Lecture 01 Introduction 管理科学英文版教学课件.pptVIP

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Lecture 01 Introduction 管理科学英文版教学课件.ppt

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Lecture 01 Introduction 管理科学英文版教学课件

ADM 2624 OR Marketing Business Report Economics Finance Quality Control Accounting Big Picture Key Points Operations Research Process Parameter vs. variable Feasibility: Break-even analysis Optimality The Modeling Process Management Science:Operations Research(OR) Chapter 2.1 , 2.3 * * Lecture Chapter 2.1: Introduction to Linear Programming (LP) History: George.Bernard. Dantzig, 1947: Simplex method Orden others in the 1950s “Linear Programming and Extensions,” 1963 Khachian 1979, ellipsoid method Karmarkar, 1984, interior point methods * * Lecture General structure of mathematical programming problems: General structure of mathematical programming problems: Max/Min z = f(x) s.t. g(x) R b or LHS R RHS f(x): objective function (what the decision maker wants) with z being the objective function value Typical objectives are Max profit, revenue, sales, utility, … or Min distances, costs, utilities. g(x): constraints (restrictions imposed by the system), R: relation (?, ?, or =), b: right-hand side value? LHS: left-hand side (a linear function that expresses reality), and RHS: right-hand side (a benchmark value). Constraints are hard and cannot be violated. This is not always the case in reality. * Lecture * Assumptions of Linear Programming Deterministic property: All parameters are assumed to be known with certainty. ? Divisibility: The variables can assume any rational value. Linearity: All functions, the objective function and the constraints, are linear. * * Lecture An LP formulation Problem description: Max profit with capacity of the assembly machine: 1,200 hrs (= 72,000 sec) Make at least 2,500 domestic frames, and Make at least 3,000 export frames. Domestic frame Export frame Unit profit contribution $40 $45 Unit assembly times 10 sec 12 sec * * Lecture Formulate the problem as an LP First step: Define variables. x1: Number of domestic frames assembled. x2: Number of export frames assembled. Max z = 40x1 + 45x2 s.t. 10x