MATHEMATICAL MODEL FOR A CROP ROTATION PROBLEM

S. Alonso, D. Ayla, A. Jhones, Juan M. Otero Pereira, G. Gomez
The production on a small area of different vegetables with periodic demands to be satisfied is the problem dealt with in this paper.

Area H is assumed to be divided into unit-fields. The estimated yield of each crop in each field is known.

A mathematical model for the production plan was needed.

The tasks are :

  • To determine the area to be allocated weekly to each crop in such a way that the fixed demands could be satisfied.
  • To describe the weekly - schedule of different agricultural operations ( soil preparation, the seeds, sowing and recolection of the harvest )
  • To allocate each crop on the appropiate area according to the neighborhood restrictions with others crops in time and/or space:
  • To have a description of the state of each field at each time
  • To have a description of the initial conditions of H for the next crop.

The dynamic and combinatorial character of the system is evident.

A mathematical model with two phases is proposed. A Linear Programming problem is constructed to solve the first two questions.

A discret simulation model represents the dynamic character of the system. A clock-variable is increased in fixed intervals ( each of them representing a week ). For each week t the set Al (t) of available fields and the sets Cp(t,j) of the possible products to be sowed in field j are described.

A binary model is formulated by using the sets Cp(t,j) in order to guarantee the allocation of each crop according to the neighborhood restrictions in space.

The change of the state of the system according to the conditions of each stage and dialog procedure complete the simulation of the crop period.

The computational support of this model includes :

  • the Data-bases in order to store the necessary information on :
  • "history" and state of each field.
  • preparation time, cost yields, vegetative cycles, etc. of each crop product.
Alonso, S., Ayla, D., Jhones, A., Otero Pereira, Juan M. and Gomez, G. (1990). MATHEMATICAL MODEL FOR A CROP ROTATION PROBLEM. Acta Hortic. 267, 379-386
DOI: 10.17660/ActaHortic.1990.267.44
https://doi.org/10.17660/ActaHortic.1990.267.44

Acta Horticulturae