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For several years now, Bordeaux's vineyards have suffered from what would appear to be an interminable crisis. Some analysts view overproduction as the cause. Others blame the product Bordeaux puts out, decrying its lack of adaptation to new consumer expectations. What is true is that Bordeaux producers do not tend to spontaneously adopt a market orientation. However, faced with a dilemma that seems to be getting worse and worse, many are starting to seek their salvation in marketing. The purpose of this paper is to address these issues.

The present article uses a series of case studies covering regions outside of Bordeaux to find concrete answers to these questions. As a methodology, these case studies have been used to illustrate different ways to develop production and sales.

Consolidating the production, increasing the sales forces efforts, reducing the number of intermediaries between production and consumption, maintaining a niche position on the global market are one of the main findings of this paper and practical implication.

Using case studies and not quantitative approach represents both limits of the approach and innovative methodology that permits rich comparison with local practices.

Analyzes a local crisis thanks to external case studies.

To use a new method based on α‐dense curved for solving problems of operational research.

The method of global optimization (called Alienor) is used for solving problems involving integer or mixed variables. A reducing transformation using α‐dense curves allows to transforms a n‐variables problem into a problem of a single variable.

Extends the basic method valid for continuous variables to problems involving integer, Boolean or mixed variables. All problems of operational research, linear or nonlinear, may be easily solved by or technique based on α‐dense curves (filling a n‐dimensional space). Industrial problems can be quickly solved by this technique obtaining the best solutions.

This method is deduced from the original works of Y. Cherruault and colleagues about global optimization and α‐dense curves. It proposes new techniques for solving operational research problems.

Some results concerning the existence of α‐dense curves with minimal length are given. This type of curves used in the reducing transformation called Alienor was invented by Cherruault and Guillez. They have been applied to global optimization in the following way: a multivariable optimization problem is transformed in an optimization problem depending on a single variable. Then this idea was extended by Cherruault and his team for obtaining general classes of reducing transformations having minimal properties (length of the α‐dense curves, minimization of the calculus time, etc.).

This paper presents an efficient algorithm for solving general constrained optimization problems that arise in operational research (OR).

An unified approach is accomplished by converting the constrained optimization problem into an unconstrained one and by using Alienor method coupled to the new optimization preserving operator^* (OPO^*) technique for the resolution.

A new algorithm for solving general constrained optimization problems with continuous objective function contributes to research in this area and in particular, to applications to OR.

Some improvements could probably be obtained at calculation time. We will in future work, develop an adaption of these methods and techniques to optimization problems with mixed variables or with integer and Boolean variables.

The new algorithm can be advantageously compared with other methods such as generalized reduced gradient. Small‐sized numerical examples are given.

A new algorithm is given which guarantees a global optimal solution is easily obtained in all cases.

To show the usefulness of the Alienor method when applied to the global optimization problems that depend on large number of variables.

The approach is to use reducing transformations. The first is due to Cherruault and the second to Mora.

It was found that the Alienor method was very efficient and reliable in solving global optimization problems of many variables. Results produced to confirm this conclusion.

The numerical results presented showed that the Alienor method was suitable for finding global minimum even in the case of a very large number of variables. The research provides a new methodology for solving such problems.

No other method, we believe, can obtain such results in so short a time for hundreds or even thousands of variables.

The new approach relies on the originality of both the Cherruault and the Mora transformations and their earlier invention of the Alienor method.

To use α‐dense curves for solving an optimization problem with constraints involving integer variables.

α‐dense curves are curves in Rⁿ depending on a single variable able to approximate a compact K⊂Rⁿ with precision α. It is proposed α‐dense curves allowing to obtain all integer points of a compact domain in Rⁿ. This transformation allows to transform the functional into a new function depending on a single variable. Then we can calculate the global optimum of the functional.

Alienor method invented by Y. Cherruault allows to find global minimum of n‐continuous variables functions. Here, α‐dense curves are extended to problems involving integer variables. The curves pass through all points having integer coordinates and belonging to the compact domain. By this method integer programming (nonlinear) problems arising in operational research have been easily and exactly solved.

It is the first time the technique based on α‐dense curves to optimization problems with integer variables are extended. This approach is totally original and allows to solve very easily and fastly nonlinear optimization problems.

To introduce Optimization‐Preserving‐Operators (O‐P‐Os), which are operators that are defined on classes of real functions that depend on a single variable, and allow us to eliminate local optima and to preserve global optima.

Outline a new method to build O‐P‐Os. These are introduced as O‐P‐O* and lead to a new approach for solving global optimization problems.

It was found that classical discretization methods for obtaining optimum of one variable function was too time‐consuming. The simple method introduced provided solutions to the test functions chosen as examples. The solutions were provided in a short time.

Provides new tools for mathematical programming and in particular the global optimization problems. The O‐P‐O* introduced innovative technique for solving such problems.

O‐P‐O* produces solutions to global optimization problems in a much improved time. The algorithm derived, and the steps for its operation proved on implementation, the efficiency of the new method. This was demonstrated by numerical results for selected functions obtained using microcomputer systems.

Provides new way of solving global optimization problems.

To introduce an algorithm to solve inequalities defined by real functions on a certain compact set D of a general metric space (E, D). The device is based on α‐dense curves.

The solution of inequalities using α‐dense curves and also an approach to a global optimization technique, similarly obtained to that of the inequalities.

A new method is presented. The algorithm for solving inequalities is described which is based on a proven result. Inequalities of n‐variable dependence are reduced by transformation using α‐dense curves.

The research is a continuation of studies that resulted in a new method called Alienor for solving global optimization problems associated with multi‐variable functions.

Based on earlier research by the authors α‐dense curves have been used which allow the transformation of a n‐variables global optimization problem into a one‐variable global one. This paper gives a new method for quickly solving the one‐variable problem.

Most of the known optimization methods for a given continuous function f defined on a compact set H = Π_i=1,..,n[a_i,b_i] require strong conditions on f. In the early 1980s, Cherruault proposed a method, called ALIENOR which was able to reduce the multidimensional optimization problem to another one‐dimensional optimization: the optimization of the restriction f_h^* of f to some adequate α‐dense curve h into the domain H. The characterization, the generation of such curves as well as the theoretic calculation times associated with them, have been studied previously by the authors. Their consequences and the general problem concerning the error in the approximation to global minimum of f and the minimization of the error itself, that such reduction produces, will be the subject of this paper.