dmo assignment 11135

8/3/2019 DMO Assignment 11135

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Table of Contents

HISTORY ............................................................................................................................................... 2 ME THODOLOGY .................................................................................................................................. 3 MATH EMATIC A L PROGR AMM ING ..................................................................................................... 4 STOCH ASTIC PROC E SS E S ................................................................................................................... 4 OR T E CHNIQU E S ................................................................................................................................. 4 TH E ORY OF R E PL AC EME NT ............................................................................................................... 5 OP E R ATION A L R E S EA RCH IN PR ACTIC E .......................................................................................... 5 SCOP E OF A PPLIC ATION .................................................................................................................... 6 A DV A NT AG E S ....................................................................................................................................... 6 LI M IT ATIONS ........................................................................................................................................ 7 R E F E R E NC E S ....................................................................................................................................... 7



INTRODUCTION

Operations research, or Operational Research in British usage is a discipline

that deals with the application of advanced analytical methods to help make

better decisions. It is often considered to be a sub-field of Mathematics. The

terms management science and decision science are sometimes used as moremodern-sounding synonyms. A decision-making problem occurs where there

are two or more alternative courses of action, each of which leads to a different

and sometimes unknown end result. Operations research is also used to

maximize the utility of limited resources. The objective is to select the best

alternative, that is, the one leading to the best result.

India was one of the first few countries who started using OR. In 1949, the first

OR unit was established in the Regional Research Laboratory at Hyderabad.

Today, OR is a popular subject in management, mechanical engineering and themathematics.

HISTORY

The ambiguous term Operations Research (OR) was coined during World War

II, when the British Military Management called upon a group of scientists

together to apply a scientific approach to the study of military operations to win

the battle. Operations Research originated in Great Britain during World War II

to bring mathematical or quantitative approaches to bear on military operations.

The main objective was to allocate the scarce resources in an effective manner to the various military operations and to the activities within each operation.

The effectiveness of operations research in military spread in it to other

government department and industry. Due to the availability of faster and

flexible computing facilities and the no. of qualified O.R. professionals, it is

now widely used in military, business, industry, transportation, public health

etc. Since its birth in the 1940's, OR has been widely recognized as an important

approach to decision-making in the management of all aspects of an

organization. Computer revolution helped OR as the problems in computation

was enormous and required a tool strong enough to handle complexity

.Electronic and Digital calculation gave way to a school of thought which was

beyond manual calculation. Further the growth of OR was boosted at every step

of computer growth. Today, OR solutions are available as software¶s which are

customised according to necessity and demand. Many legacy systems use these

as a calculation engine which gives accurate result on providing the inputs.



Two factors that helped boost the growth of OR is this research in techniques

and the computer revolution. Many theories and methods like the simplex

method (developed by George Dantzig in 1947), and many crucial tools of OR

like linear programming, dynamic programming, queuing theory and inventory

theory were relatively well developed by 1950.

METHODOLOGY

The success of operations research, where there has been success, has been theresult of the following six simply stated rules:

(1) formulate the problem

(2) construct a model of the system

(3) select a solution technique

(4) obtain a solution to the problem

(5) establish controls over the system

(6) implement the solution.

The first statement of the problem is usually vague and inaccurate. It may be acataloging of observable effects. It is necessary to identify the decision maker,

the alternatives, goals, and constraints, and the parameters of the system. A

statement of the problem properly contains four basic elements that, if correctlyidentified and articulated, greatly eases the model formulation. These elementscan be combined in the following general form: ³Given (the systemdescription), the problem is to optimize (the objective function), by choice of

the (decision variable), subject to a set of (constraints and restrictions).´

In modeling the system, one usually relies on mathematics, although graphicaland analog models are also useful. It is important, however, that the modelsuggest the solution technique, and not the other way around.

With the first solution obtained, it is often evident that the model and the problem statement must be modified, and the sequence of problem-model-technique-solution-problem may have to be repeated several times. The controls

are established by performing sensitivity analysis on the parameters. This also

indicates the areas in which the data-collecting effort should be made.



Implementation is perhaps of least interest to the theorists, but in reality it is themost important step. If direct action is not taken to implement the solution, the

whole effort may end as a dust-collecting report on a shel

MATHEMATICAL PROGR AMMING

Probably the one technique most associated with operations research is linear programming. The basic problem that can be modeled by linear programming is

the use of limited resources to meet demands for the output of these resources.This type of problem is found mainly in production systems, but is not limited

to this area.

Generally speaking, a mathematical optimization model has the following

typical components: a set of decision variables an objective function, expressed

in terms of the decision variables, that is to be minimized or maximized a set of

constraints that limit the possible values of the decision variables .

STOCHASTIC PROCESSES

A large class of operations research methods and applications deals with

stochastic processes. These can be defined as processes in which one or more of the variables take on values according to some, perhaps unknown, probability

distribution. These are referred to as random variables, and it takes only one tomake the process stochastic.

In contrast to the mathematical programming methods and applications, thereare not many optimization techniques. The techniques used tend to be morediagnostic than prognostic; that is, they can be used to describe the ³health´of asystem, but not necessarily how to ³cure´ it.

OR TECHNIQUES

Linear programming It has been used to solve problems involving assignment

of jobs to machines, blending, product mix, advertising media selection, least

cost diet, distribution, transportation and many others.

Dynamic programming It has been applied to capital budgeting, selection of advertising media, cargo loading and optimal routing problems.

Waiting line or queuing theory It has been useful to solve problems of traffic

congestion, repair and maintenance of broken-down machines, number of

service facilities, scheduling and control of air-traffic, hospital operations,

counter in banks and railway booking agencies.



I nventory control / planning These models have been used to determine

economic order quantities, safety stocks, reorder levels, minimum and

maximum stock level.

Decision theory It has been helpful in controlling hurricuanes, water pollution,

medicine, space exploration, research and development projects.

Network analysis (PERT& CPM) These techniques have been used in planning,

scheduling and controlling construction of dams, brides, roads and highways

and development & production of aircrafts, ships, computers etc.

Simulation It has been helpful in a wide variety of probabilistic marketing

situations.

THEORY OF R EPLACEMENT

It has been extensively employed to determine the optimum replacement

interval for three types of replacement problems:

i) Items that deteriorate with time.

ii) Items that do not deteriorate with time but fail suddenly.

iii) Staff replacement and recruitment.

OPER ATIONAL R ESEARCH IN PR ACTICE

Operational research is spread across various streams and domains like

manufacturing, transportation, construction, telecommunication, financial

planning , health care , military and public services. The term ³management

sciences´ is used as a synonym for Operational research. Research is also done

extensively in OR. The process begins by carefully observing and formulating

the problem including formulating the relevant problem. The next step is to fit

the problem in a scientific model as per the nature. A hypothesis is formulated

that the designed model is sufficient and precise representation of the features of the real problem in hand. Suitable experiments are conducted to prove the

validity of the hypothesis. Based on the experiments, design may be modified

and then test for the validity of the hypothesis. Operational Research requires

creative scientific research the fundamental properties of operation. OR, as

discussed earlier, also deals with practical management. OR also has a broad

point of perspective to all the factors involved and leaves behind the myopic



approach to any specific factor. Also, the best solution is obtained unlike in

mathematical analysis where a range of feasible solution may be obtained.

Operation Research is generally done by a team of statistician, mathematician

and Engineers or a collection of all the concerned teams. The team also needs to

have the necessary experience and variety of skill to give appropriateconsideration to the necessary areas of the problem.

SCOPE OF APPLICATION

There are numerous areas where operations research has been applied. The

following list is not intended to be all-inclusive, but is mainly to illustrate the

scope of applications: optimal depreciation strategies; communication network

design; computer network design; simulation of computer time-sharing systems;

water resource project selection; demand forecasting; bidding models for

offshore oil leases; production planning; classroom size mix to meet student

demand; optimizing waste treatment plants; risk analysis in capital budgeting;

electric utility fuel management; optimal staffing of medical facilities; feedlot

optimization; minimizing waste in the steel industry; optimal design of natural-

gas pipelines; economic inventory levels; optimal marketing-price strategies;

project management with CPM/PERT/GERT; air-traffic-control simulations;

optimal strategies in sports; optimal testing plans for reliability; optimal space

trajectories

ADVANTAGES

Provides a tool for scientific analysis.

Provides solution for various business problems.

Enables proper deployment of resources.

Helps in minimizing waiting and servicing costs.

Enables the management to decide when to buy and how much to buy?

Assists in choosing an optimum strategy.

Renders great help in optimum resource allocation.



Facilitates the process of decision making.

Management can know the reactions of the integrated business systems.

Helps a lot in the preparation of future managers.

LIMITATIONS

The inherent limitations concerning mathematical expressions

High costs are involved in the use of O.R. techniques

O.R. does not take into consideration the intangible factors

O.R. is only a tool of analysis and not the complete decision-making

process

Other limitations

Bias

Inadequate objective functions

Internal resistance

Competence

Reliability of the prepared solution

R EFER ENCES

http://www.doc.ic.ac.uk/~br/berc/linearprog.pdf

http://www.orms-today.org/classifieds/

http://www.scienceofbetter.org/what/index.htm

dmo assignment 11135

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