Crop succession requirements in agricultural production planning

A method is proposed to handle crop succession requirements when determining the cultivated areas of n crops for a planning period of T years. For each year, the decision variables represent the areas where a sequence of m crops is cultivated, m ≥ 1. Here, m + 1 is the length of the longest forbidden sequence of crops not containing any forbidden subsequences. The crop succession constraints are linear in the decision variables. For each year, the number of n decision variables may be reduced by forming suitable combinations of crop sequences. For this purpose, an algorithm is presented. Also, multi-year linear programming models for farm production planning containing crop succession constraints are considered. It is shown that, under some regularity conditions, a stationary cropping plan is an optimal solution of such a model. Finally, it is discussed how to determine forbidden crop sequences not containing forbidden subsequences, when a collection of forbidden sequences is given. AMS 2000 subject classifications. Primary 65K05; secondary 90B10, 90B30, 90C05.