Lecture 1 – Operations Research. Topics What is OR? Modeling and the problem solving process Deterministic vs. stochastic models OR techniques Using the Excel add-ins to find solutions Solving real problems. What is Operations Research?. Operations
The activities carried out in an organization.
The process of observation and testing characterized
by the scientific method. Situation, problem statement, model construction, validation, experimentation, candidate solutions.
An abstract representation of reality. Mathematical, physical, narrative, set of rules in computer program.
Include broad implications of decisions for the organization at each stage in analysis. Both quantitative and qualitative factors are considered.
A solution to the model that optimizes (maximizes or minimizes) some measure of merit over all feasible solutions.
A group of individuals bringing various skills and viewpoints to a problem.
Operations Research Techniques
A collection of general mathematical models, analytical procedures, and algorithms.
ToolsProblem Solving Process
Implement a Solution
Goal: solve a problem
Test the Model
and the Solution
Example: Internal nursing staff not happy with their schedules; hospital using too many external nurses.
ModelConstructing a Model
Example: Define relationships between individual nurse assignments and preference violations; define tradeoffs between the use of internal and external nursing resources.
ToolsSolving the Mathematical Model
Example: Collect input data -- nurse profiles and demand requirements; apply algorithm; post-process results to get monthly schedules.
Example: Implement nurse scheduling system in one unit at a time. Integrate with existing HR and T&A systems. Provide training sessions during the workday.
Deterministic Models Stochastic Models
• Linear Programming • Discrete-Time Markov Chains
• Network Optimization • Continuous-Time Markov Chains
• Integer Programming • Queuing
• Nonlinear Programming • Decision Analysis
Deterministic models – 60% of course
Stochastic (or probabilistic) models – 40% of course
assume all data are known with certainty
explicitly represent uncertain data via
random variables or stochastic processes
Deterministic models involve optimization
Stochastic models characterize / estimate