Linear Programming in Agriculture: Case Study in Region of Development South-Mountenia

Introduction

The paper investigates the economical activity of a vegetal farm and to optimize its profit using linear programming method. The research question is whether after applying the econometric model the returns of the economical activity is higher or not.

Optimizing crops’ structure using linear programming is widely applied in economical research. As it is all known, in literature linear programming (Kantorovich, 1987; Dantzig, 1963; von Neumann, 1954) as a specific methodology was developed by Leonid Kantorovich, a Russian mathematician who developed linear programming problems in 1939, George B. Dantzig, who published the simplex method in 1947, and John von Neumann, who developed the theory of the duality.

The work of Dantzig (1963) is recognised to be the most applicable. His original example of finding the best assignment of 70 people to 70 jobs exemplifies the usefulness of linear programming. With the help of computers, it takes only a moment to find the optimum solution by posing the problem as a linear program and applying the Simplex algorithm. The theory behind linear programming drastically reduces the number of possible optimal solutions that must be checked.

Nowadays, many changes have transformed the landscape of optimization methods and software since Dantzig, because of the Internet and the World Wide Web facilities. Gill et al. (2008) considers that it is no longer necessary for the critical mass of people to be co-located, since researchers and users can exchange code electronically as well as run problems on a machine in a remote location using software written by someone else. Even so, Dantzig’s concept of a systems optimization laboratory lives on.

Linear programming is used in all fields, including agriculture. Montazemi and Wright (1982) applied mathematical programming in agriculture, as an example of the use of operational research in developing countries. Researchers (Voicu et al., 2010; Dobre et al., 2011; Istudor et al., 2007) show the Romanian contribution to the field.

This paper is a practical approach to the method of linear programming. The relevance of outcomes consists in the opportunity of using this methodology for maximizing profits of farms, by changing the structure of crops.

Material and Method

To optimize farm profits, the linear programming method to data supplied by a farmer has been applied. Linear programming is a mathematical method for determining a way to achieve the best outcome (maximum profit or lowest cost) in a given mathematical model for some list of requirements represented as linear relationships. Linear programming is a specific case of mathematical programming. More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints.

The econometric model maximizes the profit function and it is expressed by the following relationship

max. f(x) = , j=1, 2, . . ., n

The model constrains are:

• 1.
  

  • 2.x_j

Of which:

• x_j – area of crop j

• p_j – profit of crop j

• a_ij – resource consumption per unit of production for crop j;

• bi – the volume of resources;

• j – set of crops;

• i – volume of crops.

Data have been collected from a farm whose object of activity is complex, containing numerous branches (crops), planted within ecological system. A diversified business structure has the advantage of reducing the effects of risk and uncertainty, but it cannot be overlooked the pronounced fragmentation of the area cultivated.