Management of agricultural systems using mathematical programming

Abstract

The agriculture of Santa Catarina State, South Brazil, is characterised by the predominance of small and diversified farms. The majority of the food for internal consumption (e.g. maize, black beans, rice, milk, cassava, poultry and pork) are produced by small farms, which have a decisive role in the State's agricultural production.

Over recent years, Santa Catarina has been experiencing a fall in rural population, and the State's rural income per capita/year has been decreasing in relative terms, compared to the urban areas. These factors threaten the future of the small farms, and are accentuated by the limited opportunities for credit, agricultural insurance, land ownership as well as restricted cultural, health and educational services, which diminish the attractions for rural life.

Traditionally, the small farmers in planning year-to-year adjustments use only their intuition, supported by poor informal arithmetic or budget calculations. New technologies (coming from research, for example) are incorporated into specific aspects of the farm, without considering the relationships to other factors within the whole farming system. Even the recorded data about the performance of existing farm plans, when they exist, is disorganised and inaccurate. Therefore, the plan which results from this process will seldom be the best available. This results in inefficient use of the farm's resources.

However, it follows that it is important for Santa Catarina Society that the small farms maintain and increase the production of food for internal consumption, in the cheapest possible way. To do so it is necessary to have sound management, which makes efficient use of the farm's resources, guarantees better returns to the farmers and reasonable prices to the consumers.

This research reviewed farm management analytical techniques using the system's approach, and a computer-based mathematical programming model was developed. The intention was to create a model to assist decisions about the most efficient allocation of the farm resources in order to maximise farmers' objectives in the agricultural context of Santa Catarina.

The study takes the following form:

(1) A description of the agricultural aspects of Santa Catarina.

(2) A review of the relevant literature about farm management analytical techniques and the systems approach.

(3) Development of a mathematical programming model incorporating the information gained in the above studies.

(4) Experimentation with the model in the management of the case study farming system.

(5) Discussion of the results.

A multi-period linear programming mathematical model was developed incorporating a cash flow format. The experimentation placed emphasis on four aspects considered the most important for this study: (A) gross margins variations; (B and C) changes in the cost and availability of capital and labour; and (D) risk programming, which was formally incorporated into the model, including an analysis of the trade-off between risk and profit.

The modelling exercise and results indicated that the multi-period L.P. model developed can be useful as a decision-support tool in the management of farming systems. The methodology has proven to be readily applied and appears to have the potential for widespread use in optimising management systems in the agricultural context of Santa Catarina.