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01
Introduction to Operations Research 1<br>
02
Takes in to account parameters including weight effect, fuel load, fuel flow time, pitstop crew time, pitlane time loss and tire degradation.<br>
03
Introduction Operations Research is an Art and Science
It had its early roots in World War II and is flourishing in business and industry with the aid of computer
Primary applications areas of Operations Research include ( but not limited to) forecasting, production scheduling, inventory control, capital budgeting, and transportation. 4<br>
It had its early roots in World War II and is flourishing in business and industry with the aid of computer
Primary applications areas of Operations Research include ( but not limited to) forecasting, production scheduling, inventory control, capital budgeting, and transportation. 4<br>
04
What is the application of OR in the airline industry?<br>
05
What is Operations Research? 6 Operations
The activities carried out in an organization.
Research
The process of observation and testing characterized by the scientific method. Situation, problem statement, model construction, validation, experimentation, candidate solutions.
Operations Research is a “quantitative approach” to decision making based on the scientific method of problem solving.<br>
The activities carried out in an organization.
Research
The process of observation and testing characterized by the scientific method. Situation, problem statement, model construction, validation, experimentation, candidate solutions.
Operations Research is a “quantitative approach” to decision making based on the scientific method of problem solving.<br>
06
What is Operations Research? Operations Research is the scientific approach to execute decision making, which consists of:
The art of mathematical modeling of complex situations.
The science of the development of solution techniques used to solve these models.
The ability to effectively communicate the results to the decision maker 7<br>
The art of mathematical modeling of complex situations.
The science of the development of solution techniques used to solve these models.
The ability to effectively communicate the results to the decision maker 7<br>
07
What Do OR professionals do 8 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.
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.<br>
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.<br>
08
Terminology The British/Europeans refer to “Operational Research", the Americans to “Operations Research" - but both are often shortened to just "OR".
Another term used for this field is “Management Science" ("MS"). In U.S. OR and MS are combined together to form "OR/MS" or "ORMS".
Yet other terms sometimes used are “Industrial Engineering" ("IE") and “Decision Science" ("DS"). 9<br>
Another term used for this field is “Management Science" ("MS"). In U.S. OR and MS are combined together to form "OR/MS" or "ORMS".
Yet other terms sometimes used are “Industrial Engineering" ("IE") and “Decision Science" ("DS"). 9<br>
09
Examples of OR Applications Rescheduling aircraft in response to groundings and delays
Planning production for products
Scheduling equipment operators in mail processing & distribution centers
Developing routes for product delivery
Adjusting nurse schedules in light of daily fluctuations in demand 10<br>
Planning production for products
Scheduling equipment operators in mail processing & distribution centers
Developing routes for product delivery
Adjusting nurse schedules in light of daily fluctuations in demand 10<br>
10
Operations Research Models<br>
11
Operations Research Models 12<br>
12
Operations Research Models Cont’d OR Models can be classified on the basis of following factors
1. By Degree of Abstraction
A mathematical model represent real world problems through a system of mathematical formulas and expressions based on key assumptions, estimates, or statistical analyses.
Language modeling is the use of various statistical and probabilistic techniques to determine the probability of a given sequence of words occurring in a sentence.
Examples:
Mathematical Models: Income – expenses = Profit (Profit and loss model), analysis of financial statemen, cost function.
Language model: voice assistants like Siri, Alexa, Google Homes, etc. ... Google Translator and Microsoft Translate<br>
1. By Degree of Abstraction
A mathematical model represent real world problems through a system of mathematical formulas and expressions based on key assumptions, estimates, or statistical analyses.
Language modeling is the use of various statistical and probabilistic techniques to determine the probability of a given sequence of words occurring in a sentence.
Examples:
Mathematical Models: Income – expenses = Profit (Profit and loss model), analysis of financial statemen, cost function.
Language model: voice assistants like Siri, Alexa, Google Homes, etc. ... Google Translator and Microsoft Translate<br>
13
Operations Research Models Cont’d OR Models can be classified on the basis of following factors
2. By Function
A descriptive model explains certain aspects of the problem or situation or a system so that the user can make use for his analysis.
A Predictive model based on the data collected, can predict the approximate results of the situation under question.
A normative model is one which asks what the answer to a routine problem should be
Examples:
Descriptive Models: a model suggesting most shoppers turn to the right when they enter a retail store. Retailers use this knowledge to place their high-priced items on the right side, where they’re more visible.
predictive model: Banks use historical information to predict whether or not a candidate is likely to keep up with payments.
Normative model: how managers try to find the best solution to severe issues such as the COVID-19 pandemic.<br>
2. By Function
A descriptive model explains certain aspects of the problem or situation or a system so that the user can make use for his analysis.
A Predictive model based on the data collected, can predict the approximate results of the situation under question.
A normative model is one which asks what the answer to a routine problem should be
Examples:
Descriptive Models: a model suggesting most shoppers turn to the right when they enter a retail store. Retailers use this knowledge to place their high-priced items on the right side, where they’re more visible.
predictive model: Banks use historical information to predict whether or not a candidate is likely to keep up with payments.
Normative model: how managers try to find the best solution to severe issues such as the COVID-19 pandemic.<br>
14
Operations Research Models Cont’d 3. By Structure
An Iconic or physical model is a smaller or larger physical replica of an object.
A graphical model are physical in form, but do not physically resemble the object being modeled. It expresses the conditional dependence structure between random variables. They are commonly used in probability theory, statistics
A mathematical model is a model built using the language, symbols and tools of mathematics.<br>
An Iconic or physical model is a smaller or larger physical replica of an object.
A graphical model are physical in form, but do not physically resemble the object being modeled. It expresses the conditional dependence structure between random variables. They are commonly used in probability theory, statistics
A mathematical model is a model built using the language, symbols and tools of mathematics.<br>
15
Operations Research Models Cont’d 3. By Nature of Environment
A Deterministic Model allows you to calculate a future event exactly, without the involvement of randomness. If something is deterministic, you have all of the data necessary to predict (determine) the outcome with certainty.
A probabilistic or Stochastic Model is the one having a random probability distribution or pattern that may be analyzed statistically but may not be predicted precisely.
Examples:
A Deterministic Model: timetables, pricing structures, the economic order quantity model, maps, accounting.
A probabilistic or Stochastic Model: how a portfolio may perform based on the probability distributions of individual stock returns.<br>
A Deterministic Model allows you to calculate a future event exactly, without the involvement of randomness. If something is deterministic, you have all of the data necessary to predict (determine) the outcome with certainty.
A probabilistic or Stochastic Model is the one having a random probability distribution or pattern that may be analyzed statistically but may not be predicted precisely.
Examples:
A Deterministic Model: timetables, pricing structures, the economic order quantity model, maps, accounting.
A probabilistic or Stochastic Model: how a portfolio may perform based on the probability distributions of individual stock returns.<br>
16
Operations Research Models Cont’d 3. By Time Horizon
A static model is one in which the decision variables do not involve sequences of decisions over multiple periods.
A dynamic model is a model in which the decision variables do involve sequences of decisions over multiple periods.<br>
A static model is one in which the decision variables do not involve sequences of decisions over multiple periods.
A dynamic model is a model in which the decision variables do involve sequences of decisions over multiple periods.<br>
17
History of Operations Research OR is a relatively new discipline.
90 years ago it would have been possible to study mathematics, physics or engineering at university it would not have been possible to study OR.
It was really only in the late 1930's that operationas research began in a systematic way. 18<br>
90 years ago it would have been possible to study mathematics, physics or engineering at university it would not have been possible to study OR.
It was really only in the late 1930's that operationas research began in a systematic way. 18<br>
18
19 1890
Frederick Taylor
Scientific Management
[Industrial Engineering] 1900
Henry Gannt
[Project Scheduling]
Andrey A. Markov
[Markov Processes]
Assignment
[Networks] 1910
F. W. Harris
[Inventory Theory]
E. K. Erlang
[Queuing Theory] 1920
William Shewart
[Control Charts]
H.Dodge – H.Roming
[Quality Theory] 1930
Jon Von Neuman – Oscar Morgenstern
[Game Theory] 1940
World War 2
George Dantzig
[Linear Programming]
First Computer 1950
H.Kuhn - A.Tucker
[Non-Linear Prog.]
Ralph Gomory
[Integer Prog.]
PERT/CPM
Richard Bellman
[Dynamic Prog.]
ORSA and TIMS 1960
John D.C. Litle
[Queuing Theory]
Simscript - GPSS
[Simulation] 1970
Microcomputer 1980
H. Karmarkar
[Linear Prog.]
Personal computer
OR/MS Softwares 1990
Spreadsheet Packages
INFORMS 2006-2023
You are here<br>
Frederick Taylor
Scientific Management
[Industrial Engineering] 1900
Henry Gannt
[Project Scheduling]
Andrey A. Markov
[Markov Processes]
Assignment
[Networks] 1910
F. W. Harris
[Inventory Theory]
E. K. Erlang
[Queuing Theory] 1920
William Shewart
[Control Charts]
H.Dodge – H.Roming
[Quality Theory] 1930
Jon Von Neuman – Oscar Morgenstern
[Game Theory] 1940
World War 2
George Dantzig
[Linear Programming]
First Computer 1950
H.Kuhn - A.Tucker
[Non-Linear Prog.]
Ralph Gomory
[Integer Prog.]
PERT/CPM
Richard Bellman
[Dynamic Prog.]
ORSA and TIMS 1960
John D.C. Litle
[Queuing Theory]
Simscript - GPSS
[Simulation] 1970
Microcomputer 1980
H. Karmarkar
[Linear Prog.]
Personal computer
OR/MS Softwares 1990
Spreadsheet Packages
INFORMS 2006-2023
You are here<br>
19
Operations research and problem solving & decision making<br>
20
Problem Solving and Decision Making 7 Steps of Problem Solving and decision making
(First 5 steps are the process of decision making)
Identify and define the problem.
Determine the set of alternative solutions.
Determine the criteria for evaluating the alternatives.
Evaluate the alternatives.
Choose an alternative.
---------------------------------------------------------------
Implement the chosen alternative.
Evaluate the results. 21<br>
(First 5 steps are the process of decision making)
Identify and define the problem.
Determine the set of alternative solutions.
Determine the criteria for evaluating the alternatives.
Evaluate the alternatives.
Choose an alternative.
---------------------------------------------------------------
Implement the chosen alternative.
Evaluate the results. 21<br>
21
Quantitative Analysis and Decision Making Potential Reasons for a Quantitative Analysis Approach to Decision Making
The problem is complex.
The problem is very important.
The problem is new.
The problem is repetitive. 22<br>
The problem is complex.
The problem is very important.
The problem is new.
The problem is repetitive. 22<br>
22
PHASES OF OR STUDY 23 Goal: solve a problem
Phases:
1. Definition of the problem.
2. Construction of the model.
3. Solution of the model.
4. Validation of the model.
5. Implementation of the solution.<br>
Phases:
1. Definition of the problem.
2. Construction of the model.
3. Solution of the model.
4. Validation of the model.
5. Implementation of the solution.<br>
23
The Situation 24 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.<br>
May become apparent through consumer complaints or through employee suggestions
May be a conscious effort to improve efficiency or response to an unexpected crisis.<br>
24
Problem Formulation 25 Study the relevant system and develop a well-defined statement of the problem.
Determine the appropriate objectives, variables, constraints, and their interrelationships.
Examples: maintaining stable price, profits, increasing the share in market, improving work morale etc
The OR team normally works in an advisory capacity.
The team performs a detailed technical analysis of the problem and then presents recommendations to the management.<br>
Determine the appropriate objectives, variables, constraints, and their interrelationships.
Examples: maintaining stable price, profits, increasing the share in market, improving work morale etc
The OR team normally works in an advisory capacity.
The team performs a detailed technical analysis of the problem and then presents recommendations to the management.<br>
25
Constructing a Model 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
A mathematical model is a collection of functional relationships by which allowable actions are delimited and evaluated. 26 1. Decision variables (x1, x2 ... xn) - 'n' refers to associated quantifiable decisions to be made.
2. Objective function - It is a measure of performance (profit) which is expressed as mathematical function of decision variables. For instance P=3x1 +5x2 + ... + 4xn
3. Constraints - any limitations on values that can be allocated to decision variables in terms of equations or inequalities. For instance x1 +2x2 ≥ 20<br>
A logical model is a series of rules, usually embodied in a computer program
A mathematical model is a collection of functional relationships by which allowable actions are delimited and evaluated. 26 1. Decision variables (x1, x2 ... xn) - 'n' refers to associated quantifiable decisions to be made.
2. Objective function - It is a measure of performance (profit) which is expressed as mathematical function of decision variables. For instance P=3x1 +5x2 + ... + 4xn
3. Constraints - any limitations on values that can be allocated to decision variables in terms of equations or inequalities. For instance x1 +2x2 ≥ 20<br>
26
Constructing a Model contd… The end product of OR model is a mathematical form associating the objective function, Decision variables with constraints.
The mathematical function is to optimize (maximize/ minimize) the magnitude of the objective function, at the same time fulfilling all the facility constraints.
Max P = p1(Xn) + p2(Yn)
St. (Subject to/such that)
x+ y ≤ 400
x ≥ 0 , y ≥ 0 27<br>
The mathematical function is to optimize (maximize/ minimize) the magnitude of the objective function, at the same time fulfilling all the facility constraints.
Max P = p1(Xn) + p2(Yn)
St. (Subject to/such that)
x+ y ≤ 400
x ≥ 0 , y ≥ 0 27<br>
27
Data Preparation Data preparation is complex step, due to the time required and the possibility of data collection errors.
A model with 50 decision variables and 25 constraints could have over 1250 data elements!
Often, a fairly large data base is needed.
Information systems specialists might be needed. 28<br>
A model with 50 decision variables and 25 constraints could have over 1250 data elements!
Often, a fairly large data base is needed.
Information systems specialists might be needed. 28<br>
28
Solving the Mathematical Model Many tools are available
Some lead to “optimal” solutions (deterministic Models)
Others only evaluate candidates trial and error to find “best” course of action
Sensitivity analysis 29<br>
Some lead to “optimal” solutions (deterministic Models)
Others only evaluate candidates trial and error to find “best” course of action
Sensitivity analysis 29<br>
29
Computer Software A variety of software packages are available for solving mathematical models, some are:
Spreadsheet packages such as Microsoft Excel
The Management Scientist (MS)
Quantitative system for business (QSB)
Quantitative models (QM)
Decision Science (DS) 30<br>
Spreadsheet packages such as Microsoft Excel
The Management Scientist (MS)
Quantitative system for business (QSB)
Quantitative models (QM)
Decision Science (DS) 30<br>
30
Model Testing and Validation Often, the goodness/accuracy of a model cannot be assessed until solutions are generated.
Small test problems having known, or at least expected, solutions can be used for model testing and validation.
If the model generates expected solutions:
use the model on the full-scale problem.
If inaccuracies or potential shortcomings inherent in the model are identified, take corrective action such as:
collection of more-accurate input data
modification of the model 31<br>
Small test problems having known, or at least expected, solutions can be used for model testing and validation.
If the model generates expected solutions:
use the model on the full-scale problem.
If inaccuracies or potential shortcomings inherent in the model are identified, take corrective action such as:
collection of more-accurate input data
modification of the model 31<br>
31
Implementation 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 needed
Those affected should go through training 32<br>
Often there is resistance to change, making the implementation difficult
User-friendly system needed
Those affected should go through training 32<br>
32
Implementation and Follow-Up Successful implementation of model results is of critical importance.
Secure as much user involvement as possible throughout the modeling process.
Continue to monitor the contribution of the model.
It might be necessary to refine or expand the model. 33<br>
Secure as much user involvement as possible throughout the modeling process.
Continue to monitor the contribution of the model.
It might be necessary to refine or expand the model. 33<br>
33
Report Generation A managerial report, based on the results of the model, should be prepared.
The report should be easily understood by the decision maker.
The report should include:
the recommended decision
other pertinent information about the results (for example, how sensitive the model solution is to the assumptions and data used in the model) 34<br>
The report should be easily understood by the decision maker.
The report should include:
the recommended decision
other pertinent information about the results (for example, how sensitive the model solution is to the assumptions and data used in the model) 34<br>
34
Components of OR-Based Decision Support System Data base
Graphical User Interface (GUI); web enabled using java or VBA
Algorithms,
What-if analysis
Report generators 35<br>
Graphical User Interface (GUI); web enabled using java or VBA
Algorithms,
What-if analysis
Report generators 35<br>
35
Example: Project Scheduling Consider a construction company building a 250-unit apartment complex. The project consists of hundreds of activities involving excavating, framing, wiring, plastering, painting, landscaping, and more. Some of the activities must be done sequentially and others can be done simultaneously. Also, some of the activities can be completed faster than normal by purchasing additional resources (workers, equipment, etc.).
In what ways OR can be used in construction industry?
project planning, Cost saving, EOQ, Labor scheduling, Activity scheduling, optimize construction timelines, resource allocation (delivery schedules), project management, manpower, risk analysis etc. 36<br>
In what ways OR can be used in construction industry?
project planning, Cost saving, EOQ, Labor scheduling, Activity scheduling, optimize construction timelines, resource allocation (delivery schedules), project management, manpower, risk analysis etc. 36<br>
36
Example: Project Scheduling What is the best schedule for the activities and for which activities should additional resources be purchased?
Question:
How could OR be used to solve this problem?
Answer:
OR can provide a structured, quantitative approach for determining the minimum project completion time based on the activities' normal times and then based on the activities' expedited (reduced) times by optimally scheduling the activities and resources of the project 37<br>
Question:
How could OR be used to solve this problem?
Answer:
OR can provide a structured, quantitative approach for determining the minimum project completion time based on the activities' normal times and then based on the activities' expedited (reduced) times by optimally scheduling the activities and resources of the project 37<br>
37
Example: Project Scheduling Question:
What would be the objective function? decision variables? of the mathematical model? The constraints?
Answer:
Objective function: minimize project completion time
Decision variables: planning activities based on sequencing and simultaneous timelines. identifying activities required to expedite and by how much, and when to start and finish each activity.
Constraints: do not violate any activity precedence relationships and do not expedite in excess of the funds available. 38<br>
What would be the objective function? decision variables? of the mathematical model? The constraints?
Answer:
Objective function: minimize project completion time
Decision variables: planning activities based on sequencing and simultaneous timelines. identifying activities required to expedite and by how much, and when to start and finish each activity.
Constraints: do not violate any activity precedence relationships and do not expedite in excess of the funds available. 38<br>
38
Example: Project Scheduling Question:
What would be the uncontrollable inputs?
Answer:
Expedited activity completion times of different activities
Activity expediting costs
Funds available for expediting
Precedence relationships of the activities 39<br>
What would be the uncontrollable inputs?
Answer:
Expedited activity completion times of different activities
Activity expediting costs
Funds available for expediting
Precedence relationships of the activities 39<br>
39
Example: Project Scheduling Question:
Is the model deterministic or stochastic?
Answer:
Stochastic. Activity completion times, both normal and expedited, are uncertain and subject to variation. Activity expediting costs are uncertain. The number of activities and their precedence relationships might change before the project is completed due to a project design change. 40<br>
Is the model deterministic or stochastic?
Answer:
Stochastic. Activity completion times, both normal and expedited, are uncertain and subject to variation. Activity expediting costs are uncertain. The number of activities and their precedence relationships might change before the project is completed due to a project design change. 40<br>
40
Example 2 Consider a department store that must make weekly shipments of a certain product from two different warehouses to four different stores.
a) How could a quantitative approach to decision making be used to solve this problem?
b) What would be the uncontrollable inputs for which data must be gathered?
c) What would be the decision variables of the mathematical model? the objective function? the constraints?
d) Is the model deterministic or stochastic?
e) Suggest assumptions that could be made to simplify the model.<br>
a) How could a quantitative approach to decision making be used to solve this problem?
b) What would be the uncontrollable inputs for which data must be gathered?
c) What would be the decision variables of the mathematical model? the objective function? the constraints?
d) Is the model deterministic or stochastic?
e) Suggest assumptions that could be made to simplify the model.<br>
41
Application Areas Strategic planning
Supply chain management
Pricing and revenue management
Logistics and site location
Marketing research 42 Scheduling
Portfolio management
Inventory analysis
Forecasting
Sales analysis
Auctioning
Risk analysis<br>
Supply chain management
Pricing and revenue management
Logistics and site location
Marketing research 42 Scheduling
Portfolio management
Inventory analysis
Forecasting
Sales analysis
Auctioning
Risk analysis<br>
42
Limitations of OR High Degree of Calculation
All the models require high degree of computations. We seek the help of systems which require heavy investments. Hence the application of this kind is used in large concerns only.
Quantitative Nature
All kinds of problems require variables of quantitative nature. Some times, in reality it is not possible to quantify certain things. Factors which cannot be quantified find no place in OR study.
Distance between User and Analyst.
There is a big gap between the person who is going to make use of the solution and one who actually arrives at such a solution.
Time and Money Costs.
When basic data are subjected to frequent changes, incorporating them into the OR models is a costly proposition.
Implementation
Implementation of any decision is a delicate task. It must take into account the complexities of human relations and behaviour<br>
All the models require high degree of computations. We seek the help of systems which require heavy investments. Hence the application of this kind is used in large concerns only.
Quantitative Nature
All kinds of problems require variables of quantitative nature. Some times, in reality it is not possible to quantify certain things. Factors which cannot be quantified find no place in OR study.
Distance between User and Analyst.
There is a big gap between the person who is going to make use of the solution and one who actually arrives at such a solution.
Time and Money Costs.
When basic data are subjected to frequent changes, incorporating them into the OR models is a costly proposition.
Implementation
Implementation of any decision is a delicate task. It must take into account the complexities of human relations and behaviour<br>
43
What you Should Know about Operations Research OR definition
OR terminology
How decision-making problems are characterized
OR Models
What a model is and how to assess its value
How to go from a conceptual problem to a quantitative solution
Limitations of OR 44<br>
OR terminology
How decision-making problems are characterized
OR Models
What a model is and how to assess its value
How to go from a conceptual problem to a quantitative solution
Limitations of OR 44<br>