Ch.01 Introduction to Modeling Management Science / Instructor: Bonghyun Ahn
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 2
The Management Science Approach Management science is 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. 3
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 4
Example of Model Construction (1 of 3) 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. 5
Example of Model Construction (2 of 3) 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 6
Example of Model Construction (3 of 3) 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) 7
Model Building: Break-Even Analysis (1 of 6) 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. 8
Model Building: Break-Even Analysis (2 of 6) 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. - Total Cost (TC) - total fixed cost plus total variable cost. TC = c f + vc v - Profit (Z) - difference between total revenue vp (p = unit price) and total cost, i.e. Z = vp - c - vc f v 9
Model Building: Break-Even Analysis (3 of 6) Computing the Break-Even Point - The break-even point is that volume at which total revenue equals total cost and profit is zero: vp v( - p c - f c v - ) vc = v c f = 0 - The break-even point v = c f p - c v 10
Model Building: Break-Even Analysis (4 of 6) 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) = 666.7 pairs 11
Model Building: Break-Even Analysis (5 of 6) Figure 1.2 Breakeven model Figure 1.3 Breakeven model with an increase in price 12
Model Building: Break-Even Analysis (6 of 6) Figure 1.4 Breakeven model with an increase in variable cost Figure 1.5 Breakeven model with a change in fixed cost 13
Break-Even Analysis: Excel Solution (1 of 4) Formula for v, break-even point, =D4/(D8-D6) Exhibit 1.1 14
Break-Even Analysis: Excel Solution (2 of 4) Click on Add- Ins, then the menu of Excel QM modules Enter model parameters in cells B10:B13 Exhibit 1.2 15
Break-Even Analysis: Excel Solution (3 of 4) Exhibit 1.3 16
Break-Even Analysis: Excel Solution (4 of 4) Exhibit 1.4 17
Classification of Management Science Techniques Management Science techniques Text Linear mathematical programming Linear programming models Graphical analysis Sensitivity analysis Transportation, transportation, transshipment, and assignment Integer linear programming Goal programming Probabilistic techniques Network techniques Other techniques Companion web site Probability and statistics Decision analysis Queuing Network flow Project management (PERT/CPM) Analytical hierarchy process (AHP) Nonlinear programming Simulation Forecasting Inventory Simplex method Transportation and assignment methods Nonlinear programming Game theory Markov analysis Branch and bound method 18
Characteristics of Modeling Techniques Linear Mathematical Programming Techniques - 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, AHP (analytic hierarchy process), etc. (Chap 9, 14-16) 19
Business Usage 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) 20
Management Science Models in DSS (1 of 2) A Decision Support System(DSS) 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 Uses databases & management science models Address what if questions Perform sensitivity analysis - Examples include: ERP Enterprise Resource Planning OLAP Online Analytical Processing 21
Management Science Models in DSS (2 of 2) Figure 1.7 Decision Support System 22