Workshop on Operations Research: An Introduction

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Workshop on Operations Research An Introduction

• OPTIMIZATION

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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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Introduction

• Unconstrained optimization
• Calculus methods
• Constrained optimization
• Resource constraints
• Market constraints
• Environmental constraints

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Linear Programming Terminology Basic Concepts

• Objective function
• Variables
• Constraints

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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

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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

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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.

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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

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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

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Applications

• Other Applications
• Portfolio Selection
• Project Selection
• Media Planning