Introduction to Operations Research ‐ IUT‐1397 lecture ...
Transcript of Introduction to Operations Research ‐ IUT‐1397 lecture ...
Introduction to Operations Research ‐lecture notes (Part 1)
IUT‐1397
© Dr. Ahmad Reza Pourghaderi 1
Ahmad Reza Pourghaderi (Ph.D.)
Assistant Professor of Industrial & Systems Engineering
http://pourghaderi.com/
Introduction to Operational Research
Definition of Operational Research
History of Operational Research
Features of Operational Research
Scope of Operational Research
Methodology/Approaches of Operational Research
Tools/Techniques of Operational Research
Operational Research and Management Decision-Making
Challenges in Operational Research
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Our world seems to ever become more complex and
uncertain. Future leaders must be able to act under these
conditions. Optimal decision making in many complex
systems facing big data and high uncertainty is surely
impossible without using computer based advanced
analytical methods.
Operations Research is 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.
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Saving
Lives.S
avingM
oney.S
olvingP
roblems
The In
stitute forOp
eration
s Research
and the
Man
agem
entS
ciences.
Introduction to Operations Research ‐lecture notes (Part 1)
IUT‐1397
© Dr. Ahmad Reza Pourghaderi 2
O.R. as termed in USA, Canada, Africa, Australia and Operational
Research as termed in Europe, is a Branch of applied mathematics
that uses techniques and statistics to arrive at Optimal solutions to
solve complex problems.
It is typically concerned with determining the maximum profit,
sale, output, crops yield and efficiency
And minimum losses, risks, cost, and time of some objective
function.
It have also become an important part of INDUSTRIAL
ENGINEERING PROFESSION.
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O.R. is the application of modern methods of mathematical
science to complex problems involving management of large
systems of men, machines, materials, and money in industry,
business, government and defense. The distinctive approach is to
develop a scientific model of the system incorporating
measurement of factors such as chance and risk, to predict and
compare the outcome of alternative decisions, strategies or
controls.
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O.R.
O.R. is a scientific approach to problem solving for management.
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Complete and more stories on:www.informs.org/Impact
Introduction to Operations Research ‐lecture notes (Part 1)
IUT‐1397
© Dr. Ahmad Reza Pourghaderi 3
T S P Visit a set of cities/locations and minimize total travel cost
1
4
2
53
Can you guess some of the applications?
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TSP Try to find the best/shortest route?
How many possibilities are there?
1 – 5 – 3 – 4 – 2 – 1 is the optimal route for the travelling salesman.
Duration of the route is 6500 meters.
Locations 1 2 3 4 5
1 0 600 1000 1900 1100
2 600 0 1900 1900 1500
3 1000 1900 0 1700 1200
4 1900 1900 1700 0 1900
5 1100 1500 1200 1900 0
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https://www-m9.ma.tum.de/games/tsp-game/index_en.htmlIsfahan University of Technology - Industrial & Systems Engineering Department Ahmad Reza Pourghaderi - pourghaderi.com
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Introduction to Operations Research ‐lecture notes (Part 1)
IUT‐1397
© Dr. Ahmad Reza Pourghaderi 4
V R P Visit a set of cities/locations and
minimize total travel cost
Assume given locations of N
points, a depot, a matrix of costs
to travel between locations, a
demand for each point, a vehicle
capacity
Can you optimally solve it?
Find an allocation of points to vehicles and a set of vehicle routes
ending and beginning at the depot that minimizes either vehicle
distance, number of vehicles, or a combination of the two
Assumes number of vehicles knownIsfahan University of Technology - Industrial & Systems Engineering Department Ahmad Reza Pourghaderi - pourghaderi.com
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There is no clear history that marks the Birth if O.R., it is generally
accepted that the field originated in England during the World War II.
Some say that Charles Babbage (1791-1871) is the Father of O.R
because his research into the cost of transportation and sorting of
mail led to England’s University Penny Post in 1840.
Modern Operations Research originated at the Bowdsey Research
Station in U.K. in 1937 to analyze and improve the working of the
UK’s Early Warning Radar System.
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Given a set of elements
1,2, … , 𝑛 (called the universe) and
a collection 𝑆 of 𝑚 sets
whose union equals the universe,
the set cover problem is to identify
the smallest sub-collection of 𝑆 whose union equals the universe.
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Introduction to Operations Research ‐lecture notes (Part 1)
IUT‐1397
© Dr. Ahmad Reza Pourghaderi 5
It is an Act of winning wars without actually fighting.
Aurther Clark
It is a Scientific Approach to problem solving for executive
management.
H.M. Wagner
It is Art of giving bad answers to problem which otherwise have
worse answers.
T.L. Saaty
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Decision-Making
Scientific Approach
Inter-Disciplinary Team Approach
System Approach
Use of Computers
Objectives
Human Factors
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Every industrial organization faces multifaceted problems to
identify best possible solution to their problems.
OR aims to help the executives to obtain optimal solution with the
use of OR techniques.
It also helps the decision maker to improve his creative and
judicious capabilities, analyze and understand the problem
situation leading to better control, better co-ordination, better
systems and finally better decisions.
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Introduction to Operations Research ‐lecture notes (Part 1)
IUT‐1397
© Dr. Ahmad Reza Pourghaderi 6
OR applies scientific methods, techniques and tools for the
purpose of analysis and solution of the complex problems.
In this approach there is no place for guesswork and the person
bias of the decision maker.
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Basically the industrial problems are of complex nature and
therefore require a team effort to handle it.
This team comprises of scientist, mathematician and
technocrats. Who jointly use the OR tools to obtain a optimal
solution of the problem. They tries to analyze the cause and
effect relationship between various parameters of the problem
and evaluates the outcome of various alternative strategies.
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The main aim of the system approach is to trace out all
significant and indirect effects for each proposal on all sub-
system on a system and to evaluate each action in terms of
effects for the system as a whole.
The inter-relationship and interaction of each sub-system can be
handled with the help of mathematical/analytical models of OR
to obtain acceptable solution.
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Introduction to Operations Research ‐lecture notes (Part 1)
IUT‐1397
© Dr. Ahmad Reza Pourghaderi 7
The models of OR need lot of computation and therefore, the use of
computers becomes necessary.
With the use of computers it is possible to handle complex problems
requiring large amount of calculations.
The objective of the operations research models is to attempt and to
locate Best or Optimal Solution.
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Operational Research always try to find the best and optimal
solution to the problem.
For this purpose objectives of the organization are defined and
analyzed. These objectives are then used as the basis to
compare the alternative courses of action.
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In deriving, Quantitative Solutions we do not consider human
factors, which doubtlessly play a great role in the problems.
So, study of O.R. is incomplete without study of human factors.
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Introduction to Operations Research ‐lecture notes (Part 1)
IUT‐1397
© Dr. Ahmad Reza Pourghaderi 8
The scope of OR is not only confined to any specific agency like defense
services but today it is widely used in all industrial organizations. It attempts to
resolve the conflicts of interest among the components of organization in a way
that is best for the organization as a whole. It can be used for solving different
types of problems, such as:
Finance, Budgeting and Investment:
Cash flow analysis, long range capital requirement, investment portfolios, dividend
policies, claim procedure, and credit policies.
Marketing:
Product selection, pricing, competitive actions, number of salesmen, frequencies of
calling on, and advertising strategies with respect to cost and time.
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Purchasing:
Buying policies, varying prices, Determination of quantities and timing of purchases,
Bidding policies, Replacement policies, and Exploitation of new material resources.
Production Management:
Physical distribution: Location and size of warehouses, distribution centers and retail
outlets, distribution policies.
Facilities Planning: Number and location of factories, warehouses etc. Loading and
unloading facilities.
Manufacturing: Production scheduling and sequencing stabilisation of production,
employment, layoffs, and optimum product mix.
Maintenance policies, crew size.
Project scheduling and allocation of resources.
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Personnel Management:
Mixes of age and skills, shift scheduling, Education planning, Recruiting policies, and Job
assignments.
Research and Development:
Areas of concentration for R&D, Reliability and alternate decisions, Determination of
time-cost trade off and control of development projects.
Healthcare Operations Management:
Operating room planning and scheduling, resource planning for equipment, rooms and
staff, medical Inventory management, planning and managing emergency services, Organ
donation and transplant, modeling spread of epidemics and planning response,
treatment method selection, financial planning and pricing in health care
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Introduction to Operations Research ‐lecture notes (Part 1)
IUT‐1397
© Dr. Ahmad Reza Pourghaderi 9
How to decide on the best locations of medical clinics and emergency vehiclesfor providing maximum Healthcare coverage to a given population?
How many base locations of medical ambulances are needed if the totaldistance from the locations to the hospitals must be less than a given number?
How should radiation treatment be planned for minimizing the treatment timeof a cancer patient?
How should the nurses in a trauma center be scheduled and re-rostered tomaintain an adequate service level even in the worst-case scenario?
Many problems like these need to be addressed in Healthcare, and OperationsResearch (OR) provides numerous methodologies and solution techniques fortackling them.
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HEALTHCARE
Data
Solution
Find a Solution
Tools
Situation
Formulate the Problem
Problem Statement
Test the Model and the Solution
Procedure
Establish a Procedure
Implement the Solution
Construct a Model
Model
Implement a Solution
Goal: solve a problem
• Model must be valid• Model must be tractable• Solution must be useful
OR
May involve current operations orproposed developments due toexpected market shifts
May become apparent throughconsumer complaints or throughemployee suggestions
May be a conscious effort toimprove efficiency or respond to anunexpected crisis
Example: Internal nursing staff not happy with their schedules; hospital using too many external nurses.
Data
Situation
Introduction to Operations Research ‐lecture notes (Part 1)
IUT‐1397
© Dr. Ahmad Reza Pourghaderi 10
Define variables
Define constraints
Identify data requirements
Example: Maximize individual nurse preferences subject to demand requirements, or minimize nurse dissatisfaction costs.
Formulate the Problem
Problem Statement
Data
Situation
Describe system
Define boundaries
State assumptions
Select performance measures
Problem must be translated fromverbal, qualitative terms tological, quantitative terms
A logical model is a series of rules,usually embodied in a computerprogram
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 offunctional relationships by which allowableactions are delimited and evaluated.
Many tools are available asdiscussed in this course
Some lead to “optimal” solutions
Others only evaluate candidates trial and error to find “best” courseof action
Example: Collect input data -- nurse profiles and demand requirements; apply algorithm; post-process results to get monthly schedules.
Model
Solution
Find asolution
Tools
Introduction to Operations Research ‐lecture notes (Part 1)
IUT‐1397
© Dr. Ahmad Reza Pourghaderi 11
A solution to a problem usually implieschanges for some individuals in theorganization
Often there is resistance to change, makingthe implementation difficult
A user-friendly system is needed
Those 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.
Inventory Control Models:
Operation Research study involves balancing inventory costs against one or more of the
following costs:
Shortage costs.
Ordering costs.
Storage costs.
Interest costs.
This study helps in taking decisions about:
? How much to purchase.
? When to order.
? Whether to manufacture or to purchase i.e., make and buy decisions.
The most well-known use is in the form of Economic Order Quantity (EOQ) equation for finding
economic lot size.
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Waiting Line Models:
It deals with the situations in which queue is formed, e.g. customers waiting for services,
machines waiting for repairmen, and aircrafts waiting for landing strips, etc. These models are
used for minimizing the waiting time and idle time together with the costs associated
therewith.
Waiting line models are of two types:
Queuing theory, which is applicable for determining the number of service facilities and/or
the timing of arrivals for servicing.
Sequencing theory which is applicable for determining the sequence of the servicing.
Replacement Models:
These models are used for determining the time of replacement or maintenance of item, which
may either:
Become obsolete, or
Become inefficient for use, and
Become beyond economical to repair or maintain
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Introduction to Operations Research ‐lecture notes (Part 1)
IUT‐1397
© Dr. Ahmad Reza Pourghaderi 12
Allocation/Assignment Models:
These models are used to solve the problems arising when:
There are number of activities which are to be performed and there are number of
alternative ways of doing them,
The resources or facilities are limited, which do not allow each activity to be performed
in best possible way. Thus these models help to combine activities and available
resources so as to optimize and get a solution to obtain an overall effectiveness.
Competitive Strategies:
Such type of strategies are adopted where, efficiency of decision of one agency is
dependent on the decision of another agency. Examples of such strategies are game of
cards or chess, fixing of prices in a competitive market where these strategies are termed
as “theory”.
Simulation Models: an experimental method used to study behavior over time.
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Network Models:
This is an approach to planning, scheduling and controlling complex projects.
Transportation Models:
Transportation problems deals with transportation of a product from a number of
sources with limited supplies to number of destinations with specified demands at
the total transportation cost.
The main objective of transportation is to Schedule Shipment from sources to
destinations in such a way so as to Minimize the Total Transportation Cost.
Decision & Game Theory:
Decision Theory is primarily considered with decision making under the conditions
of Risk and Uncertainty
Game Theory is concerned with: Decision Making under Conflicts of Interest
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Operation Research increases the creative capabilities of adecision maker.
It increases the effectiveness of managerial decisions.
Management is most of the time making decisions. It is thus adecision science which helps managers to take better decisions.
Nowadays, business problems have become so complex that it isalmost impossible for a human being to comprehend allimportant factors, OR Techniques can be helpful in suchsituations.
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Introduction to Operations Research ‐lecture notes (Part 1)
IUT‐1397
© Dr. Ahmad Reza Pourghaderi 13
Magnitude of Computation
Non-Quantifiable Factors
Distance between User and Analyst
Time and Money Costs
Implementation
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Operations research models try to find out optimal solution taking
into account all the factors.
These factors are usually enormous in real management problems.
Expressing them in quantity and establishing relationships among
these, Require voluminous calculations which can be handled only
by computers.
Sometime we need to use High Performance Computers (HPC)
Sometimes even using HPCs cannot provide satisfactory results.
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OR provides solution only when all elements related to a problem can
be quantified.
All relevant variables do not lend themselves to quantification.
Factors which cannot be quantified, find no place in OR study.
Some of qualitative factors such as emotional factors are very
difficult (some say impossible but I dot believe in them) to be
quantified.
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Introduction to Operations Research ‐lecture notes (Part 1)
IUT‐1397
© Dr. Ahmad Reza Pourghaderi 14
OR being specialist’s job requires a mathematician or statistician or
ideally an Industrial Engineer, who might not be aware of the business
problems.
Similarly, a manager fails to understand the complex working of OR.
Thus there is a gap between the two. Management itself may offer a lot
of resistance due to conventional thinking.
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When basic data are subjected to frequent changes, incorporating
them into the OR models is a costly proposition.
Moreover, a fairly good solution at present may be more desirable
than a perfect OR solution available after sometime. The
computational time increases depending upon the size of the
problem and accuracy of results desired.
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Implementation of any decision is a delicate task. It must take into
account the complexities of human relations and behaviors.
Sometimes, resistance is offered due to psychological factors
which may not have any bearing on the problem as well as its
solution.
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