless of

number of units produced.

Variable Cost (cv) - unit production cost of product.

Volume (v) – the number of units produced or sold

Total variable cost (vcv) - function of volume (v) and

unit variable cost.

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Model Building:

Break-Even Analysis (3 of 9)

Model Components

Total Cost (TC) - total fixed cost plus total variable cost.

TC = c f − vcv

Profit (Z) - difference between total revenue vp (p = unit

price) and total cost, i.e.

Z = vp - c f - vcv

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Model Building:

Break-Even Analysis (4 of 9)

Computing the Break-Even Point

The break-even point is that volume at which total

revenue equals total cost and profit is zero:

vp − c f − vcv = 0

v( p − cv ) = c f

The break-even point v = cf

p − cv

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Model Building:

Break-Even Analysis (5 of 9)

Example: Western Clothing Company

Fixed Costs: cf = $10000

Variable Costs: cv = $8 per pair

Price : p = $23 per pair

The Break-Even Point is:

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

= 666.7 pairs

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Model Building:

Break-Even Analysis (6 of 9)

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Model Building:

Break-Even Analysis (7 of 9)

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Model Building:

Break-Even Analysis (8 of 9)

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Model Building:

Break-Even Analysis (9 of 9)

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

Exhibit 1.1

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

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

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

Exhibit 1.4 1-21

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

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Classification of Management Science Techniques

Figure 1.6 Modeling Techniques 1-23

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Characteristics of Modeling Techniques

Linear Mathematical Programming - clear objective;

restrictions on resources and requirements; parameters

known with certainty. (Chap 2-6, 9)

Probabilistic Techniques - results contain uncertainty.

(Chap 11-13)

Network Techniques - model often formulated as

diagram; deterministic or probabilistic. (Chap 7-8)

Other Techniques - variety of deterministic and

probabilistic methods for specific types of problems

including forecasting, inventory, simulation, multicriteria,

etc. (Chap 10, 14-16)

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Business Use of Management Science

Some application areas:

- Project Planning

- Capital Budgeting

- Inventory Analysis

- Production Planning

- Scheduling

Interfaces - Applications journal published by Institute

for Operations Research and Management Sciences

(INFORMS)

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Decision Support Systems (DSS)

A decision support system is a computer-based system that helps

decision makers address complex problems that cut across different

parts of an organization and operations.

Features of Decision Support Systems

Interactive

Use databases & management science models

Address “what if” questions

Perform sensitivity analysis

Examples include:

ERP – Enterprise Resource Planning

OLAP – Online Analytical Processing

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Management Science Models

Decision Support Systems (2 of 2)

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Support System

1-27

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