introduction of OR

1. OPERATION
RESEARCH
S.Muthuganesh M.Sc.,B.Ed
Assistant Professor
Department of Computer Science
Vivekananda College
Tiruvedakam West
ganesh01muthu@gmail.com

2. • Discrete mathematics, linear algebra, number theory, and graph
theory are the math courses most relevant to the computer science
profession. Different corners of the profession, from machine learning
to software engineering, use these types of mathematics. Without
these math classes, you may struggle to manage data structures,
databases, and algorithms.

3. OPERATION RESEARCH
•Operations- The activities carried out in an
organization related to attain its goals and
objectives.
•Research- Any form of systematic and
organized investigation to establish facts.

4. Decision making is a key part of our daily
life.
•Decision making is a key part of our daily life.
I need a AC Should I buy it now?
Is it affordable now?
Which company should I go for?
•Final decision should be to maximise benefits and minimise
effort and time

5. Who is software Engineer?
• A software engineer is a person who applies the principles of
software engineering to the design, development, maintenance,
testing, and evaluation of computer software.

7. Requirement gathering and analysis
• Business requirements are gathered in this stage. This stage is the main focus of
the project managers and client.
• Meetings with managers, clients and users are held in order to determine the
requirements like;
• Who is going to use the system?
• What data should be input into the system?
• What data should be output by the system?
• These are general questions that get answered during a requirements gathering ..

8. Design
• In this stage the system and software design is prepared from the requirement
specifications which were studied in the first stage.
• System Design helps in specifying hardware and system requirements and also
helps in defining overall system architecture.
• The system design specifications serve as input for the next phase of the model

9. Implementation / Coding
• On receiving system design documents, the work is divided in
modules/units and actual coding is started.
• in this stage the code is produced so it is the main focus for the
developer.
• This is the longest phase of the software development life cycle.

10. Testing
• After the code is developed it is tested against the requirements to
make sure that the product is actually solving the needs addressed
and gathered during the requirements phase.

11. Deployment
• After successful testing the product is delivered / deployed to the
customer for their use.

12. Steps of involving Operation
Research

13. WHY NEED FOR CS

14.  Define the problem and gather
the data
 Formulate a mathematical model
to represent the problem
 Derive a solutions from the
model
 Validate the model

15. Define the problem
How to define the problem?
•Study the relevant system (business, industry etc) and
develop a well defined statement of problem to be
considered.
•It helps to determine objectives (Ex: Minimize cost of
operation, maximize the profit of company, maintain high
level of safety) , constraints (limited resources),
interrelationship, possible alternatives, time limits for
making decision and so on.

16. Example
• How many bowls and mugs should be produced to maximize profits given labour
and materials constraints .Product resource requirements and unit profit:
Total labour hours available is 40 hours and total clay is 120 lb

17. Model
• Models are representations of real objects or situations and can be
presented in various forms. The purpose of any model is that it
enables us to make inferences about the real situation by studying
and analysing the model .
• Maximize Z = 40x1 + 50x2 subject to:
1x1 + 2x2 ≤40
4x1 + 3x2 ≤ 120
x1, x2 ≥ 0

18. Derive a solution from the model
• Numerous algorithms are available to solve the problem (ex: simplex
algorithm, Graphical method)
• A common theme in OR is search for an optimal or best solution .

19. Install and Maintain the Solution
• Once we get the optimal values of x and y and objective function
instructions are given to the concerned personal to manufacture the
products as per the optimal solution, and maintain the same until
further instructions.

20. DEFINITIONS
OPERATIONAL RESEARCH IS THE SCIENTIFIC
STUDY OF OPERATIONS TO MAKE BETTER
DECISIONS.
IN SIMPLE TERMS OR IS
DESCRIBED AS “THE SCIENCE OF
BETTER”.

21. HISTORY
•During 2nd World War how to use the limited
military resources effectively to win the battle by
UK?
•They studied strategic and tactical problems
associated with air and land defence of the country,
and won the war
•This technique was named OR (British Air Ministry
official named A. P. Rowe

22. Operation Research in India
• In India, Operational Research or Operation Research came into existence in
1949 with the opening of an Operational Research Unit at the Regional Research
Laboratory at Hyderabad.
• In 1953, an Operational Research Unit was established in the Indian Statistical
Institute, Calcutta for the application of Operational Research methods in
national planning & survey .
• Operational Research Society of India was formed in 1957.
• It became a member of the International Federation of Operational Research
Societies in 1959

23. OBJECTIVE OF OR
•Develop new knowledge about the program & its
utilization
•Identify & solve program problems in a timely
manner
•Help policy-makers & program managers to make
decision with evidence based answers
•Improve efficiency & effectiveness of program
using scientifically valid methods

24. Definition
• “Operational Research is the application of scientific methods, techniques and
tools to problems involving the Operations of a system so as to provide those in
control of the system with optimum solutions to the problem”.
- C.W.Churchman, R.L.Ackoff & E.L.Arnoff
• “Operational Research is the art of giving bad answers to problems which
otherwise have worse answers”.
- T.L.Saaty

26. Models in Operational Research
•A model in Operational Research is a simplified
representation of an operation or a process in which
only the basic aspects or the most important features
of a typical problem under investigation are
considered.

27. Characteristics of model
• Assumptions should be simple and few.
•Variables should be as less as possible.
•It should be able to adopt the system environmental changes
without change in its framework.
•It should be easy to construct

28. Physical Models
• These models provide a physical appearance of the real object under
study either reduced in size or scaled up physical models are useful
only in design problems because they are easy to observe, build and
describe.
Example:
Model airplane, Model car, Model railway.

29. Iconic models
• Iconic model retain some of the physical properties
and characteristics of the system they represent.
• An Iconic Model is a look-alike representation of some
specific entity
Example
a house

30. Analogue models
• The models represent a system by the set of properties different from that of the
original system and does not resemble physically.

31. Symbolic Models
These models use letters, numbers and other symbols to
represent the properties of the system.Verbal Models : These models
describes a situation in written or spoken language.
eg:- Written Sentences, books etc.,
• Mathematical Models: These models involve the use of mathematical
Symbols, letters, numbers and mathematical operators (+, -, ÷, ×) to
represent relationship among various variables of the systems to
describe its properties or behaviour

32. Descriptive Models
• These models simply describe some aspects of a situation, based on
observation, survey, questionnaire results or other available data of a
situation and do not predict or recommend.
Eg:- Plant layout diagram

33. Predictive Models
• These models are used to predict the outcomes due to a given set of
alternatives for problem. These models do not have an objective
function as a part of the model to evaluate decision alternatives

34. Static Models
• Static models present a system at some specified time and do not
account for changes over time.

35. Dynamic Models
• In a dynamic model, time is considered as one of the variables
and admit the impact of changes generated by time in the selection
of the optimal courses of action.

36. Deterministic Models
• If all the parameters, constants and functional relationships are
assumed to be known with certainty when the decision is made, then
the model is said to be deterministic

37. Probabilistic (Stochastic Models)
• Models in which atleast one parameter or decision variable is a random variable
are called probabilistic (or Stochastic) models.
• Since atleast one decision variable is random, therefore, an independent
variable which is the function of dependent variable(s) will also be random.
• This means consequences or payoff due to certain changes in the independent
variable cannot be predicted with certainty.
• However, it is possible to predict a pattern of values of both the variable by
their probability distribution.
• Eg:- Insurance against risk of fire, accidents, sickness etc.

38. Analytical Models
• These models have a specific mathematical structure and thus can be
solved by known analytical or mathematical techniques. Any
optimization model ( which requires maximization or minimization of
an objective function) is an analytical model

39. Simulation Models
• These models also have a mathematical structure but are not solved
by applying mathematical structure but are not solved by applying
mathematical techniques to get a solution.
• Instead, a simulation model is essentially a computer assisted
experimentation on a mathematical structure of a real-life problem in
order to describe and evaluate its behaviour under certain
assumptions over a period of time.

40. Applications of OR
• Everyone in the world is required to make decisions at every step of
his/her life. Though we may not be particularly conscious of it, we
make decisions every day and every hour of our active life.
• Example Food making process

41. Finance, Budgeting and Investment:
• i. Cash flow analysis, long range capital requirement, investment
portfolios, dividend policies,
• ii. Claim procedure, and
• iii. Credit policies.
• The pricing and selling of industrial products are considered in
sections on decision theory.

42. Marketing
• i. Product selection, competitive actions,
• ii. Number of salesmen, frequencies of calling on, and
• iii. Advertising strategies with respect to cost and time.
Producers
Assessing the product potential of products
Substitutes available
Market structure
Market share
Determine best mix of the products for a plant with available resources, so as to
get maximum profit or minimum cost of production.
Consumers
• Awareness to various innovative products
• Assessing market scenario

43. Purchasing
• i. Buying policies, varying prices,
• ii. Determination of quantities and timing of purchases,
• iii. Bidding policies,
• iv. Replacement policies, and
• v. Exploitation of new material resources
• Optimal buying decisions and reordering with or without price quantity discount
and transportation planning.

44. Army
• The modern field of operations research (OR) arose during World War II in an
effort to enhance the effectiveness of weapons and equipment used in the
battlefield.
• Since then, OR techniques have been used to solve many sophisticated and
complex defense-related problems not only limited to combat operations but
also encompassing logistics, manpower planning, equipment procurement,
training, infrastructure defense, and many other areas.

45. Production Management
i. Physical distribution: Location and size of warehouses, distribution centres and
retail outlets, distribution policies.
ii. Facilities Planning: Number and location of factories, warehouses etc. Loading
and unloading facilities.
iii. Manufacturing: Production scheduling and sequencing stabilisation of produc-
tion, employment, layoffs, and optimum product mix.
iv. Maintenance policies, crew size.
v. Project scheduling and allocation of resources

46. Research and Development
i. Areas of concentration for R&D.
ii. Reliability and alternate decisions.
iii. Determination of time-cost trade off and control of development
projects.

47. Agriculture
• Where to start farming?
• What should be the size of the farm?
• What type of farming should he have, viz. grain farming, hog farming, dairy
farming, beef cattle, or some other type?
• what resources should he acquire and in what quantities? Whether should he
have one tractor or two, small, medium or large in size.
• Some of these decisions are taken after a good deal of time devoted to thinking;
whereas others have to be spontaneous .
• We can also apply this technique to maximise cultivator’s profit, involving
cultivation of number of items with different returns and cropping time in
different type of lands having variable fertility

48. General methods for OR

49. Analytical or Deductive Methods
• In these methods classical optimization techniques such as Calculus,
Finite Differences, etc., are used for solving an O.R. model. The kind
of mathematics required depends upon the nature Of the model. For
the area indicated by the mathematical function may be evaluated
through the use of Integral Calculus.

50. Numerical Methods
• Numerical methods are concerned with the iterative or trial and error
procedures, through the use of numerical computation at each step.
• These numerical methods are used when some analytical methods
fail to derive the solution.
• The algorithm is started optimality/ with a trial The (initial) trial
solution is and then continued replaced by with the a improved set of
rules for improving the process it.

51. Monte Carlo Methods
• These involve the use of probability and sampling concepts. The various steps are
associated with a Monte Carlo method are as follows .
a) For appropriate model of the system, make sample observations and determine the
probability distribution for the variables of interest.
b) Convert the probability distribution to cumulative distribution.
c) Select the sequence of random numbers with the help of random tables.
d) Determine the sequence of values of variables of interest with the sequence of
random numbers obtained in the above step.
e) Fit an appropriate standard mathematical function to the values obtained in step
The Monte Carlo method is essentially a simulation technique in which statistical
distribution functions are created by generating a series of random numbers.

52. SCIENTIFIC METHOD IN O.R.

53. SCIENTIFIC METHOD IN O.R.
• The scientific method in Operations Research consists of the following three
phases .
Judgement Phase, This phase includes
• (i) identification of the real-life problem,
• (ii) selection of an appropriate goal and the values of various variables related to
the goals,
• (iii) appropriate scale of measurement, and
• (iv) formulation of an appropriate model of the problem, abstracting the essential
information so that a solution at the decision-maker's goal can be sought.

54. Research Phase
• This phase is the largest and longest among the other two. However, the
remaining two are also equally important as they provide the basis for a scientific
method. This phase utilizes : (i) observations and data collection for a better
understanding of what the problem is,
• (ii) formulation of hypothesis and models,
• (iii) observation and experimentation to test the hypothesis on the basis of
additional data,
• (iv) analysis of the available information and verification of the hypothesis using
pre-established measures of effectiveness.
• (v) Predictions of various results from the hypothesis, and
• (vi) generalization of the results and consideration of alternative methods.

55. Action Phase
• This phase consists of making recommendations for decision process
by those who first posed the problem for consideration, or by anyone
in a position to make a decision influencing the operation in which
the problem occurred.

56. Transportation Problem (TP)

57. Introduction
• The transportation problem is a special type of linear programming problem
where the objective is to minimise the cost of distributing a product from a
number of sources or origins to a number of destinations.
• The origin of a transportation problem is the location from which shipments are
despatched. (e.g. factory, manufacturing facility)
• The destination of a transportation problem is the location to which shipments
are transported. (e.g. warehouse, store)
• The unit transportation cost is the cost of transporting one unit of the
consignment from an origin to a destination.

58. Structure of TP
Basic Notation:
m = number of sources (i = 1 … m)
n = number of destinations (j = 1 … n)
c i,j = unit cost of shipping from source i to destination j
x i,j = amount shipped from source i to destination j
a i = supply at source i
b j = demand at destination j

59. Basic structure of transportation problem:
In the above table D1, D2, D3 and D4 are the destinations where the products/goods are to be
delivered from different sources S1, S2, S3 and S4. Si is the supply from the source Oi. dj is the
demand of the destination Dj. Cij is the cost when the product is delivered from source Si to
destination Dj.

60. The solution of a transportation problem involves the
following major steps
• Step l. Formulate the given problem as a linear programming problem.
• Step 2. Set up the given L.P.P. in the tabular form known as a transportation table.
• Step 3, Find an initial basic feasible solution that must satisfy all the supply and
demand conditions
• Step 4. Examine the solution obtained in step 3 for optimality, i.e., examine
whether an improved transportation schedule with lower cost is possible.
• Step 5. If the solution is not optimum, modify the shipping schedule by including
that unoccupied cell whose inclusion may result in an improved solution.
Step 6. Repeat step 3 until no further improvement is possible.

61. FINDING AN INITIAL BASIC FEASIBLE SOLUTION
There are several methods available to obtain an initial basic
feasible solution. However, we shall discuss here the following three
1.North-West Corner Method,
2.Least-Cost Method, and
3.Vogel'sApproximation Method

62. North-West Corner Rule (NWCR)
• It is a simple and efficient method to obtain an initial basic feasible solution. Various
steps of the method are
Step l. Select the north-west (upper left hand) corner cell of the transportation table and
allocate as much as possible so that either the capacity of the first row is exhausted or
the destination requirement of the first column is satisfied, i.e., = min. (al, b1).
Step 2. If bl > al, we-move down vertically to the second row and make the second
allocation of magnitude X21 = min. ((a2, bl —x1 1) in the cell (2, l).
If b1 < a1, we move right horizontally to the second column and make the second
allocation of magnitude X12= min. (a1 —x11, b2) in the cell (l, 2).
If b1 =a1, there is a tie for the second allocation. One can make the second allocation of
magnitude.
X12 = min. (a1 —a1, b1) = 0 in the cell (l, 2).
or X21 = min. (a2,b1 —b1) = 0 in the cell (2, l).
Step 3. Repeat steps I and 2 moving down towards the lower right corner of the
transportation table until all the rim requirements are satisfied.

63. Assignment problem
• An assignment problem is a particular case of transportation problem
where the objective is to assign a number of resources to an equal
number of activities so as to minimise total cost or maximize total
profit of allocation.

64. Structure of AP

65. Mathematical formulation of AP