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

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

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

The Management Science Process Figure 1.1 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

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

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

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

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

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) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

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

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

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

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

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) = 666.7 pairs Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

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

Break-Even Analysis (6 of 9) Model Building: Break-Even Analysis (6 of 9) Figure 1.2 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Break-Even Analysis: An increase in price (7 of 9) Figure 1.3 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Break-Even Analysis: An increase in variable cost (8 of 9) Figure 1.4 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Break-Even Analysis: an increase in fixed cost (9 of 9) Figure 1.5 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

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.

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

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

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

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.

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

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

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

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?

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

Figure 1.6 Modeling Techniques Classification of Management Science Techniques Figure 1.6 Modeling Techniques Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 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) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 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) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

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

Management Science Models Decision Support Systems (2 of 2) Figure 1.7 A Decision Support System Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Management science is an art.