Optimization model to support sustainable crop planning for reducing unfairness among farmers

Agri-food production must increase while food waste needs to be reduced for improving the position of farmers. To do so it is necessary to sustainably manage agri-food supply chains beginning with the crop planning decisions. Although the centralized approach has usually been adopted for this purpose, it can lead to unfair solutions due to inequitable distribution of profits among farmers causing their unwillingness to collaborate in the implementation of decisions made. To solve this, in this paper a novel centralized multi-objective mathematical programming model is proposed to support the sustainable crop planning definition for a region that jointly optimize three objectives aligned to the sustainability aspects: supply chain profits maximization (economic objective), waste minimization (environmental objective) and unfairness among farmers minimization (social objective), being the last two objectives novel in the crop planning literature. It has also shown the conflicting nature of the three objectives finding trade-offs among them. Other novelties of this proposal are: (1) anticipation of operative decisions (such as harvest, transport, sale, clearance sale, waste and unmet demand) when defining the crop planning, (2) possibility of clearing the oversupply of crops as a means of increasing the farmers’ profits and reducing waste, and (3) the modelling of a agri-food supply chain characterized by the lack of intermediaries between farmers and retailers, fostering the freshest product delivery and farmers’ power position. The model is solved by applying the weighted sum method concluding that the crop waste generated along the chain and the unfairness among farmers can be considerably reduced by little decreasing the optimal SC profits.