# Excel Operations Research Applications

Document Sample

```					 Workshop on Operations
Research: An Introduction

OPTIMIZATION

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

   Unconstrained optimization
–   Calculus methods
   Constrained optimization
–   Resource constraints
–   Market constraints
–   Environmental constraints]

Workshop on Operations
Research, Feb. 18, 2007
Linear Programming: Terminology &
Basic Concepts

   Objective function

   Variables

   Constraints

Workshop on Operations
Research, Feb. 18, 2007
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
Linear Programming: Terminology &
Basic Concepts

   LP solution
–   Graphical method if only two variables
   Sensitivity analysis
–   What if analysis
   Changes in resource availability (right hand side of
constraints)
   Changes in objective function coefficients
–   Reduced costs
–   Binding and non-binding constraints

Workshop on Operations
Research, Feb. 18, 2007
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
Extensions of LP & Mathematical
Programming

   Special Cases
–   Transportation Problem
–   Assignment Problem
–   Network models
   Integer and Mixed Integer Programs
   Non-linear Programming
   Dynamic Programming
Workshop on Operations
Research, Feb. 18, 2007
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
Applications

   Other Applications
–   Portfolio Selection
–   Project Selection
–   Media Planning

Workshop on Operations
Research, Feb. 18, 2007

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