Introduction to Management Science

Chapter One

1

What is Management Science?

• Management Science is a “discipline” that attempts to aid managerial decision making by applying a scientific approach to managerial problems that involve quantitative factors.

2

Why Study Management Science?

• Gain an appreciation for the relevance and power of MS.

• Learn to recognize when MS can (and cannot) be fruitfully Applied

• Learn how to apply the major techniques of MS to analyze a variety or managerial problems.

• Develop an understanding of how to interpret the results of a MS study.

3

The Nature of Management Science

• MS is a Discipline– Current Roots in 1940’s and 50’s

• Operations Research, OR, MS, MS/OR

– Simplex algorithm, Danzig (1947)

• MS aids managerial decision making• MS uses a scientific approach

4

Management Science Uses a Scientific Approach

• Define the problem and gather data.• Formulate a model (typically a mathematic model) to

represent the problem.• Develop a computer-based procedure for deriving

solutions to the problem from the model.• Test the model and refine it as needed.• Apply the model to analyze the problem and develop

recommendations for management.• Help to implement the team’s recommendations that

are adopted by management

5

1-6

Special Products Break-Even Analysis

• The Special Products Company produces expensive and unusual gifts.

• The latest new-product proposal is a limited edition grandfather clock.

• Data:– If they go ahead with this product, a fixed cost of $50,000 is

incurred.– The variable cost is $400 per clock produced.– Each clock sold would generate $900 in revenue.– A sales forecast will be obtained.

Question: Should they produce the clocks, and if so, how many?

1-7

Expressing the Problem Mathematically

• Decision variable:– Q = Number of grandfather clocks to produce

• Costs:– Fixed Cost = $50,000 (if Q > 0)– Variable Cost = $400 Q– Total Cost =

• 0, if Q = 0• $50,000 + $400 Q, if Q > 0

• Profit:– Profit = Total revenue – Total cost

• Profit = 0, if Q = 0• Profit = $900Q – ($50,000 + $400Q) = –$50,000 + $500Q, if Q > 0

1-8

Special Products Co. Spreadsheet

34567

E FResults

Total Revenue =UnitRevenue*MIN(SalesForecast,ProductionQuantity)Total Fixed Cost =IF(ProductionQuantity>0,FixedCost,0)

Total Variable Cost =MarginalCost*ProductionQuantityProfit (Loss) =TotalRevenue-(TotalFixedCost+TotalVariableCost)

Range Name CellFixedCost C5MarginalCost C6ProductionQuantity C9Profit F7SalesForecast C7TotalFixedCost F5TotalRevenue F4TotalVariableCost F6UnitRevenue C4

3456789

B C D E FData Results

Unit Revenue $900 Total Revenue $180,000Fixed Cost $50,000 Total Fixed Cost $50,000

Marginal Cost $400 Total Variable Cost $80,000Sales Forecast 300 Profit (Loss) $50,000

Production Quantity 200

1-9

Analysis of the Problem

$

$40,000

$80,000

$120,000

$160,000

$200,000

0 40 80 120 160 200

Revenue = $900 x

Fixed cost

Loss

Profit

Cost = $50,000 + $400 x

x

Break-even point = 100 units

1-10

Management Science Interactive Modules

• Sensitivity analysis can be performed using the Break-Even module in the Interactive Management Science Modules (available on your MS Courseware CD packaged with the text).

– Here we see the impact of changing the fixed cost to $75,000.

1-11

Special Products Co. Spreadsheet

Range Name CellFixedCost C5MarginalCost C6ProductionQuantity C9Profit F7SalesForecast C7TotalFixedCost F5TotalRevenue F4TotalVariableCost F6UnitRevenue C4

3456789

B C D E FData Results

Unit Revenue $900 Total Revenue $270,000Fixed Cost $50,000 Total Fixed Cost $50,000

Marginal Cost $400 Total Variable Cost $120,000Sales Forecast 300 Profit (Loss) $100,000

Production Quantity 300 Break-Even Point 100

3456789

E FResults

Total Revenue =UnitRevenue*MIN(SalesForecast,ProductionQuantity)Total Fixed Cost =IF(ProductionQuantity>0,FixedCost,0)

Total Variable Cost =MarginalCost*ProductionQuantityProfit (Loss) =TotalRevenue-(TotalFixedCost+TotalVariableCost)

Break-Even Point =FixedCost/(UnitRevenue-MarginalCost)