Samenvatting operations research
Chapter 1: introduction
“a scientific approach to the solution of problems in the management of complex systems”
Operations Research & Analytics are proven scientific mathematical processes that enable
organizations to turn complex challenges into substantial opportunities by transforming
data into information, and information into insights that save lives, save money and solve
problems.
History
• WW II
• industrialisation
•++ break-throughs (simplex method in the fifties)
•++ computational power of PC’s
A model represents or describes perceptions of a real situation, simplified, using a formal,
theoretically based language of concepts and their relationships (that enables manipulation
of these entities), in order to facilitate management, control, understanding or some other
manipulation of that situation.
,The Nature of Operations Research
• Process
• Carefully observe and formulate the problem
• Gather data
• Construct a mathematical model
• Test whether the model represents the actual situation
• Modify the model as appropriate and validate again
• Broad viewpoint
• Considers what is best for organization as a whole
• Attempts to identify best possible course of action
• Team approach
• Consists of individuals with diverse backgrounds and skills
• Necessary for considering ramifications of problem throughout organization
,Chapter 2: Overview of the Operations Research Modeling Approach
OR/Analytics Cycle
Defining the Problem and Gathering Data (business situation)
• Elements of problem definition
• Identify the appropriate objectives
• Identify constraints
• Identify interrelationships with other areas of the organization
• Identify alternative courses of action
• Define the time constraints
• OR team typically works in an advisory capacity
• Management makes the final decisions
• Identify the decision maker
• Probe his/her thinking regarding objectives
• Objectives need to be specific
• Also aligned with organizational objectives
• Example of an objective in a for-profit organization
• Maximum profit in the long run
• Minimum environmental impact
• Minimum employee turnover
• More typical objective
• Satisfactory profit combined with other defined objective
• Gathering relevant data necessary for:
• Complete problem understanding
• Input into mathematical models
• Problem: too little data available
• Solution: build management information system to collect data
• Problem: too much data available
• Solution: data mining methods
, Formulating a Mathematical Model (mathematical problem)
• Models
• Idealized representations
• Examples: model airplanes, portraits, …
• Mathematical models
• Expressed in terms of mathematical symbols
• Example: Newton’s Law: F = ma
• Mathematical model of a business problem
• Expressed as system of equations
Ingredients of a Mathematical Model
Formulating a Mathematical Model
• Determining parameter values
• Often difficult
• Done by gathering data
• Typical expression of the problem
• Choose values of decision variables so as to maximize the objective function
Subject to the specified constraints
• Real problems often do not have a single “right” model
• What are the advantages of a mathematical model over a verbal description of the
problem?
• More concise
• Reveals important cause and effect relationships
• Clearly indicates what data is relevant
• Forms a bridge to use computers for analysis
• What are the disadvantages of mathematical models?
• Often must simplify assumptions to make problem solvable
• Judging a model’s validity
• Desire high correlation between model’s prediction and real-world outcome
• Testing (validation phase)
Chapter 1: introduction
“a scientific approach to the solution of problems in the management of complex systems”
Operations Research & Analytics are proven scientific mathematical processes that enable
organizations to turn complex challenges into substantial opportunities by transforming
data into information, and information into insights that save lives, save money and solve
problems.
History
• WW II
• industrialisation
•++ break-throughs (simplex method in the fifties)
•++ computational power of PC’s
A model represents or describes perceptions of a real situation, simplified, using a formal,
theoretically based language of concepts and their relationships (that enables manipulation
of these entities), in order to facilitate management, control, understanding or some other
manipulation of that situation.
,The Nature of Operations Research
• Process
• Carefully observe and formulate the problem
• Gather data
• Construct a mathematical model
• Test whether the model represents the actual situation
• Modify the model as appropriate and validate again
• Broad viewpoint
• Considers what is best for organization as a whole
• Attempts to identify best possible course of action
• Team approach
• Consists of individuals with diverse backgrounds and skills
• Necessary for considering ramifications of problem throughout organization
,Chapter 2: Overview of the Operations Research Modeling Approach
OR/Analytics Cycle
Defining the Problem and Gathering Data (business situation)
• Elements of problem definition
• Identify the appropriate objectives
• Identify constraints
• Identify interrelationships with other areas of the organization
• Identify alternative courses of action
• Define the time constraints
• OR team typically works in an advisory capacity
• Management makes the final decisions
• Identify the decision maker
• Probe his/her thinking regarding objectives
• Objectives need to be specific
• Also aligned with organizational objectives
• Example of an objective in a for-profit organization
• Maximum profit in the long run
• Minimum environmental impact
• Minimum employee turnover
• More typical objective
• Satisfactory profit combined with other defined objective
• Gathering relevant data necessary for:
• Complete problem understanding
• Input into mathematical models
• Problem: too little data available
• Solution: build management information system to collect data
• Problem: too much data available
• Solution: data mining methods
, Formulating a Mathematical Model (mathematical problem)
• Models
• Idealized representations
• Examples: model airplanes, portraits, …
• Mathematical models
• Expressed in terms of mathematical symbols
• Example: Newton’s Law: F = ma
• Mathematical model of a business problem
• Expressed as system of equations
Ingredients of a Mathematical Model
Formulating a Mathematical Model
• Determining parameter values
• Often difficult
• Done by gathering data
• Typical expression of the problem
• Choose values of decision variables so as to maximize the objective function
Subject to the specified constraints
• Real problems often do not have a single “right” model
• What are the advantages of a mathematical model over a verbal description of the
problem?
• More concise
• Reveals important cause and effect relationships
• Clearly indicates what data is relevant
• Forms a bridge to use computers for analysis
• What are the disadvantages of mathematical models?
• Often must simplify assumptions to make problem solvable
• Judging a model’s validity
• Desire high correlation between model’s prediction and real-world outcome
• Testing (validation phase)
