DOKUZ EYLÃœL UNIVERSITY INDUSTRIAL ENGINEERING SEDA GEZMEN 2009503034. OPERATION RESEARCH. INTRODUCTION.
Operation research encompasses a wide range of problem-solving techniques and methods applied in the pursuit of improved decision-making and efficiency.Work in operational research and management science may be characterized as one of three categories.
Fundamental or foundational work takes place in three mathematical disciplines: probability,optimization and dynamical systems theory.
The major sub-disciplines in modern operational research, as identified by the journal OPERATIONAL RESEARCHare:
-Computing and information technologies
-Environment, energy and natural resources
-Manufacturing ,service sciences and supply chain management
-Policy modeling and public sector work
The goal of operational research is to provide a framework for constructing models of decision making problems, finding the best solutions with respect to given measure of merit , and implementing the solutions in an attempt to solve the problems .
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 migt be appropriate for this discussion, for indeed problem situations that are amenable to objective analysis arise in every area of human activity.
The figure in the above shows the situation with vague outlines because most problems are poorly defined in their original conception.Historical data describing organizational operations and performance may be present in various forms.The data may be immediately relevent to the situation or investigations may reveal the need for additional data collection.
Formulate the Problem
The first analytical step of the solution process is to formulate the problem in more precise terms.
At the formulation stage, statement of objectives, constraints on solutions, approprite assumptions, descriptions of processes, data requirments, alternatives for action and metrics for measuring progress are introduced.
Implemet a Solution
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 percieveit.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.
It shows an arc from the statement directly back to situation because careful examination of a problem often leads to solution without complex mathematics.For complex situations or for problems involving uncertainty, the OR process usually continues to the next step.
The figure shows the problem statement with more definition than the situation; however, greater simplification is still necessary before a computer-based analysis can be performed.This is achieved by constructing 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 irrelevent 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 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.
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.
Here tools available to the analyst are used to obtain a solution to the mathematical 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.
To carry out this task the analyst must have a broad knowledge of avaliable solution methodologies.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.
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.
Once a solution accepted a procedure must be designed to retain control of the implementation effort.Problems are usually ongoing rather than unique.Solution are implemented as procedures to be used repeatedly in an almost automatic fashion under perhaps changing condition.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.
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 problem that no longer exsist 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.
A solution to a problem usually implies changes for some individuals in the organization.Because resistance to changes is common, the implementation of solution 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.
Combining the steps we obtain the complete OR process.In practice, the process may not be well defined and steps may not be executed in a strict order.Rather there many loops in the process, with experimentation and observation at each step suggesting modifications to decision made earlier.