Break Even Analysis

US2018

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Management Science

Chapter 1

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Chapter Topics

The Management Science Approach to Problem Solving

Management Science and Business Analytics

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 is 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, business analytics, etc., involves a philosophy of problem solving in a logical manner.

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The Management Science Process

Figure 1.1 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.

Problem Definition - The 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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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)

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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

Example of Model Construction (2 of 3)

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Example of Model Construction (3 of 3)

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)

Model Solution:

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Management Science and Business Analytics

Business analytics uses large amounts of data with management science techniques to help managers make decisions

Brings together information technology, statistics, management science, and mathematical modeling

Big data

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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 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.

Model Building: Break-Even Analysis (2 of 9)

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Model Components

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

Profit (Z) - difference between total revenue vp (p = unit price) and total cost, i.e.

Model Building: Break-Even Analysis (3 of 9)

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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:

The break-even point

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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 of jeans

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Model Building:

Break-Even Analysis (6 of 9)

Figure 1.2 Break-even model

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Model Building:

Break-Even Analysis (7 of 9)

Figure 1.3 Break-even model with an increase in price

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Model Building:

Break-Even Analysis (8 of 9)

Figure 1.4 Break-even model with an increase in variable cost

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Model Building:

Break-Even Analysis (9 of 9)

Figure 1.5 Break-even model with a change in fixed cost

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Break-Even Analysis: Excel Solution (1 of 4)

Exhibit 1.1

Formula for v,

break-even point,

=D4/(D8-D6)

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Break-Even Analysis: Excel QM Solution (2 of 4)

Enter model parameters in cells B10:B13

Click on “Excel QM,” then on

Alphabetical” list of models

and select “Breakeven Analysis”

Exhibit 1.2

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Exhibit 1.3 Western Clothing Company in QM

Break-Even Analysis: Excel QM Solution (3 of 4)

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

Exhibit 1.4 QM break-even graph for Western Clothing Company

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Figure 1.6 Classification of management science techniques

Classification of Management Science Techniques

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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, AHP (analytic hierarchy process), etc. (Chap 9, 14-16)

Characteristics of Modeling Techniques

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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)

Business Usage of Management Science

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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

Uses databases & management science models

Address “what if” questions

Perform sensitivity analysis

Examples include:

ERP – Enterprise Resource Planning

OLAP – Online Analytical Processing

Management Science Models in

Decision Support Systems (DSS)

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Figure 1.7 A decision support system

Management Science Models

Decision Support Systems (2 of 2)

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All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher.

Printed in the United States of America.

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