Ch01management Science

Chapter 1- Management Science 1

Chapter 1- Management Science

Chapter Topics

• The Management Science Approach to Problem Solving

• Model Building: Break-Even Analysis

• Computer Solution

• Management Science Modeling Techniques

• Business Use of Management Science Techniques

Chapter 1- Management Science 2

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.

Chapter 1- Management Science 3

The Management Science Process

Figure 1.1 The Management Science Process

Chapter 1- Management Science 4

Steps in the Management Science Process

• Observation - Identification of a problem that exists in the system or organization.

• Definition of the Problem - problem must be clearly and consistently defined showing its boundaries and interaction 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.

Chapter 1- Management Science 5

Example of Model Construction (1 of 2)Problem Definition

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.

Chapter 1- Management Science 6

Example of Model Construction (2 of 2)Mathematical Model

Variables: x = number of units (decision variable)

Z = total profit

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

Chapter 1- Management Science 7

Model BuildingBreak-Even Analysis (1 of 7)

• 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.

Chapter 1- Management Science 8

Model BuildingBreak-Even Analysis (2 of 7)

Model Components

Fixed costs (cf) - costs that remain constant regardless of number of units produced

Variable cost (cv) - unit cost of product

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

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

Profit(Z) - difference between total revenue vp (p=price) and total cost:

Z = vp - cf - vcv

Chapter 1- Management Science 9

Model BuildingBreak-Even Analysis (3 of 7)

Computing the Break-Even Point

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

V = cf/(p-cv)

Example: Western Clothing Company

cf = $10000

cv = $8 per pair

p = $23 per pair

v = 666.7 pairs, break-even point

Chapter 1- Management Science 10

Model BuildingBreak-Even Analysis (4 of 7)

Graphical Solution

Figure 1.2 Break-even model

Chapter 1- Management Science 11

Model BuildingBreak-Even Analysis (5 of 7)

Sensitivity Analysis

Figure 1.3 Break-even model with a change in price

Chapter 1- Management Science 12

Model BuildingBreak-Even Analysis (6 of 7)

Sensitivity Analysis (variable cost)

Figure 1.4Break-even model with a change in variable cost

Chapter 1- Management Science 13

Model BuildingBreak-Even Analysis (7 of 7)Sensitivity Analysis (fixed cost)

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

Chapter 1- Management Science 14

Computer Solution (1 of 5)

Excel Spreadsheets

Exhibit 1.1

Chapter 1- Management Science 15

Computer Solution (2 of 5)Excel QM

Exhibit 1.2

Chapter 1- Management Science 16

Computer Solution (3 of 5)Excel QM (continued)

Exhibit 1.3

Chapter 1- Management Science 17

Computer Solution (4 of 5)QM for Windows

Exhibit 1.4

Chapter 1- Management Science 18

Computer Solution (5 of 5)QM for Windows (continued)

Exhibit 1.5

Chapter 1- Management Science 19

Management Science Modeling Techniques

Figure 1.6

Chapter 1- Management Science 20

Characteristics of Modeling Techniques

• Linear mathematical programming: clear objective; restrictions on resources and requirements; parameters known with certainty.

• Probabilistic techniques: results contain uncertainty.

• Network techniques: model often formulated as diagram; deterministic or probabilistic.

• Forecasting and inventory analysis techniques: probabilistic and deterministic methods in demand forecasting and inventory control.

• Other techniques: variety of deterministic and probabilistic methods for specific types of problems.

Chapter 1- Management Science 21

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