Operations research (also referred to as decision science, or management science) is an interdisciplinary mathematical science that focuses on the effective use of technology by organizations.
DEFINITIONS
* OR is a scientific method of providing executive departments with a quantitative basis for decisions regarding the operations under their control. – Morse & Kimball
* Operations research is a scientific approach to problem solving for executive management. – H.M. Wagner
* Operations research is an aid for the executive in making this decisions by providing him with the needed quantitative information based on the scientific method of analysis. – C. Kittel
# PHASES OPERATIONS RESEARCH
# 1. Recognize the Problem
# 1. Recognize the Problem
* Decision making begins with a situation in which a problem is recognized.
* The problem may be actual or abstract, it may involve current operations or proposed expansions or contractions due to expected market shifts, it may become apparent through consumer complaints or through employee suggestions, it may be a conscious effort to improve efficiency or a response to an unexpected crisis.
* It is impossible to circumscribe the breadth of circumstances that might be appropriate for this discussion, for indeed problem situations that are amenable to objective analysis arise in every area of human activity.
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# 2. Formulate the Problem
* At the formulation stage,
* statements of objectives, constraints on solutions, appropriate assumptions, descriptions of processes, data requirements, alternatives for action and metrics for measuring progress are introduced.
* Because of the ambiguity of the perceived situation, the process of formulating the problem is extremely important. The analyst is usually not the decision maker and may not be part of the organization, so care must be taken to get agreement on the exact character of the problem to be solved from those who perceive it. There is little value to either a poor solution to a correctly formulated problem or a good solution to one that has been incorrectly formulated.
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# 3. Construct a Model
* A mathematical model is a collection of functional relationships by which allowable actions are delimited and evaluated. Although the analyst would hope to study the broad implications of the problem using a systems approach, a model cannot include every aspect of a situation.
* A model is always an abstraction that is, by necessity, simpler than the reality.
* Elements that are irrelevant or unimportant to the problem are to be ignored, hopefully leaving sufficient detail so that the solution obtained with the model has value with regard to the original problem.
* The statements of the abstractions introduced in the construction of the model are called the assumptions. It is important to observe that assumptions are not necessarily statements of belief, but are descriptions of the abstractions used to arrive at a model. The appropriateness of the assumptions can be determined only by subsequent testing of the model’s validity.
* Models must be both tractable -- capable of being solved, and valid -- representative of the true situation. These dual goals are often contradictory and are not always attainable. We have intentionally represented the model with well-defined boundaries to indicate its relative simplicity.
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# 4. Find a Solution(1)
* The next step in the process is to solve the model to obtain a solution to the problem. It is generally true that the most powerful solution methods can be applied to the simplest, or most abstract, model.
* Some methods can prescribe optimal solutions while other only evaluate candidates, thus requiring a trial and error approach to finding an acceptable course of action.
* It may be necessary to develop new techniques specifically tailored to the problem at hand. A model that is impossible to solve may have been formulated incorrectly or burdened with too much detail. Such a case signals the return to the previous step for simplification or perhaps the postponement of the study if no acceptable, tractable model can be found.
# 4. Find a Solution(2)
* Of course, the solution provided by the computer is only a proposal. An analysis does not promise a solution but only guidance to the decision maker.
* Choosing a solution to implement is the responsibility of the decision maker and not the analyst. The decision maker may modify the solution to incorporate practical or intangible considerations not reflected in the model.
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# 5. Establish the Procedure(1)
* Once a solution is accepted a procedure must be designed to retain control of the implementation effort.
* Problems are usually ongoing rather than unique. Solutions are implemented as procedures to be used repeatedly in an almost automatic fashion under perhaps changing conditions.
* Control may be achieved with a set of operating rules, a job description, laws or regulations promulgated by a government body, or computer programs that accept current data and prescribe actions.
# 5. Establish the Procedure(2)
* Once a procedure is established (and implemented), the analyst and perhaps the decision maker are ready to tackle new problems, leaving the procedure to handle the required tasks.
* But what if the situation changes?
* An unfortunate result of many analyses is a remnant procedure designed to solve a problem that no longer exists or which places restrictions on an organization that are limiting and no longer appropriate.
* Therefore, it is important to establish controls that recognize a changing situation and signal the need to modify or update the solution.
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# 6. Implement the Solutio n
* A solution to a problem usually implies changes for some individuals in the organization. Because resistance to change is common, the implementation of solutions is perhaps the most difficult part of a problem solving exercise.
* Some say it is the most important part. Although not strictly the responsibility of the analyst, the solution process itself can be designed to smooth the way for implementation.
* The persons who are likely to be affected by the changes brought about by a solution should take part, or at least be consulted, during the various stages involving problem formulation, solution testing, and the establishment of the procedure.
# TECHNIQUES OF OR(1)
* 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.
* Inventory control / planning- These models have been used to determine economic order quantities, safety stocks, reorder levels, minimum and maximum stock level.
# TECHNIQUES OF OR(2)
* 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 replacement- 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.
# What is a Mathematical Model?
* The majority of practical decision problems are described in very vague terms. Therefore, a most-important step in a scientific or quantitative analysis of a problem is to formulate a model that adequately captures the essence of a problem. The result of such a formulation, or an abstraction, is called a mathematical optimization model.
* 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
# 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
# Application Fields
* Industry
* Defense
* Planning
* Agriculture
* Public utilities
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