Mathematical Programming Model for Multi-Objective Smallholder Farming Systems in North-East Nigeria

Farm households in North-east Nigeria (NEN) are mostly smallholders engaging predominantly in crop production. Provision of household food requirements is a vital objective in smallholder agriculture. However, its inclusion as a constraint in cropping patterns can affect farm-level returns associated with lower food crop value. A representative sample of 120 farmers was taken to model the farming system in NEN. The purpose was to evaluate the effect of food security as a constraint on farm income. Twenty (20) cropping activities were identified in the farming system: six sole cropping and fourteen inter-cropping patterns. Nine most popular cropping activities, practiced by 82.5% of the respondents, were selected as cropping activities for the model. The inter-cropping activities consist of food and cash crops. Farm level Mathematical programming techniques were constructed to model the farming system under choice constraints. First, a baseline model, the conventional linear programming (LP) technique, was constructed to model the system as a profit maximization problem. A combination of nine (9) most popular cropping activities and resources used were incorporated in the baseline model. The model selected Maize and Bambara nuts as the optimal activity to be cultivated on 1.3 ha with a profit of ₦734,763.73. The profit from the optimal activity in the baseline model was compared with that of the activity with the highest profit in the current plan; the result suggested a potential 21% increase in profit. Input resources such as land, fertilizer, and agrochemicals were not fully utilized as indicated in their respective slack values. Labour for processing and harvesting legumes was the binding resource with shadow prices in the optimal plan. This was due to capital constraints to hire. The second technique, however, presented a multi-objective programming (MOP) technique, with multiple model outputs to reflect farmers varying objectives such as profit maximization, food security objective, and their respective resource requirements. Two different solutions were obtained from this model: one with only maize as a food security constraint and the second with maize and beans as food security constraints. The estimated profit obtained from the two solutions in the MOLP final plans revealed 7% and 21% reduction in net profit, respectively, relative to the optimal solution obtained in the baseline profitability model. Therefore, this study recommends the extension of both LP and MOP results for consideration as a flexible decision-making support tool for the farming system in the study area. In the sensitivity analysis, the interaction between input (credit) and output was demonstrated so that intended decision-makers could understand the response of credit to farm profit. It is therefore recommended that government and non-government agencies should structure accessible and affordable sources of farm finance for farmers in the study area.