Articulo en ingles de aplicación lineal a las empresas

ARTICULO EN INGLES DE PROGRAMACION LINEAL.

MARLY CONSTANZA CASTAÑEDA ESCOBAR

COD: 20151134610

PRESENTADO A: ALFONSO MANRRIQUE

DOCENTE AREA DE PROGRAMACION LINEAL.

UNIVERSIDAD SURCOLOMBIANA

FACULTAD DE ECONOMIA Y ADMISTRACION

PROGRAMA DE ADMINISTRACION DE EMPRESAS

NEIVA-HUILA

2018

Alvarado Boirivant,

 THE LINEAR PROGRAMMING APPLICATION OF THE SMALL AND MEDIUM COMPANIES

Reflexiones, vol. 88, núm. 1, 2009

ISSN: 1021-1209

 Universidad de Costa Rica

THE LINEAR PROGRAMMING APPLICATION OF THE SMALL

AND MEDIUM COMPANIES

This article assesses the application of a mathematical method, Linear Programming, for providing supporting information in managerial decision making processes of small and medium-sized businesses (PYMES in Spanish). These productive entities are efficient stimulants in social development, but the technique of Linear Programming has not been utilized to its maximum potential by developers and advisors of the PYMES sector. This research, then, attempts to discover, in detail, the methodological peculiarities of this technique through the presentation of a model generated for one small productive business. The results will provide clear evidence that Linear Programming constitutes a powerful analytical instrument for members of the PYMES.

The times of food crisis, of crisis global financial and global poverty increase, results of the globalized neoliberal process based on obedience to the guidelines that dictated and continue to dictate financial institutions international, force us today to raise the urgent rescue of the SME sector as strategic instrument for the development of poor and developing countries. With this initiative favors the generation of employment, the democratization of opportunities and participation of citizens, that is, social inclusion. This rescue work is urgent in the face of the permanent threat of transnational corporations, whose strategic plans include the attack aimed at the extinction of SMEs, even in many of these large companies that position is explicit in its mission. Under these conditions, efforts must be made from various fronts to strengthen SMEs, namely: credit support, insurance, training, incentives, technology, roads, collection centers, markets, etc. But an important front must be formed by a wide group of advisors and extension agents, who promote the use of mathematical methods that have been left for years in the abandonment and that have shown in other latitudes and in diverse occasions, that are important base for the taking of right decisions: we are talking in particular about linear programming applied in small and medium enterprises to minimize their costs or maximize their income, without ever losing the perspective that social development is a right of peoples and the distribution of wealth It must be fairer every day. This paper presents, in the first place, a general description of the mathematical method called Linear Programming, then its importance is detailed and the procedure performed to build a real linear programming model of income maximization generated is shown as an example. by the author. Finally, the interpretation and discussion of the results related to decision making is presented.

Linear programming and its importance

According to Beneke and Winterboer (1984: 5) the mathematical methods of optimization (those that allow to identify the maximum or minimum values ​​of certain mathematical expressions) reached a remarkable development in the decade of the 40s. These authors affirm that already in 1945 Stiegler defines and solves the particular problem of obtaining the minimum cost diet for cattle feed. From 1949 an extraordinary number of publications appears on the theoretical basis of linear programming as well as its applications to the various branches of the economy. They deserve special mention, for the decisive influence they had on the improvement and dissemination of these mathematical techniques, the work and activities of the Cowles Commission for research in econoomics, the Rand Corporation, the Mathematics Department of Princeton University and the Carnegie Institute of Technology. Moya (1998: 63) mentions that it was George B. Dantzig and another group of associates who, in 1947, following the request of military authorities of the United States government, undertook to investigate how mathematics could be applied. statistics to solve problems of planning and programming for purely military purposes. In that same year Dantzig and his collaborators pose for the first time the basic mathematical structure of the problem of linear programming. In the beginning linear programming was known as "Programming in a Linear Structure". According to Anderson and others (2004: 224), in 1948 Tjalling Koopmans told Dantzig that the name was too long and that it was convenient to change it, before which Dantzig agreed and the name was replaced by the "Linear Programming", which it is used even today. In general terms, it can be said that any phenomenon involving a certain number of non-negative variables (that is, variables whose value is positive or zero), which can be linked to each other through inequality or equality relationships and that reflect the limitations or restrictions that the phenomenon presents in order to optimize an objective, can be formulated as a mathematical programming model. If both the constraints and the objective function can be stated by linear expressions, we are facing a particular field of mathematical programming called "linear programming". In this case the word "programming" does not refer to computer programming; but it is used as a synonym for planning. Linear programming deals with the planning of activities to obtain a optimal result, that is, the result that best reaches the specified goal (according to the mathematical model) among the solution alternatives. For Weber (1984: 718), the problem of linear programming deals with the maximization or minimization of a linear function of several primary variables, called objective function, subject to a set of linear equalities or inequalities called constraints, with the additional condition that none of the variables can be negative. This last condition can be avoided, when the problem requires it, through the ingenious artifice of expressing the variable of interest as the difference of two non-negative variables. In summary, it is stated that linear programming is a mathematical method of problem solving where the objective is to optimize (maximize or minimize) a result by selecting the values ​​of a set of decision variables, respecting restrictions related to resource availability , technical specifications, or other conditions that limit the freedom of choice. As a case of special interest we have that through linear programming we can represent a production system through a model or matrix that includes: - Costs and revenues generated per unit of activity (objective function). - Contributions and requirements of inputs and outputs per unit of each activity considered (input / output coefficients). - Availability of resources, technical and business specifications to be respected (values ​​on the right side of the restrictions). In particular, linear programming is a mathematical method that allows analyzing and choosing the best among many alternatives. In general terms we can think of the lineal programming as a means to determine the best way to distribute a limited amount of resources in order to achieve an expressive objective in maximizing or minimizing a certain amount. The general model of a linear programming problem consists of two very important parts: the objective function and the constraints.

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