Optimisation of Crop Rotation Schedules on Smallholder Farms in Benue State Using Integer Programming

This study applies integer programming to the optimisation of crop rotation schedules for smallholder farmers in Benue State, North Central Nigeria, a state widely described as the food basket of the nation due to its diverse agricultural output including yam, sorghum, rice, soybean, cassava, and vegetables. Smallholder farmers in the state typically make crop sequencing decisions based on tradition and incomplete information about nutrient cycling, pest management, and market price seasonality, leading to sub-optimal use of finite land resources. A binary integer programming model is formulated to schedule crops across five seasons over a three-year planning horizon on a representative 2-hectare smallholder plot, with constraints capturing nitrogen fixation and depletion dynamics, pest break requirements, seasonal labour availability, and minimum subsistence food production levels. Input data including crop-specific yields, input costs, market prices, and nitrogen balance coefficients are obtained from the Benue State Agricultural Development Programme's extension records and published agronomic research. The model is solved using branch-and-bound algorithms implemented in the Python PuLP library. Results demonstrate that the optimised rotation schedule increases expected net farm income by approximately 28 percent relative to the traditional rotation practice documented in surveyed farms, primarily through improved exploitation of legume nitrogen fixation credits and better alignment of cash crops with peak seasonal prices. Keywords: integer programming, crop rotation, smallholder farming, optimisation, Benue State