Operations Research An Introduction Introduction to Operations

Operations Research An Introduction

Introduction to Operations Research n Operations Research, in simple terms, is the research of operations. n An operation may be called a set of acts required for the achievement of a desired outcome. n Operations research could be thought of as a systematized effort to solve a given problem through careful investigation. n OR is a systematic method consisting of stating the problem in clear terms, collecting facts and data, analyzing them and reaching certain conclusions in the form of solution to the problem.

Origin n During World War II, the military management in England called a team of scientists to study the strategic and tactical problems of air and land defence. n The objective was to find out the most effective allocation of limited military resources to the various military operations and to the activities within each operation. n This group of scientists formed the first OR team.

Development n The encouraging results of these efforts led to the formation of more such teams in British armed services and the use of such scientific teams soon spread to the United States, Canada and France. n The new revolution began around 1940 s when electronic computers became commercially available and these were used for OR complex computational problems. n In 1950, OR was introduced as a subject for academic study in American Universities. n To increase the impact of OR the Operations Research Society of America was formed in 1950. n In 1953, the Institute of Management Science (IMS) was established. In the same year Other countries followed suit to establish International Federation of OR societies.

OR in India n OR came into existence with the opening of an OR unit in 1949 at the Regional Research Laboratory at Hyderabad. n An OR unit was established in 1953 in the Indian Statistical Insititute, Calcutta to apply OR methods in National Planning and Survey. n Operations Research Society of India (ORSI) was formed in 1957 and its first conference was held in Delhi in 1959. n The first MSc course on OR was started by Delhi University in 1963. n At the same time, Institutes of Management at Calcutta and Ahmedabad introduced OR in their MBA courses.

Definitions n OR is a scientific method of providing executive departments with a quantitative basis for decisions regarding the operations under their control. – Morse & Kimball n OR is the art of giving bad answers to the problems, in which otherwise, worse answers are given. – Thomas L. Saaty n OR is the application of scientific methods to problems arising from operations involving integrated systems of men, machines and materials. It normally utilizes the knowledge and skill of an inter-disciplinary research team to provide the managers of such systems with optimum operating solutions. – Fabrycky and Torgersen

Scope of Operations Research n In Agriculture: q q n In LIC: q q n a) what should be the premium rates for various modes of policies b) how best the profits could be distributed in the cases of with profit policies, etc… In Finance: q q n a) optimum allocation of land to various crops in accordance with the climatic conditions b) optimum distribution of water from various resources like canal for irrigation purposes. a) to maximize the per capita income with minimum resources b) to determine the best replacement policies etc. In Industry: q OR is used to the industry in deciding optimum allocation of various limited resources such as men, machines, material, money, time etc. to arrive at the optimum decision.

Scope of Operations Research n In Marketing: q q q n In Personal Management: q q q n a) where to distribute the products for sale so that total cost of transportation is minimum b) the size of the stock to be maintained to meet the future demand c) how to select the best advertising media with respect to time, cost, etc… a) to appoint the most suitable persons on optimum salary b) to determine the best age of retirement for the employees c) to find out the number of persons to be appointed when the work load is seasonal In Production Management: q q a) to find out the number and size of the items to be produced b) in scheduling and sequencing the production run by proper allocation of machines c) in calculating the optimum product mix d) to select, locate and design the sites for the production plants.

Techniques of OR n n n n n Distribution (Allocation) Models Production / Inventory Models Waiting Line Models Markovian Models Competitive Strategy Models (Game Theory) Network Models Job Sequencing Models Replacement Models Simulation Models

Methodology of OR Formulate the Problem Model Building 1. 2. Physical models 1. 1. 2. 4. 1. 2. 3. 6. Symbolic models Obtaining Input Data Solution of Mode 3. 5. Iconic models Analogue models Feasible & infeasible solutions Optimal & non-optimal solutions Unique & multiple solutions Model Validation Implementation

Types of Mathematical Models 1. Quantitative versus qualitative 2. Standard versus custom made 3. Probabilistic versus deterministic 4. Descriptive versus optimising 5. Static versus dynamic 6. Simulation versus non-simulation

Characteristics of OR n n n n System or Executive Orientations of OR The Use of Inter-disciplinary Teams Application of Scientific Method Uncovering of New problems Improvement in the Quality of Decisions Quantitative Solutions Human Factors To Optimize the Total Output

Role of QT in Business & Industry 1. 2. 3. 4. 5. 6. 7. 8. 9. They provide a tool for scientific analysis They provide solution for various business problems They enable proper deployment of resources They help in minimising waiting & servicing costs They enable the management to decide when to buy & how to buy They assist in choosing an optimum strategy They render great help in optimum resource allocation They facilitate the process of decision making Through various quantitative techniques management can know the reactions of the integrated business systems

Limitations of OR n n n Information Gap Quantification Techniques Finite Variables Limited number of Constraints Single Objective Function