Management Science Chapter 1 Copyright 2010 Pearson Education

Management Science Chapter 1 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 1 -1

Chapter Topics n The Management Science Approach to Problem Solving n Model Building: Break-Even Analysis n Computer Solution n Management Science Modeling Techniques n Business Usage of Management Science Techniques n Management Science Models in Decision Support Systems Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 1 -2

The Management Science Approach n Management science uses a scientific approach to solving management problems. n It is used in a variety of organizations to solve many different types of problems. n It encompasses a logical mathematical approach to problem solving. n Management science, also known as operations research, quantitative methods, etc. , involves a philosophy of problem solving in a logical manner. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 1 -3

The Management Science Process Figure 1. 1 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 1 -4

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. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 1 -5

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. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 1 -6

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. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 1 -7

Example of Model Construction (3 of 4) Variables: X = # units to produce (decision variable) Z = total profit (in $) Model: Z = $20 X - $5 X (objective function) 4 X = 100 lb of steel (resource constraint) Parameters: values) $20, $5, 4 lbs, 100 lbs (known Formal Specification of Model: maximize Z = $20 X - $5 X subject to 4 X = 100 1 -8

Example of Model Construction (4 of 4) Model Solution: Solve the constraint equation: 4 x = 100 (4 x)/4 = (100)/4 x = 25 units Substitute this value into the profit function: Z = $20 x - $5 x = (20)(25) – (5)(25) = $375 (Produce 25 units, to yield a profit of $375) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 1 -9

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. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 1 -10

Model Building: Break-Even Analysis (2 of 9) Model Components n Fixed Cost (cf) - costs that remain constant regardless of number of units produced. n Variable Cost (cv) - unit production cost of product. n Volume (v) – the number of units produced or sold n Total variable cost (vcv) - function of volume (v) and unit variable cost. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 1 -11

Model Building: Break-Even Analysis (3 of 9) Model Components n Total Cost (TC) = total fixed cost plus total variable cost. n Profit (Z) = difference between total revenue vp (p = unit price) and total cost, i. e. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 1 -12

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 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 1 -13

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 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 1 -14

Break-Even Analysis: Computer solution Excel Western Clothing Company Example Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 1 -15

Model Building: Break-Even Analysis (6 of 9) Figure 1. 2 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 1 -16

Break-Even Analysis: An increase in price (7 of 9) Figure 1. 3 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 1 -17

Break-Even Analysis: An increase in variable cost (8 of 9) Figure 1. 4 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 1 -18

Break-Even Analysis: an increase in fixed cost (9 of 9) Figure 1. 5 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 1 -19

Exercise 1 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. a. For a monthly volume of 300 tables, determine the total cost, total revenue, and profit. 1 -20

Exercise 1 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. a. For a monthly volume of 300 tables, determine the total cost, total revenue, and profit. Answer: n Fixed cost (cf) = $8, 000 n Total variable cost (vcv ) = (300)*(65) = $19, 500 n Total cost = $8, 000 + $19, 500 = $27, 500 n Total revenue (vp) = (300)*(180) = $54, 000 n Profit = $54, 000 - $27, 500 = $26, 500 1 -21

Exercise 1 b. Determine the monthly break-even volume for the Willow Furniture Company. 1 -22

Exercise 1 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 1 -23

Exercise 2 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. 1 -24

Exercise 2 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 1 -25

Exercise 3 Graphically illustrate the break-even volume for the Evergreen Fertilizer Company determined in Exercise 2 1 -26

Exercise 3 Graphically illustrate the break-even volume for the Evergreen Fertilizer Company determined in Exercise 2 1 -27

Exercise 4 n 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? 1 -28

Exercise 4 Fixed cost (cf) = $150 + $500 = $650 n Total variable cost (vcv ) = none n Volume (p) = 100 students n Total revenue (vp) = 100 p To break even vp = cf + vcv 100 p = 650 P= $6. 50 Therefore they should charge $6. 50 for each ticket n 1 -29

Classification of Management Science Techniques Figure 1. 6 Modeling Techniques Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 1 -30

Characteristics of Modeling Techniques n n 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) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 1 -31

Business Use of Management Science n Some application areas: - Project Planning - Capital Budgeting - Inventory Analysis - Production Planning - Scheduling n Interfaces - Applications journal published by Institute for Operations Research and Management Sciences (INFORMS) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 1 -32

Management science is an art. 1 -33