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

1-2 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

1-3 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.

1-4 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Figure 1.1 The Management Science Process

1-5 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.

1-6 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 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. Example of Model Construction (1 of 4)

1-7 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 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. Example of Model Construction (2 of 4)

1-8 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 (3 of 4)

1-9 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Example of Model Construction (4 of 4) 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) Model Solution:

1-10 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.

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

1-12 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 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. Model Building: Break-Even Analysis (3 of 9)

1-13 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

1-14 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Model Building: Break-Even Analysis (5 of 9) Example: Western Clothing Company Fixed Costs: c f = $10000 Variable Costs: c v = $8 per pair Price : p = $23 per pair The Break-Even Point is: v = (10,000)/(23 -8) = pairs

1-15 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Model Building: Break-Even Analysis (6 of 9) Figure 1.2

1-16 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Model Building: Break-Even Analysis (7 of 9) Figure 1.3

1-17 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Model Building: Break-Even Analysis (8 of 9) Figure 1.4

1-18 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Model Building: Break-Even Analysis (9 of 9) Figure 1.5

1-19 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Figure 1.6 Modeling Techniques Classification of Management Science Techniques

1-20 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 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) Characteristics of Modeling Techniques

1-21 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 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) Business Use of Management Science

1-22 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 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 Decision Support Systems (DSS)

1-23 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Figure 1.7 A Decision Support System Management Science Models Decision Support Systems (2 of 2)

1-24 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall