OPERATION RESEARCH

1. OPERATION RESEARCH Chapter 1 Introduction to Operation Research

2. OR - one of the important branches of the management, and closely related with applied mathematics and industrial engineering. •   Helps in decision-making procedure and also help in deciding trade off between risk and return trade off. • I.e. highest profit/return/benefit with lowest of cost/ efforts/ money/time/risk. • OR uses mathematical modeling, statistics, and algorithms to arrive at optimal or good decisions in complex problems. • In the simple term, the main objective of OR is to find a best possible solution of a problem mathematically, which improves the performance of the system. • Examples: • ·        To find appropriate product mix from large number of products with different profit contribution and different production requirements. • ·        To plan public transportation network in a town

3. History • ·  It was first used in World War II by UK to find best strategic and tactical position for air and land defense of the country with aim to most effective utilization of human resource to win the battle.

4. Definition • OR as the application of scientific methods, techniques and tools to operation of a system with optimumsolutions to the problems. • OR is the use of scientific methods to provide criteria for decisions regarding man, machine, and systems involving repetitive operations. • OR is the application/use of scientific methods/tools/techniques • To find optimum soln for the problem of operation system. • To provide criteria for decisions regarding man/machine/system which involve repetitive operations.

5. Scope/Application of OR • In defence: Þ   Carried out by Air Force, Army, and Navy (water defence) Þ   All have four sub components: administration, intelligence, operations and training, and supply. Þ   OR used in each component to gain maximum gains. (Here one action in one component may have the adverse effect on other components.) Þ   OR is used to coordinate the activities of all the components to get maximum benefit.

6. In Industry • With the technological revolution and with the application of division of labor and assembly production it is necessary to get maximum production with less time and cost. OR used in find out preference of the activity and with efficient production. • OR used to coordinate between various department of the industry to achieve their own and overall goal of organisation. • The goal of each dept may conflict with each other and may not achieve overall objective of an organization. OR methods and techniques used in overcoming this difficulty by integrating various activity of various components together.

7. Planning • OR methods used by government for careful planning of economic development infrastructure in particular states. Þ   logistics companies - routing and planning, Þ   local government - deployment of emergency services, and Þ   policy studies and regulation - environmental pollution, air traffic safety, AIDS, and criminal justice policy.

8. Agriculture and Hospitals • OR can be used in the field of agriculture to maximize the agriculture output. OR can be used in the area of farming, forestry, stock raising, fishery, etc. • OR methods can be used in the big hospitals for finding out the waiting patients for the treatments; time taken by doctors to examine patient and average time for each patient is taking for curing their problems.

9. Transportation • Various OR techniques used in various kind of transportation services to find out shortest route, arrival and departure time. • constructing a telecommunications network at low cost. • road traffic management i.e. allocation problems. • managing freight transportation and delivery systems managing the flow of raw materials and products in a supply chain based on uncertain demand for the finished products • airline - scheduling planes and crews, pricing tickets, taking reservations, and planning the size of the fleet, • determining the routes of city buses/trains so that as few buses/trains are needed as possible

10. R & D • OR methods also used in controling of R & D Projects, product planning etc. • pharmaceutical - R& D management

11. Features of OR A)      Decision Making: The primary objective of OR is to address the decision- making process. Decision-making is a systematic process that involves following steps: i)         Define problem and establish criteria for which decision is to be taken i.e. criteria may maximization of profit, utility, and minimization of cost etc. ii)        Find out other alternative course of action iii)       Determine the model that can be used and parameter of the process iv)       Evaluate the alternatives and choose optimum one.

12. Identify the Problem or Opportunity Understand the System Formulate a Mathematical Model Verify the Model Select the Best Alternative Present the Results of the Analysis Implement and Evaluate Methodology of Operations Research*The Seven Steps to a Good OR Analysis Feedback loops at all levels! *Adapted from Winston, Wayne L., Operations Research: Applications and Algorithms, 3rd Edition, Duxbury Press, 1994, p. 2. MATH 327 - Mathematical Modeling

13. Decision variables These are the unknown variables initially. These variables are to be determined form the solution of the model. While the decision parameters are the variables which can be controlled. • Objective functions It is the minimum requirement of the system that must be fulfilled. It also used to measure effectiveness of the system. From the decision variables and objective function should be defined clearly to find the solution. • Some of the common objective functions are maximizaiton of profit, production rate, resource utilization and minization of cost,

14. Constraints • Each and every problem in OR must have a specific constraint for which the solution must be find out. • Constraints limit the decision variables for their feasible range or values. • Constraints is also represented in the form of mathematical functions. • Every mathematical model viewed in the values of decision variables like xj, where J=1,2,3----n which is used to optimize objective function of z. where z = f (x1, x2, x3 -----xn) and subject to constraints Gi (x1,x2 ---xn). • Here x1,x2,---xn must be non negative so xj>/ 0.

16. Diet Problem • Vitamin – A and Vitamin – B are found in food – 1 and food – 2. • One unit of food –1 contains 5 units of vitamin – A and 2 units of vitamin – B. • One unit of food – 2 contains 6 units of vitamin – A and 3 units of vitamin – B. • The minimum daily requirement of a person is 60 units of vitamin – A and 80 units of Vitamin – B. • The cost per one unit of food – 1 is Rs. 5/- and one unit of food – 2 is Rs. 6/-. Assume that any excess units of vitamins are not harmful. • Find the minimum cost of the mixture (of food–1 and food–2) which meets the daily minimum requirements of vitamins.

17. Mathematical Model of the Diet Problem: Suppose x1 = the number of units of food–1 in the mixture, • x2 = the number of units of food–2 in the mixture.

18. Summary • OR approach is useful in each and every industry to find out optimum solution of the problem. • To find Optimum solution proper construction of model is necessary. • With proper understanding of phases and structure of the model the complex problem can also be solved easily.