CSC 212 INTRODUCTION TO OPERATIONAL RESEARCH

 CSC 212

INTRODUCTION TO OPERATIONAL RESEARCH

INTRODUCTION

Operations Research (OR) İs a science which deals with problem, formulation, solutions and finally appropriate decision making. This subject is new and started after World War 1, when the failures of missions were very high. Scientists and techno crates formed team to study the problem arising out of difficult situations and at the later stage solutions to these problems. It is research deigned to determine most efficient way to do something new. OR is the Use of mathematical models, statistics and algorism to aid in decision-making. It is most often used to analyze complex Real life problems typically with the goal of improving or optimizing performance. Decision making is the main activity of an engineer/manager. Some decisions can be taken by common sense, sound judgment and experience without using mathematics, and some cases this may not, be possible and use of other techniques is inevitable, with the growth of technology, the World has seen remarkable changes in the size and complexity of-organizations. An integral part of this had been the division of labor and segmentation of management responsibilities in these organizations. The results have been remarkable but with this, increasing specialization has created a new problem to meet out organizational challenges. The allocation of limited resources to various activities has gained significant importance in the competitive market. These types of problems need immediate attention which is made possible by the application of OR techniques. The tools of operations, research are not from any one discipline; rather Mathematics, Statistics, Economics, Engineering, Psychology, etc. have contributed to this newer discipline of knowledge. Today, it has become a professional discipline that deals with the application of scientific methods for decision-making, and especially to the allocation of scare resources.

2. BACKGROUND OF OPERATIONS RESEARCH

The effectiveness of operations research in military spread interest in it to other governmental departments and industry. In the U.S.A. the National Research Council formed a commits on operations research in 1951, and the first book on the subject "Methods. Of Operations Research", by Morse and Kimball, was published. In 1932 the Operations Research Society of America came into being. Today, almost all organizations make use of OR techniques for decision-making at all levels. This general Acceptance to OR has come as managers have learned the advantage of the scientific approach to all industrial problems. Some of the Indian organizations using operations research techniques to solve their varied complex problems are: Railways, Defense, Indian Airlines, and Fertilizer Corporation of India, Delhi Cloth Mills., Tata Iron and Steel Co. etc.

A purpose of OR is to provide a rational basis for making decisions in the absence of complete is science devoted to describing, understanding and predicting the behavior of Information. OR can also be treated as systems, particularly man-machine systems.

3. MEANING OF OR

Defining OR is difficult task as its boundaries and content are not yet fixed. It can be regarded as use of mathematical aid quantitative techniques to substantiate the decision being taken. Further, it is multidisciplinary which takes tools from subjects like mathematics, statistics, engineering, economics, psychology etc, and uses them to score the consequences of possible alternative actions. Today it has become professional discipline that deals with the application of scientific methods to decision-making. Salient aspects related to definition stressed by various experts on the subject are as follows:

(a) Pocock stresses that OR is an applied science; he states "OR is scientific methodology-analytical, experimental, quantitative--which by assessing the overall implication of various alternative courses of action in a management system, provides an improved basic for management decisions".

(b) Morse and Kimball have stressed the quantitative approach of OR and have described it as "a Scientific method of providing executive departments with a quantitative basis to decisions regarding the operations under their control

(c) Miller and Starr see OR as applied decision theory. They state "OR are an applied decision theory. Uses any scientific, mathematical or logical means to attempt to cope with the problems that Confront the executive, when he tries to achieve a thoroughly--going rationality in dealing with His decision problem".

(d) Saaty considers OR as tool of improving the quality of answers to problems. He says, "OR is the art of giving bad answers to problems which otherwise have worse answers".

Few other definitions of OR are as follows:

. "OR is concerned with scientifically deciding how to best design and operate man-machine System usually requiring the allocation of scare resources."

Operations Research Society, America

, "OR is essentially a collection of mathematical techniques and tools which in conjunction with

System approach, are applied to solve practical decision problems of an economic or engineering nature".

- Daellenbach and George

OR utilizes the planned approach (updated scientific method) and an interdisciplinary team in

Order to represent complex functional relationships as mathematical modest for the purpose of

Providing a quantitative analysis'.

-Thieraub and Klekamp

. "OR is a scientific knowledge through interdisciplinary team effort for the purpose of deter rainingthe best utilization of limited resources."

- H.A. Taha

"OR is a scientific approach to problem solving for executive management"

- H.M. Wagner

4. FEATURES OF OR

The significant features of operations research include the followings:

(i).Decision-making. 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. lt 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.

(ii) Scientific Approach. OR applies scientific methods, techniques and tools for the purpose of Analysis and solution of the complex problems: n this approach there is no place for guess work and the person bias of the decision maker.

(iii) Inter-disciplinary Team Approach. 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 an optimal solution of the problem. The tries to analyze the cause and effect relationship between various parameters of the problem and evaluates the outcome of various alternative strategies.

(iv). System Approach. The main aim of the system approach is to trace for each proposal all significant and indirect effects on all sub-system on a system and to evaluate each action in terms of effects for the system as a whole. The interrelationship and interaction of each sub-system can be handled with the help of mathematical/analytical models of OR to obtain acceptable solution.

(v) Use of Computers. 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 under the specified conditions. For the above purpose, it is necessary that a measure of effectiveness has to be declined which must be based on the goals of the organization. These measures can be used to compare the alterative courses of action taken during the analysis.

5. PHASES OF OR STUDY

OR is a logical and systematic approach to provide a rational basis for decision-making. The phases of OR must be logical and systematic. The various steps required for the analysis of a problem under OR are as follows:

Step i. Observe the Problem Environment

The first step of OR study is the observation or the environment in which the problem exists. The active constitute this step are visits, conferences, observations, research etc. with the help

 of such activities, the OR analysis gets sufficient information and support to proceed and is better prepared to formulate its nature

Step ii. Analyze and Define the Problem

In this step not only the problem is defined out also uses Objectives and limitations of the study that are stressed the light of the problem. The end results of this step are clear grasp of need for a solution and understanding nature.

Step iii. Develop a Model

The next step is to develop model, which is representation of same real or abstract situation. OR models are basically mathematical models representing systems, process or environment in form of equation, relationships or formulae. The activities in this step is to defining interrelationships among variables, formulating equations, sine known OR models or searching suitable alternate models. The proposed Model may be field tested and modified in order to work under stated environmental constraints. A model may also be modified if the management is not satisfied with the answer that it gives.

Step IV. Selection of Data Input

It is an established fact that without authentic and appropriate data the results of the OR models cannot be trusted. Hence, taping right kind of data is a vital step in OR process. Important activities in this step are analyzing internal-external data and facts, collecting opinions and using computer data banks. The purpose of this step is to have sufficient input to operate and test, the model.

Step V. Solution and Testing

In this step the solution of the problems is obtained with the help of model and data input such a solution is not implemented immediately and this solution is used to test the model and to find its limitations if any. If the solution is not reasonable or if the model is not behaving properly, updating and modification of the model is considered at this stage. The end result of this step is solution that is desirable and supports current organizational Objectives.

Step VI. Implementation of the Solution

This-is the Last phase of the OR study. In OR the decision-making is scientific bur implementation of decision involves many behavioral issues. Therefore, implementation authority has to resolve the behavioral issues, involving the workers and supervisors. To avoid further conflicts. The gap between management and OR scientist may offer some resistance but must be eliminated before solution is accepted in totality. Both the parties should play positive role, since the implementation will help the organization as a whole, A properly implemented solution obtained through OR techniques results in improved working conditions and wins management support.

6. OUTLINES OF OR MODELS

In OR the problem is expressed in the form of a model. Where, a model is a theoretical abstraction (approximation) of a real-life problem. It can be defined as 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. OR analysts have given special impetus to the development and use of techniques like, linear programming, waiting line theory. Game theory, inventory controls and simulation. In addition, some other common tools are non-linear programming integer programming, dynamic programming, sequencing theory, Markov process, network scheduling PERT and CPM, symbolic logic, information theory and utility/value theory. The list, of course, is not exhaustive. The detailed discussion on above will be presented in appropriate chapters, however, brief explanation of these is given below:

(i) Linear Programming (L.P.)

Linear programming is basically a constrained optimization technique which tries to optimize some criterion within some constraints. It consists of an objective function which is some measure of effectiveness like profit, loss or return on investment and several boundary conditions putting restriction on the use of resources. Objective function and boundary conditions are linear in nature. There are methods available to solve a linear programming

(ii) Waiting Line or Queuing Theory 

These deals with the situation in which queue is formed or the customers have to wait for service or machines repairmen and therefore concept of a queue is involved. If we assume that there are costs associated with line, and if there are costs of adding more service facilities, we want to minimize the sum of costs of waiting the cost of providing service facilities. Waiting line theory helps to make calculations like number of expected member of people in queue, expected waiting time in the queue, expected idle time for the server, etc. This calculation then can be used to determine the desirable number of service facilities or number of servers.

(ii) Game Theory

It is used for decision-making under conflicting situations where there are one or more opponents. The opponents, in game theory, are called players. The motives of the players are victimized. The success of one player tends to be at the cost of others and hence they are in conflict. Game theory models, a conflict situation arises and helps to improve the decision process by formulating appropriate strategy.

(iv) Inventory Control Models

These models deal with the quantities which are either to be purchased or stocked since each factor involves cost. The purchase and material managers are normally encounter such situations. Therefore, inventory models provide rational answer to these questions in different situations of supply and demand for different kind of materials. Inventory control models help managers to decide ordering time, reordering level and optimal ordering quantity. The approach is to prepare a mathematical model of the' situation that expressed total inventory costs in terms of demand, size of order, possible over or under stocking and other relevant factors and then to determine optimal order size, optimum order level etc. using calculus, or some. Other technique.

(v) Simulation

It is basically data generating technique, where sometimes it is risky, cumbersome, or time consuming to conduct real study or experiment to know more about situation or problem. The available analytical methods cannot be used in all situations due to target number of variables or target number of interrelationships among the variables and thecomplexity of relationship it is' not possible to develop an analytical model representing the real situation. Sometimes, even building of model is possible but its solution may not be possible. Under such situations simulation is used. It should be noted that simulation does not solve the problem by itself, but it only generates the required information or data needed for decision problem or decision-making.

(vi)  Non-Linear Programming

These models may be used when either the objective function or some of the constraints are not linear in nature. Nonlinearity may be introduced by such factors as discount on price of purchase of large quantities and graduatedincome tax etc. Linear programming may be employed to approximate the non-linear conditions, but the approximation becomes poorer as the range is extended. Non-linear methods may be used to determine the approximate area in which a solution lies and linear methods may be used to obtain a more exact solution.

(vii)Integer Programming

This method can be used when one or more of the variables can only take integer values. Examples arc the number house and so on, approximate solutions can be obtained without using integer programming methods, but the approximation generally becomes poorer as the number becomes smaller. There are techniques to obtain solution of Integer programming problems.

(viii) Dynamic Programming

This is a method of analyzing multistage decision processes, in which each elementary decision is dependent upon those preceding it as well as upon external factors. It drastically reduces the computational efforts otherwise necessary to analyze results of all possible combinations of elementary decisions.

(ix) Sequencing Theory

This is related to waiting line theory and is applicable when the facilities are fixed, but the order of servicing may be controlled. The scheduling of service or the sequencing of jobs is done to minimize the relevant costs and time.

(xii) Information Theory.

Information theory is an analytical process transferred from the electrical communications field to operations research. 1It sacks to evaluate the effectiveness of information flow within a. Given system, despite its application mainly to communication networks, it has had a indirect influence in simulating the examination of business organizational structures with a view to improving information or communication flow

(xiv) Utility/Value Theory

It deals with assigning numerical significance to the worth of alternative choices. To date, this has been only a concept and is in the stage of elementary model formulation, and experimentation and can be useful in decision-making process.

7. SCOPE OF OPERATIONS RESEARCH

As presented in the earlier paragraphs, 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 can be used to find the best solution to any problem be it simple or complex. It is. Useful in every field of human activities, where optimization of resources is required in the best way. Thus, 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. The main fields where OR is extensively used are given below, however, this list is not exhaustive but only illustrative.

(i) National planning and Budgeting

OR is used for the preparation of Five Year Plans, annual budgets, forecasting of income and expenditure, scheduling of major projects of national importance, estimation of GNP, GDP, population, employment and generation of agriculture yields etc.

(ii) Defense Services

Basically formulation of OR started from USA army, so it has wide application in the areas such as development of new technology, optimization of cost and time, tender evaluation, setting and layouts of defense projects, assessment of "Threat analysis", strategy of battle, effective maintenance and replacement of equipment, inventory control, transportation and supply depots etc.

(iii) Industrial Establishment and Private Sector Units

OR can be effectively used in plant location and setting finance planning, product and process planning, facility planning and construction, production planning and control, purchasing, maintenance management and personnel management etc. to name a few. Research and development being the heart of technological growth, OR has wide scope for and can be applied in

(iv) R & D and Engineering

Technology forecasting and evaluation, technology and project management, preparation of tender and negotiation, value engineering, work/method study and so on. OR can help in taking business decisions under risk and uncertainty, capital investment and returns, business

(v) Business Management and Competition

Strategy formation, optimum advertisement outlay, optimum sales force and survey and their distribution, market analysis and market research techniques etc. in the area of agriculture and irrigation also OR can be useful for project management construction of major dame

(vi) Agriculture and Irrigation

Minimum cost, optimum at location of supply and collection points for fertilizer/seeds and agriculture output optimum mix of fertilizers for better yield.

(vii) Education and Training

OR can be used for obtaining optimum number of schools with their locations, optimum mix of students/teacher student ratio, optimum financial output and other relevant information in training of graduates to meet out the national requirements.

(vii) Transportation

Transportation models of OR can be, applied to real life problems to forecast public transport requirements, optimum routing, forecasting of income and expenses, project management for railways, railway network distribution, etc. In the same way it can be useful in the field of communication.

(ix) Home Management and Budgeting

OR can be effectively used for control of expenses to maximize savings, time management, work study methods for all related works. Investment of surplus budget, appropriate insurance of life and properties and estimate of depreciation and optimum premium of insurance etc.