An efficient solution method for an agri-fresh food supply chain: hybridization of Lagrangian relaxation and genetic algorithm.

In the traditional agri-fresh food supply chain (AFSC), geographically dispersed small farmers transport their products individually to the market for sale. This leads to a higher transportation cost, which is the primary cause of farmers' low profitability. This paper formulates a traditional product movement problem in AFSC. First, the aggregate product movement model is combined with the vehicle routing model to redesign an existing AFSC (the ETKA Company; the most extensive domestic agri-fresh food supply chain in Iran) based on the available data. For the four-echelon, multi-period supply chain under investigation, a mixed integer linear programming (MILP) model is developed for the location-inventory-routing problem of perishable products via considering the clustering of farmers to minimize the total distribution cost. Considering the complexity of the problem, an efficient and effective "matheuristic" is introduced based on hybridizing the Lagrangian relaxation and genetic algorithm (GA). The solution obtained by the proposed "matheuristic" algorithm is robust and efficient in comparison with an exact solver, GA, and the Lagrangian relaxation approach individually. The comparison analysis reveals that the location-inventory-routing model is efficient, leading to a reduction in total distribution cost by 33% compared to the existing supply chain. Finally, the findings encourage further development and application of the proposed "matheuristic" to solve other complicated location-inventory-routing problems heuristically.