Multi-Objective Optimisation of Production Mix in a Multi-Product Agro-Processing Company in Benue State

This research applies multi-objective optimisation to the production mix problem of a multi-product agro-processing company in Benue State, North Central Nigeria, simultaneously optimising revenue, resource utilisation, and environmental impact objectives. Benue State is Nigeria's most productive agricultural state, supplying significant volumes of soybeans, sorghum, cassava, and yam to industrial processors; however, multi-product processors face complex trade-offs in allocating limited processing capacity, storage, and labour across competing product lines with different margin and market demand profiles. This study formulates a multi-objective linear programming model with three objective functions: maximisation of total contribution margin, maximisation of labour utilisation, and minimisation of total production-related effluent generation. The model is solved using the weighted sum method and the epsilon-constraint method to generate the Pareto-optimal frontier. Company data covering twelve months of production, cost, and effluent records are used to parameterise the model, and uncertainty in selling prices and demand forecasts is addressed through robust optimisation extensions. Results reveal significant trade-offs between the revenue maximisation and environmental minimisation objectives, with the Pareto frontier providing management with a decision-support tool for navigating these trade-offs transparently. Implementation guidance is developed for integrating the model into monthly production planning meetings. Keywords: multi-objective optimisation, production mix, Pareto frontier, agro-processing, Benue State