Operations research

The operations research (also called decision-making aid ) can be defined like the whole of the methods and rational techniques of analysis and synthesis of the phenomena of Organization usable to work out better decisions.

operations research (RO) proposes conceptual models to analyze complex situations and makes it possible to the decision makers to make the most effective choices.

The field is strongly related to the Ingénierie of the systems.

History

Leitartikel: History of operations research in France

As of the 17th century, Mathematician S as Blaise Pascal try to solve problems of decision in the dubious one with the expectation. Others, with 18th and 19th century, solve combinative problems. At the beginning of the 20th century, the study of the Stock management can be regarded as being at the origin of modern operations research with the Formule of the economic batch (known as formula of Wilson) suggested by Harris in 1913.

But it is only with the Second world war that the practice will be organized for the first time and will acquire its name. In 1940, Patrick Blackett has by the staff English to direct the first operational research team, to solve certain problems such as the optimal establishment of Radar S of monitoring. The qualifier “operational” comes owing to the fact that the first application of an work group organized in this discipline had milked with the operations Militaire S. the denomination remained thereafter, even if the field Militaire is not more the main thing Field of application of this discipline.

After the war, the techniques developed considerably, grace, in particular, with the explosion of the capacities of calculation of the Ordinateur S. the scopes of application also multiplied.

Types of dealt with problems

Operations research can help the decision maker when this one is confronted with a combinative problem , competing Aléatoire or .

A problem is known as combinative when it includes/understands a great number of acceptable solutions among which one seeks a solution optimal or close to the optimum. Typical example: to determine where to install 5 distribution centers among 30 possible sites of establishment, so that the costs of transport between these centers and the customers are minimum. This problem cannot be solved by a simple enumeration of the possible solutions by the human spirit, since there are 30 X 29 X 28 X 27 X 26/(5x4x3x2) = 142 506 (!). And even if a problem of this size can be solved by enumeration by a computer, the decision makers are regularly confronted with problems infinitely more complex, where the number of acceptable solutions amounts of billion billion (see combinative Explosion).

A problem is known as Aléatoire if it consists in finding a solution optimal vis-a-vis a difficulty which arises in dubious terms. Typical example: knowing the random distribution number of people entering municipal authorities in one minute and the random distribution of the duration of treatment of the case of a person, to determine the minimum number of counters to open so that a person has less than 5% of chances to have to wait more than 15 minutes.

A problem is known as competing if it consists in finding a solution optimal vis-a-vis a problem whose terms depend on the interrelationship between its own intrigues and those of other decision makers. Typical example: to fix a policy of Price of sale, knowing that the results of such a Politique depend on the policy which competitors will adopt.

Practical applications

The problems which the R.O can help to solve are is strategic (one can quote the choice to invest or not, the choice of an establishment, the dimensioning of a fleet of vehicles or an housing stock…) or operational (in particular the Scheduling, stock management, forecasts of sales…).

The Project management S is a very important component of the community of operations research. Many work treats scheduling and Project management S, but also Logistique (turned of vehicle, conditioning…), of Planning, and problems of Timetable.

Within the framework of the Manufacturing industry, operations research in particular makes it possible to find plans of productions (Ordonnancement of production), as well as possible to lay out the machines in a workshop, to decrease the wasting of the raw materials (problems of cutting) or energy or even to optimize the conditioning and the delivery of the intermediate or finished products.

In the field of the Finance, the problems of Investissement are traditional problems of operations research. They in general consist in maximizing the profit (or the hope of profit) obtained starting from an amount given by as well as possible combining the various possibilities offered to the investor.

Operations research has also applications in the field of the energy. It is usually used in the Oil industry, mainly in the establishment of the plans of production, the provisioning of the crudes, the use of the units of refining, and the choice of the most profitable channels of distribution. In the same way, the operators of the market of the electricity largely call upon operations research so much for strategic problems (for example of the investments on the network) that for more operational questions (stability of the network, forecasts…). For more details, to see procurement, production and distribution Plan of oil

The applications in the field of the Informatique are very numerous too they. One can quote, inter alia, the choice of the localization and the number of waiters to set up, of storage capacity, the computing power and the flow of the Réseau, the choice of a data-processing Architecture (application centralized/distributed, treatments in real-time or remote, mesh network or out of star, etc), and the Ordonnancement in the operating systems.

Establishment in the world of the companies

Very few companies employ operational researchers to help the Décideur to solve his problems. When such problems arise, they are generally subjected at a large consultancy or the department of operations research of a university (although the current trend is with the externalisation of these university competences via of private small firms called Spin-off, meeting the needs for the industrial world better). Let us note that certain simple problems can be solved with the center even of the company, the majority of the universities having integrated courses of introduction to operations research into the programs of the engineers, the mathematicians, the data processing specialists, the management auditors and, less often, of the economists.

In spite of its intrinsic importance, the R.O is used still little in the industrial world, either because of the lack of (in) training of the decision makers, or by the lack of relevance of the tool or its difficulty of implementation. The principal fears emitted by the decision makers as for the application of models R.O in its company are:

a taking into account limited of the factors

For the strategic questions, the “pure and perfect” answer of a mathematical solution seems seldom applicable de facto . Even if operations research integrates many factors, so certain aspects are relatively easy with to model with the mathematical direction of the term (the cost, profitability, the distance, the duration, rate, for example), other elements are on the other hand more difficult to model: legal constraints, commercial will to make stopping with a competitor, importance of the relations with the elected officials, social climate, etc the weight of these elements in the decision is however important, sometimes determinant.

an important investment

the mathematical tool itself requires an elevated level of mathematical knowledge, a good aptitude to model the problems and to describe the factors; these constraints are consuming time and money (that it is by internal development, which consumes resources; or by external development, which consumes money). It is then necessary to find a balance between the required investment and the repercussions envisaged.

For not very frequent events

the company does not profit from the effect of experiment: of once on the other, the problem relates to a different service, or the persons in charge changed between two studies. It is thus difficult to maintain competences R.O inside the company.

The decision maker will have to take these various aspects of counts when it will or not decide to implement models of operations research in his company.

Relationships to other disciplines

Operations research is at the crossroads of various sciences and technologies. For example, the economic analysis is often necessary to define the objective to be reached or to identify the constraints of a problem.

It is also related to the Ingénierie of the systems. Compared to this one, the field of application of operations research is centered historically more on the dubious events and industry, and its methods more particularly mathematical.

Operations research uses many methods resulting from various theories Mathématiques. In this direction, part of operations research can be regarded as a branch of the Mathématiques applied. Mathematics, in particular the Statistical , also contributes to effectively pose the terms of a problem.

The Graph theory is used as support with the resolution of a vast sample of problems, in particular unquestionable resulting from the traditional Algorithmique, such as the problems of shorter way, the Problème of the sales representative, the problems of scheduling of tasks, the problems of planning or the problems of optimization of flow.

Progress of the Informatique is closely related to the increase in the applications of operations research. An important computing power is necessary to the solution to problem of big size. This power is however far from constituting a panacea: the Théorie of complexity teaches us that certain problems cannot be solved in an optimal way in a reasonable time, even if one considers computers a billion times more powerful than those today.

Several methods of solution to problem result from the Artificial intelligence. Whereas the approach of the artificial intelligence is to propose generic methods of resolution, operations research uses these methods by specializing them to make them more effective to solve more restricted classes of problems.

One can also quote the Game theory, well-known of the economists, which helps to solve the competing problems.

Principal (classes of) methods

polynomial Algorithmes

Certains problems of operations research is not Np-complete S. In this case, one uses a polynomial algorithm to solve it, if the polynomial is of degree reasonable.

dynamic Programming

Certains problems has good characteristic which make it possible to solve them using a formula of recurrence. The methods of dynamic Programming can then possibly make it possible to solve the problem with a polynomial complexity or pseudo-polynomial E.

Processus Stochastique S

the stochastic Processus relate to all the random problems, in particular problems of reliability (of systems, electronics components…) and of the phenomena of waiting.

data-processing Simulation

simulation is often employed to solve problems of RO, in particular in the nonacademic medium.

linear and nonlinear Programming

the linear Programming is very often used to solve combinative problems. It makes it possible to very effectively solve the problems in which the variables are continuous. When there are discrete variables, linear programming and arborescent methods (see hereafter) can be combined.

the nonlinear programming can also be used. The possibility of using nonlinear constraints or functions objectives offers a power of very important modeling but the algorithms of resolution of the nonlinear programs are significantly less effective than those of the linear programming.

arborescent Methods

the methods of the type A* or Branch and bound is usually used to find the solution exact of a problem of operations research. For an effective resolution, a particular care is taken to the calculation of higher or lower terminals for the value of the solution.

the Programmation by constraints makes it possible to effectively implement quickly and of such tree-searching methods. Several libraries (software) of optimization commercial or not rest on this approach (ILOG Solver, Chip, Mozart/Oz, FaCiLe). A many software of optimization of real problems uses this technology thus.

Heuristic S and Métaheuristique S

When the optimal solution cannot be obtained in a reasonable time, one often has recourse to approximate methods of type Heuristique or Métaheuristique.

Works of introduction

Robert Faure, Bernard Lemaire and Christophe Picouleau. '' Précis of Operations research '' - Methods and exercises of application - 5th edition. Dunod.

Dominique de Werra, Thomas Mr. Liebling and Jean-François Hêche. operational for engineers '' - French Presses polytechnic and academics. 2003.

Eric Jacquet-Lagrèze. '' Programming Linear - Modeling and implemented data-processing '' Collection: P.I.Q. Pocket - Editor: Economica

External bonds

ROADEF : French company of operations research and decision-making aid
INFORMS Resources
Continuation of articles of modeling, optimization and complexity of the algorithms in direct connection with operations research

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