1. Management Science Chapter 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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3. 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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4. The Management Science Process
Figure 1.1
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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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6. Example of Model Construction (1 of 4)
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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7. Example of Model Construction (2 of 4)
A variable is a symbol used to represent an item that can take on any value.
Parameters are known, constant values that are often coefficients of variables in equations.
Data are pieces of information from the problem environment.
A model is a functional relationship that includes variables, parameters, and equations.
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8. Example of Model Construction (3 of 4)
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

9. Example of Model Construction (4 of 4)
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.
Profit (Z) = difference between total revenue vp (p = unit price) and total cost, i.e.
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13. 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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14. Break-Even Analysis (5 of 9)
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)
= pairs
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15. Western Clothing Company Example
Break-Even Analysis: Computer solution Excel
Western Clothing Company Example
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16. Break-Even Analysis (6 of 9)
Model Building:
Break-Even Analysis (6 of 9)
Figure 1.2
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17. Break-Even Analysis: An increase in price (7 of 9)
Figure 1.3
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18. Break-Even Analysis: An increase in variable cost (8 of 9)
Figure 1.4
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19. Break-Even Analysis: an increase in fixed cost (9 of 9)
Figure 1.5
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20. Exercise1
The Willow Furniture Company produces tables. The fixed monthly cost of production is $8,000, and the variable cost per table is $65. The tables sell for $180 apiece.
For a monthly volume of 300 tables, determine the total cost, total revenue, and profit.

21. Exercise1
The Willow Furniture Company produces tables. The fixed monthly cost of production is $8,000, and the variable cost per table is $65. The tables sell for $180 apiece.
For a monthly volume of 300 tables, determine the total cost, total revenue, and profit.
Answer:
Fixed cost (cf) = $8,000
Total variable cost (vcv ) = (300)*(65) = $19,500
Total cost = $8,000 + $19,500 = $27,500
Total revenue (vp) = (300)*(180) = $54,000
Profit = $54,000 - $27,500 = $26,500

22. Exercise1
b. Determine the monthly break-even volume for the Willow Furniture Company.

23. Exercise1
b. Determine the monthly break-even volume for the Willow Furniture Company.
Answer:
To break even
The company needs to produce almost 70 tables per month to break even

24. Exercise2
Evergreen Fertilizer Company produces fertilizer. The company's fixed monthly cost is $25,000, and its variable cost per pound of fertilizer is $0.15. Evergreen sells the fertilizer for $0.40 per pound. Determine the monthly break-even volume for the company.

25. Exercise2
Evergreen Fertilizer Company produces fertilizer. The company's fixed monthly cost is $25,000, and its variable cost per pound of fertilizer is $0.15. Evergreen sells the fertilizer for $0.40 per pound. Determine the monthly break-even volume for the company.
Evergreen must produce 100,000 lb per month to break even

26. Exercise3
Graphically illustrate the break-even volume for the Evergreen Fertilizer Company determined in Exercise2

27. Exercise3
Graphically illustrate the break-even volume for the Evergreen Fertilizer Company determined in Exercise2

28. Exercise4
Students are organizing a contest. They know that at least 100 students will attend. The rental fee for the hall is $150 and the winning student will receive $500. In order to guarantee that they break even, how much should they charge for each ticket?

29. Exercise4 Fixed cost (cf) = $150 + $500 = $650
Total variable cost (vcv ) = none
Volume (p) = 100 students
Total revenue (vp) = 100p
To break even
vp = cf + vcv
100p = 650
P= $6.50
Therefore they should charge $6.50 for each ticket

30. Figure 1.6 Modeling Techniques
Classification of Management Science Techniques
Figure Modeling Techniques
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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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34. Management Science Models Decision Support Systems (2 of 2)
Figure 1.7 A Decision Support System
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35. Management science is an art.