1 1 Operations Research The OR Process 2005.9.13.
-
date post
20-Dec-2015 -
Category
Documents
-
view
216 -
download
0
Transcript of 1 1 Operations Research The OR Process 2005.9.13.
11
Operations ResearchOperations Research
The OR Process
2005.9.13
2
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
Lecture 1 – Operations ResearchLecture 1 – Operations Research
3
Systems ApproachInclude broad implications of decisions for the organization at each stage in analysis. Both quantitative and qualitative factors are considered.
Optimal SolutionA solution to the model that optimizes (maximizes or minimizes) some measure of merit over all feasible solutions. TeamA group of individuals bringing various skills and viewpoints to a problem. Operations Research TechniquesA collection of general mathematical models, analytical procedures, and algorithms.
4
It is a Process
It assists Decision Makers
It has a set of Tools
It is applicable in many Situations
What is OR?What is OR?
5
1. OR professionals aim to provide rational bases for decision making by seeking to understand and structure complex situations and to use this understanding to predict system behavior and improve system performance.
2. Much of this work is done using analytical and numerical techniques to develop and manipulate mathematical and computer models of organizational systems composed of people, machines, and procedures.
Definition of OR?Definition of OR?
6
Data
ManufacturingPlanning
Design
Scheduling
Dealing with Defects
Dealing with Variability
Dealing with Inventory
…
Situation
The Process: Recognize the ProblemThe Process: Recognize the Problem
7
Service Industries
Logistics
Transportation
Environment
Health Care
Situations with complexity
Situations with uncertaintyData
Situation
Other applicationsOther applications
8
Data
Solution
Find a Solution
Tools
Situation
Formulate the Problem
Problem Statement
Test the Model and the Solution
Solution
Establish a Procedure
Implement the Solution
Construct a Model
Model
Implement a Solution
Goal: solve a problemModel must be validModel must be tractableSolution must be useful
Problem Solving ProcessProblem Solving Process
9
Define the problem
Delimit the system
Select measures
Formulate the Problem
Problem Statement
Data
Situation
Determine variables
Identify constraints
Formulate the ProblemFormulate the Problem
10
• May involve current operations or proposed expansions due to expected market shifts
• May become apparent through consumer complaints or through employee suggestions
• May be a conscious effort to improve efficiency or response to an unexpected crisis.
Example: Internal nursing staff not happy with their schedules; hospital using too many external nurses.
Data
Situation
The SituationThe Situation
11
Define variables
Define constraints
Data requirements
Example: Maximize individual nurse preferences subject to demand requirements.
Formulate the Problem
Problem Statement
Data
Situation
• Describe system• Define boundaries • State assumptions• Select performance measures
Problem FormulationProblem Formulation
12
Long-term planning
– FTRs, PTRs, PTFs
– Shifts
– Days off
Weekly scheduling
– Vacations, leave
– Overtime
– PTFs, casuals
– Task assignments
Real-time control
– Emergencies
– Daily adjustments
– Sick leave
– Overtime
Personnel Planning and Scheduling: Personnel Planning and Scheduling: Example of Bounding a ProblemExample of Bounding a Problem
13
Construct a ModelConstruct a Model
Math. Programming Model
Stochastic Model
Statistical Model
Simulation Model
Construct a Model
Model
Formulate the Problem
Problem Statement
Data
Situation
14
Problem must be translated from verbal, qualitative terms to logical, quantitative terms
A logical model is a series of rules, usually embodied in a computer program
Example: Define relationships between individual nurse assignments and preference violations; define tradeoffs between the use of internal and external nursing resources.
Constructa Model
Model
Formulate the Problem
Problemstatement
Data
Situation
• A mathematical model is a collection of functional relationships by which allowable actions are delimited and evaluated.
Constructing a ModelConstructing a Model
15
Many tools are available as discussed in this course
Some lead to “optimal” solutionsOthers only evaluate candidates trial and
error to find “best” course of action
Example: Read nurse profiles and demand requirements, apply algorithm, post-processes results to get monthly schedules.
Model
Solution
Find asolution
Tools
Solving the Mathematical ModelSolving the Mathematical Model
16
Linear Programming
Nonlinear Programming
Regression
Direct Search
Stochastic Optimization
Trial and Error
Construct a Model
Model
Formulate the Problem
Problem Statement
Data
Situation
Solution
Find a Solution
Tools
Find a SolutionFind a Solution
17
Production software
Easy to use
Easy to maintain
Acceptable to the user
Solution
Establish a Procedure
Solution
Find a Solution
Tools
Construct a Model
Model
Formulate the Problem
Problem Statement
Data
Situation
Establish a ProcedureEstablish a Procedure
18
The model must be valid
The model must be tractable
The solution must be useful
Data
Solution
Find a Solution
Tools
Situation
Formulate the Problem
Problem Statement
Test the Model and the Solution
Solution
Establish a Procedure
Implement the Solution
Construct a Model
Model
Implement a Solution
The Goal is to Solve the ProblemThe Goal is to Solve the Problem
19
Change for the organization
Change is difficult
Establish controls to recognize change in the situation
Solution
Establish a Procedure
Solution
Find a Solution
Tools
Construct a Model
Model
Formulate the Problem
Problem Statement
Data
Situation
Implement the Solution
Implement the SolutionImplement the Solution
20
A solution to a problem usually implies changes for some individuals in the organization
Often there is resistance to change, making the implementation difficult
User-friendly system neededThose affected should go through training
Situation
Procedure
Implement the Procedure
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.
ImplementationImplementation
21
Data base (nurse profiles, external resources, rules)
Graphical User Interface (GUI); web enabled using java or VBA
Algorithms, pre- and post- processor
What-if analysis
Report generators
Components of Components of OR-Based Decision Support SystemOR-Based Decision Support System
22
Real World Situation
Problems
Models
Methods
TP
LP NFP
simplexinterior
LP
TP
DS
Real WorldSituation
Problems
Models
Methods
Problems, Models and MethodsProblems, Models and Methods
23
Operations Research Models
Deterministic Models Stochastic Models
• Linear Programming • Discrete-Time Markov Chains
• Network Optimization • Continuous-Time Markov Chains
• Integer Programming • Queueing
• Nonlinear Programming • Decision Analysis
24
Deterministic models – 60% of course
Stochastic (or probabilistic) models – 40% of course
Deterministic models assume all data are known with certainty
Stochastic models explicitly represent uncertain data via random variables or stochastic processes.
Deterministic models involve optimization
Stochastic models characterize / estimate system performance.
Deterministic vs. Stochastic ModelsDeterministic vs. Stochastic Models
25
Rescheduling aircraft in response to groundings and delaysPlanning production for printed circuit board assemblyScheduling equipment operators in mail processing & distribution centersDeveloping routes for propane deliveryAdjusting nurse schedules in light of daily fluctuations in demand
Examples of OR ApplicationsExamples of OR Applications
26
Problem formulation
Model building
Data collection
Data analysis
Coding
Experimental design
Analysis of results
Fine-tune model
Model verification and
validation
No
Yes
2
4
6
8
1
3
5
7
Steps in OR StudySteps in OR Study
27
How decision-making problems are characterized
OR terminology
What a model is and how to assess its value
How to go from a conceptual problem to a quantitative solution
How to find solutions with the Excel add-ins
What you Should Know about What you Should Know about Operations ResearchOperations Research
128
Operations Research/Management ScienceOperations Research/Management Science
Institute for Operations Research and the Management Sciences
OR/MS Professionals aim to provide rational bases for decision making by seeking to understand and structure complex situations and to use this understanding to predict system behavior and improve system performance. Much of this work is done using analytical and numerical techniques to develop and manipulate mathematical and computer models of organizational systems composed of people, machines, and procedures.
29
OperationsThe activities carried out in an organization. ResearchThe process of observation and testing characterized by the scientific method. Situation, problem statement, model construction, validation, experimentation, candidate solutions. ModelAn abstract representation of reality. Mathematical, physical, narrative, set of rules in computer program.
What is Operations Research?What is Operations Research?
30
Philosophy Why are we here?
Theology What is going to become of us?
Science What is it, how and why does it work?
Mathematic How do we prove it?
Engineering How do we make it?
OR/MS How do we get it to work efficiently (optimally)?
Psychology How do we feel about it?
Sociology How does it affect us and how do we affect it?
Politics How can we agree on getting it to work?
Business How do we convert it to an opportunity and make money out of it?
Law How do we create doubt about why it happened so we can win and make big money?
Psychiatry What is the bright side of looking at it?
Medicine How do we get it going again?