Operations Research
Chapter 1: Introduction
Operations Research = a scientific approach to the solution of problems in the
management of
complex systems
-> the goal is to improve decision making by using available data in a company
(is not only about money, is way broader)
History
° WW II
was the first trigger for Operations Research
-> managing of resources and use them in the most efficient way became
important
° industrialization
-> multiple break-throughs ex. Simplex method
-> higher computational power of PC’s
Example of use
UPS with ORION project
-> plans trajectories in the most efficient way for deliverers
Operations Research includes a lot of
different concepts
-> we are going to focus mainly on
‘optimization’
OR/Analytics Cycle
Often, the problem is arguable BUT the solution too
-> need to formulate a problem well and agree on the formulation
goal: create a mathematical model for a real world problem
! the answer of the model need to be translated back into the real
world !
-> always need to think well about which data are needed
-> model need to be tested + modified if needed
1
,Progression of Analytics
OR focuses on predictive and prescriptive
analytics
-> offers a high business value
(goes further than being descriptive)
2
,Chapter 2: Overview of the Operations Research Modeling
Approach
Are going to look at all the steps of the OR cycle
Business situation
We have a real world problem that need to be defined/identified
-> need to identify the appropriate objectives (need to be specific)
ex. Optimize what?
-> need to identify the constraints
ex. budget
-> identify interrelationships with other areas of the organization
-> identify alternative courses of action
Gathering data
-> need to gather relevant information/data
2 possible problems
° not enough data -> build management information system
° too much data -> use data mining methods
Mathematical Model
Model = idealized representation
BUT even simplistic models can give very good results
Will express the objective and restrictions in mathematical expressions
° decision variables
-> represent the decisions to be made
-> x1, x2, … xn
° objective function
-> performance measure expressed as a function of the decision variables
ex. P = 3x1+ x2 + … + 5xn
° constraints
-> mathematical expressions for the restrictions
-> are often expressed as inequalities
° parameters of the model
= constants in the equation ex. 10
BUT determining parameters is often difficult
! important to know !
-> there can me more than 1 model for the same problem
-> assumptions need sometimes to be simplified in order to find a feasible
solution
-> need a lot of testing in order to validate a model
Advantages of mathematical models
° more concise (bondig)
° reveals important cause and effect relationships
° clearly reveals what data is relevant
° forms a bridge to use computers for analysis
-> will put all we have in a spreadsheet
3
, Spreadsheet model
Will search for an optimal solution via algorithms
-> put mathematical model into a software
-> sometimes will not reach an optimal solution BUT a satisfactory solution
Model and Managerial Insights
After finding a satisfactory solution, we need to do some analysis
different sorts of tests
° postoptimality analysis
-> analysis dine after finding an optimal solution
-> ‘what-if’ analysis: what would happen if different assumptions were made?
=> outcome of the model should change
if not THEN your model is not valid
° sensitivity analysis
-> determines which variables affect the solution the most
(will play around with those variables)
-> looking for the most crucial parameters of the model
° model validation
-> detect bugs in coding
-> looking whether when changing a variable, the output changes too
=> if yes, is the change in output logic?
° retrospective test
-> using historical data to reconstruct the past
-> looking whether the model can predict the future based on historical data
-> test if the model has a predictive value (is what we want in OR)
Communicate to real world – business situation
Are again in the business situation because we need to communicate the results
to the reals world
-> need to support decisions and help making well-informed decisions
-> the implementation phase is very important
success of implementation depends on support
from:
- top management
- operations management
! important to know !
in this course we will not focus on the implementation phase
BUT need to know that this phase is crucial in the real world
-> need to develop procedures to put system into operation
-> need to gather feedback (revisit assumptions if needed)
Chapter 3: Introduction to linear programming
Introduction
4
Chapter 1: Introduction
Operations Research = a scientific approach to the solution of problems in the
management of
complex systems
-> the goal is to improve decision making by using available data in a company
(is not only about money, is way broader)
History
° WW II
was the first trigger for Operations Research
-> managing of resources and use them in the most efficient way became
important
° industrialization
-> multiple break-throughs ex. Simplex method
-> higher computational power of PC’s
Example of use
UPS with ORION project
-> plans trajectories in the most efficient way for deliverers
Operations Research includes a lot of
different concepts
-> we are going to focus mainly on
‘optimization’
OR/Analytics Cycle
Often, the problem is arguable BUT the solution too
-> need to formulate a problem well and agree on the formulation
goal: create a mathematical model for a real world problem
! the answer of the model need to be translated back into the real
world !
-> always need to think well about which data are needed
-> model need to be tested + modified if needed
1
,Progression of Analytics
OR focuses on predictive and prescriptive
analytics
-> offers a high business value
(goes further than being descriptive)
2
,Chapter 2: Overview of the Operations Research Modeling
Approach
Are going to look at all the steps of the OR cycle
Business situation
We have a real world problem that need to be defined/identified
-> need to identify the appropriate objectives (need to be specific)
ex. Optimize what?
-> need to identify the constraints
ex. budget
-> identify interrelationships with other areas of the organization
-> identify alternative courses of action
Gathering data
-> need to gather relevant information/data
2 possible problems
° not enough data -> build management information system
° too much data -> use data mining methods
Mathematical Model
Model = idealized representation
BUT even simplistic models can give very good results
Will express the objective and restrictions in mathematical expressions
° decision variables
-> represent the decisions to be made
-> x1, x2, … xn
° objective function
-> performance measure expressed as a function of the decision variables
ex. P = 3x1+ x2 + … + 5xn
° constraints
-> mathematical expressions for the restrictions
-> are often expressed as inequalities
° parameters of the model
= constants in the equation ex. 10
BUT determining parameters is often difficult
! important to know !
-> there can me more than 1 model for the same problem
-> assumptions need sometimes to be simplified in order to find a feasible
solution
-> need a lot of testing in order to validate a model
Advantages of mathematical models
° more concise (bondig)
° reveals important cause and effect relationships
° clearly reveals what data is relevant
° forms a bridge to use computers for analysis
-> will put all we have in a spreadsheet
3
, Spreadsheet model
Will search for an optimal solution via algorithms
-> put mathematical model into a software
-> sometimes will not reach an optimal solution BUT a satisfactory solution
Model and Managerial Insights
After finding a satisfactory solution, we need to do some analysis
different sorts of tests
° postoptimality analysis
-> analysis dine after finding an optimal solution
-> ‘what-if’ analysis: what would happen if different assumptions were made?
=> outcome of the model should change
if not THEN your model is not valid
° sensitivity analysis
-> determines which variables affect the solution the most
(will play around with those variables)
-> looking for the most crucial parameters of the model
° model validation
-> detect bugs in coding
-> looking whether when changing a variable, the output changes too
=> if yes, is the change in output logic?
° retrospective test
-> using historical data to reconstruct the past
-> looking whether the model can predict the future based on historical data
-> test if the model has a predictive value (is what we want in OR)
Communicate to real world – business situation
Are again in the business situation because we need to communicate the results
to the reals world
-> need to support decisions and help making well-informed decisions
-> the implementation phase is very important
success of implementation depends on support
from:
- top management
- operations management
! important to know !
in this course we will not focus on the implementation phase
BUT need to know that this phase is crucial in the real world
-> need to develop procedures to put system into operation
-> need to gather feedback (revisit assumptions if needed)
Chapter 3: Introduction to linear programming
Introduction
4
