IOC-II
Introduction to Operation
Research
Class: B.TECH
SUBJECT TEACHER: MS. RUTUJA K. SHIVDAS
TOPIC: UNIT: 1
What you think of about operation research????
What are the areas of applications??
INTRODUCTION
❑OR is an applied mathematics subject and it is offered in many management and engineering
programs in university due to its diverse application areas.
❑Numerous synonyms for operations research are in common use. The British like operational
research and the Americans like management science, but a preferable term to describe this
subject is decision analysis.
It involves applying scientific principles to solve problems and optimize processes within
organizations.
It involves the following:
Problem Definition: Clearly identifying the problem to be solved.
Model Formulation: developing a mathematical model that represents the problem.
Model Solution: Employing algorithms to solve the model and obtain optimal solutions.
Implementation: translating the solutions into practical actions.
Definitions of Operations Research
● O.R. is the art of winning wars without actually fighting. - Aurther Clarke
● It is concerned with scientifically deciding how to best design and operate man-machine systems usually under
conditions requiring the allocation of scarce resources. -O.R. Society of America
● O.R. is the art of giving bad answers to problems which otherwise have worse answers. -T.L. Saaty
● O.R. is applied decision theory. It uses any scientific, mathematical or logical means to attempt to cope with
the problems that confront the executive, when he tries to achieve a thorough-going rationality in dealing with
his decision problems. -D.W. Miller and M.K. Starr
● Operational research is a scientific approach to problems solving for executive management. -H.M. Wagner
● O.R. 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 solution to the problem. -Churchman,
Ackoff and Arnoff
● O.R. is the study of administrative system pursued in the same scientific manner in which systems in Physics,
Chemistry and Biology are studied in natural sciences.
History of OR
❑ Based on the history of Operations Research, it is believed that Charles Babbage (1791-1871) is the
father of Operational Research due to the fact that his research into the cost of transportation and
sorting of mail resulted in England’s universal Penny Post in 1840.
❑ The name operations research evolved in the year 1940. During World War 2, a team of scientist
(Blackett’s Circus) in UK applied scientific techniques to research military operations to win the war
and the techniques thus developed was named as operation research.
❑ As a formal discipline, operations research originated from the efforts of army advisors at the time of
World War II. In the years following the war, the methods started to be employed extensively to
problems in business, industry and society. Ever since then, OR has developed into a subject
frequently employed in industries including petrochemicals, logistics, airlines, finance, government,
etc.
History of Operation Research
❑After World World War II (The Catalyst):
• During WWII, the British military formed teams of scientists to analyze and optimize military
operations, such as radar usage, and anti-submarine warfare.
❑Post-World War II Expansion:
• Following the war, the success of OR in military contexts led to its adoption in other sectors.
• Consultants and academics recognized parallels between military and business problems and
began applying OR techniques to optimize business operations, logistics, and resource
allocation.
• The development of computers further facilitated the application of OR techniques, allowing for
the analysis of larger and more complex datasets.
• OR expanded into various fields, including healthcare, transportation, finance, and government.
OR in India
❑ India was among the few nations which began utilizing O.R. In 1949, the first Operational Research
unit was established at Hyderabad which was named Regional Research Laboratory located. At the
same time an additional unit was launched in Defense Science Laboratory to fix the Stores, Purchase
and Planning Problems.
❑ In 1953 at Calcutta, an O.R. unit was established in Indian Statistical Institute. The objective was to
use O.R. techniques in National Planning and Survey. In 1955, Operations Research Society of
India was created, which is among the first members of International Federation of Operations
Research societies. Today, the utilization of O.R. techniques have spread out from army to a wide
range of departments at all levels.
Optimization
❑ It is the process of finding the best possible solution
to a problem given a set of constraints or
limitations.
❑ e optimization models are mathematical models
designed to help the managers make better
decisions.
❑ An optimization model has three main components:
An objective function. This is the function that
needs to be optimized. A collection of decision
variables. The solution to the optimization problem
is the set of values of the decision variables for
which the objective function reaches its optimal
value. A collection of constraints that restrict the
values of the decision variables.
Optimization
Optimization
❑ Constraints limit the possible values for the decision variables in an optimization model. There are
several types of constraints. The classes that implement them all inherit from the constraint class.
❑ The Lower Bound and Upper Bound properties specify lower and upper bounds for the value of the
constraint. After the solution of the model has been computed, the Value property returns the value of
the constraint in the optimal solution.
❑ In the simplest case, an optimization problem consists of maximizing or minimizing a real function
by systematically choosing input values from within an allowed set and computing the value of the
function. The generalization of optimization theory and techniques to other formulations comprises a
large area of applied mathematics.
Optimization (Examples of Constraints in Operations
Research)
Examples of Constraints in Operations Research:
1. Production Planning:
● A company has limited raw materials (e.g., wood, steel) or machine time.
● Constraint: The amount of raw materials used cannot exceed the available supply, and the machine time used cannot
exceed the total available machine hours.
● Example: A furniture company has 100 units of wood and 50 hours of machine time available. They want to
determine how many chairs and tables to produce to maximize profit. Constraints would be:
● Wood Used <= 100 units
● Machine Time Used <= 50 hours
2. Diet Planning:
● A person needs to consume a certain amount of calories, protein, vitamins, etc.
● Constraint: The daily intake of each nutrient must meet the minimum recommended level.
● Example: A person needs at least 2000 calories and 50 grams of protein per day. Constraints would be:
● Total Calories >= 2000
● Total Protein >= 50 grams
Examples of Constraints in Operations
Research:
Solve
3. Transportation:
● A trucking company has limited truck capacity and must deliver goods to multiple locations.
● Constraint: The total weight and volume of goods transported in each truck cannot exceed its capacity.
● Example: A trucking company has a truck with a capacity of 10 tons and 50 cubic meters. They need to transport
goods to three different locations. Constraints would be:
4. Resource Allocation:
● A project manager has a limited budget and a deadline to complete tasks.
● Constraint: The total cost of the project cannot exceed the budget, and the project must be completed by the
deadline.
● Example: A construction company has a budget of $1 million and 1 year to complete a building. The project
has multiple tasks. Constraints would be:
Solution
Transportation:
● A trucking company has limited truck capacity and must deliver goods to multiple locations.
● Constraint: The total weight and volume of goods transported in each truck cannot exceed its capacity.
● Example: A trucking company has a truck with a capacity of 10 tons and 50 cubic meters. They need to transport goods to three
different locations. Constraints would be:
● Total weight of goods <= 10 tons
● Total volume of goods <= 50 cubic meters
Resource Allocation:
● A project manager has a limited budget and a deadline to complete tasks.
● Constraint: The total cost of the project cannot exceed the budget, and the project must be completed by the deadline.
● Example: A construction company has a budget of $1 million and 1 year to complete a building. The project has multiple tasks.
Constraints would be:
● Total Project Cost <= $1,000,000
● Project Duration <= 1 year
Objectives of OR
❑ Operations research in an organisation is responsible for managing and operating as efficiently
as possible within the given resources and constraints
❑ OR is basically a problem-solving and decision-making tool used by organisations for
enhancing their productivity and performance. Apart from this, certain other objectives of OR
are as follows:
❑ Solving operational questions
❑ Solving queries related to resources’ operations such as human resource scheduling, machine
and material scheduling, utilisation of funds, etc
❑ Making informed decisions
❑ Improving the current systems
❑ Predicting all possible alternative outcomes
❑ Evaluating risks associated with each alternative
Limitations of Operations Research
Dependence on an Electronic Computer: O.R. techniques try to find out an optimal solution taking into
account all the factors. In the modern society, these factors are enormous and expressing them in quantity and
establishing relationships among these require voluminous calculations that can only be handled by
computers.
Non-Quantifiable Factors: provide a solution only when all the elements related to a problem can be
quantified. All relevant variables do not lend themselves to quantification. Factors that cannot be quantified
find no place in O.R. models.
Distance between Manager and Operations Researcher: O.R. being specialist's job requires a
mathematician or a statistician, who might not be aware of the business problems. Similarly, a manager fails
to understand the complex working of O.R. Thus, there is a gap between the two.
Money and Time Costs: When the basic data are subjected to frequent changes, incorporating them into the
O.R. models is a costly affair. Moreover, a fairly good solution at present may be more desirable than a
perfect O.R. solution available after sometime.
Implementation: Implementation of decisions is a delicate task. It must take into account the complexities of
human relations and behaviour.
Advantages of Operation Research
❑ Improved Decision-Making: OR provides quantitative insights that support informed decision-
making.
❑ Increased Efficiency: By optimising resource allocation and processes, OR can lead to
significant efficiency gains.
❑ Cost Reduction: OR can help identify cost-saving opportunities and reduce waste.
❑ Enhanced Performance: OR can improve the overall performance of organisations by
optimising key metrics.
❑ Risk Management: OR can be used to assess risks and develop strategies for mitigating them.
Applications of Operation Research
❑ Inventory Management: Optimising inventory levels to balance demand with supply, minimising costs, and avoiding
stockouts.
❑ Transportation and Logistics: Planning efficient routes, scheduling vehicles, and optimising supply chains to reduce
transportation costs and improve delivery times.
❑ Production Planning: Determining optimal production schedules, resource allocation, and capacity planning to
maximise output and minimise costs.
❑ Project Management: Developing project schedules, allocating resources, and managing risks to ensure timely
completion and within budget.
❑ Financial Modeling: analysing financial data, forecasting future trends, and making informed investment decisions.
❑ Healthcare: optimising patient scheduling, resource allocation, and treatment planning to improve patient care and
reduce costs.
❑ Network Design: Designing communication networks, transportation networks, and distribution networks to minimise
costs and maximise efficiency.
❑ Resource Allocation: Allocating limited resources to competing demands in a way that maximizes overall utility or
objective function.
Techniques of Operations Research
Linear Programming. Linear Programming (LP) is a mathematical technique of assigning a fixed amount of resources to
satisfy a number of demands in such a way that some objective is optimized and other defined conditions are also satisfied.
. In Linear programming the objective function (profit, loss or return on investment) and constraints are linear.
Example: Furniture Production
A furniture company makes two types of products: tables and chairs.
● Resources: They have limited wood and labor time.
● Profit: They make a profit of $50 on each table and $20 on each chair.
● Goal: Determine how many tables and chairs to produce to maximize profit.
Similarly the problem can be of minimization.
Techniques of Operations Research
❑ Transportation Problem. The transportation problem is a special type of linear programming problem,
where the objective is to minimize the cost of distributing a product from a number of sources to a number of
destinations.
❑ Objective:
❑ The goal is to determine how many fans each factory should ship to each warehouse to minimize the total
transportation cost while meeting the demand of each warehouse and not exceeding the supply of each
factory. Example:
❑ Factory A can produce 40 fans, and its cost to W1 is $2 per fan. W1 needs 45 fans.
❑ Factory B can produce 30 fans, and its cost to W1 is $5 per fan.
❑ Factory C can produce 30 fans, and its cost to W1 is $8 per fan.
❑ Assignment Problem. when the problem involves the allocation of n different facilities to n different tasks,
it is often termed as an assignment problem.
❑ Queuing Theory. The queuing problem is identified by the presence of a group of customers who arrive
randomly to receive some service. This theory helps in calculating the expected number of people in the
queue, expected waiting time in the queue, expected idle time for the server, etc. Thus, this theory can be
applied in such situations where decisions have to be taken to minimize the extent and duration of the queue
with minimum investment cost.
❑ Inventory Models: Inventory model make a decision that minimize total inventory cost. This
model successfully reduces the total cost of purchasing, carrying, and out of stock inventory.
❑ Network Scheduling
Network scheduling methods are useful in planning, scheduling and monitoring projects of
large scales common in construction industry, information technology, etc.
For example, network scheduling is used for assembly line scheduling, inventory planning
and control, launching new advertisement campaigns, installing new equipment, controlling
projects, etc.
Network Analysis (PERT/CPM):
Used for planning, scheduling, and controlling complex projects by identifying critical paths
and potential delays.
Game Theory:
Analyzes strategic interactions between multiple decision-makers, where the outcome of
one player's decisions depends on the actions of others.
Linear Programming
❑ Linear The word linear is used to describe the relationship among two or more variables
which are directly proportional.
❑ For example, if the production of a product is proportionately increased, the profit also
increases proportionately, then it is a linear relationship. A linear form is meant a
mathematical expression of the type,
Example of Linear programming
Available Machine Hrs= 40
Pr 1.
Solution
