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Workshop on Operations Research: An Introduction

Workshop on Operations Research: An Introduction. OPTIMIZATION. Overview. Introduction Basics of Linear Programming Formulation Graphical representation & solution Solution with Excel Solver Interpretation of Results Extensions of LP and Mathematical Programming Applications in business.

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Workshop on Operations Research: An Introduction

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  1. Workshop on Operations Research: An Introduction OPTIMIZATION Workshop on Operations Research, Feb. 18, 2007

  2. Overview • Introduction • Basics of Linear Programming • Formulation • Graphical representation & solution • Solution with Excel Solver • Interpretation of Results • Extensions of LP and Mathematical Programming • Applications in business Workshop on Operations Research, Feb. 18, 2007

  3. Introduction • Unconstrained optimization • Calculus methods • Constrained optimization • Resource constraints • Market constraints • Environmental constraints] Workshop on Operations Research, Feb. 18, 2007

  4. Linear Programming: Terminology & Basic Concepts • Objective function • Variables • Constraints Workshop on Operations Research, Feb. 18, 2007

  5. Linear Programming: Terminology & Basic Concepts • Formulation • Algebraic / mathematical description of the problem • Objective function and constraints must be linear • Feasible solution • Feasible region • Optimal solution Workshop on Operations Research, Feb. 18, 2007

  6. Linear Programming: Terminology & Basic Concepts • LP solution • Graphical method if only two variables • Spreadsheets with Excel solver • Sensitivity analysis • What if analysis • Changes in resource availability (right hand side of constraints) • Changes in objective function coefficients • Shadow prices • Reduced costs • Binding and non-binding constraints Workshop on Operations Research, Feb. 18, 2007

  7. Linear Programming: Terminology & Basic Concepts • Shadow Price (of a constraint) • Change in the value of the objective function for a unit change in the right hand side of the constraint • Estimate of the value of an additional unit of the resource • Shadow price of a nonbinding constraint is zero • Reduced cost (of a variable) • Change in the value of the objective function due to the additional restriction that the variable be greater than or equal to one. Workshop on Operations Research, Feb. 18, 2007

  8. Extensions of LP & Mathematical Programming • Special Cases • Transportation Problem • Assignment Problem • Network models • Integer and Mixed Integer Programs • Quadratic Programming • Non-linear Programming • Dynamic Programming Workshop on Operations Research, Feb. 18, 2007

  9. Applications • Primarily a planning tool • Applications in Operations • Plant / Facilities location & capacity planning • Allocation of products to plants • Production Planning • Scheduling • Logistics Planning • Transportation & Distribution • Vehicle Routing Workshop on Operations Research, Feb. 18, 2007

  10. Applications • Other Applications • Portfolio Selection • Project Selection • Media Planning Workshop on Operations Research, Feb. 18, 2007

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