Mathematical modeling for sustainable agri-food supply chain

Recently, industry, suppliers, distributors, academia, governments, and even consumers have focused on agri-food supply chain sustainability, environmental concerns, and managing energy and other resources essential for human survival. A supply chain model is a network of facilities and operations involving processes related to procuring raw materials from suppliers, producing and developing products on production sites, and ultimately distributing products at final consumption destinations. This study aims to propose a multi-stage model for sustainable supply chain network design. After an overview of operations research methods for sustainable supply chain network design, this study proposed a hybrid method based on multi-criteria decision-making (MCDM) and optimization techniques in operations research. The criteria extracted from library resources were selected using the Delphi method in the first step. Then, the criteria for selecting suppliers, transformer sites, and critical distribution hubs were weighted using the best–worst method. After weighing the criteria using the Complex Proportional Assessment of alternatives (COPRAS) technique, eight raw material suppliers, three potential transformer sites, and five main distribution hubs were selected for supply chain network design. The second part presented a multi-objective mixed-integer linear programming model to optimize the designed supply chain network. All three sustainability dimensions, i.e., economic, social, and environmental, were considered in developing the supply chain network. In the economic dimension, we sought to minimize total costs consisting of transportation costs, the cost of construction, maintenance, and closure of transformer and distribution sites, the cost of the capacity change of transformer and distribution sites, and the cost of production. In the social dimension, we sought to maximize the number of job opportunities created in each facility. We sought to minimize carbon and nitrous oxide footprints and water consumption in the environmental dimension. Furthermore, a fourth objective function was presented to minimize product delivery time in addition to the three dimensions of sustainability. Then the proposed mathematical programming model was solved using the LP-metric method, and the necessary comparisons were made between the results. Finally, agri-food industry executives were given a decision-making tool by generating Pareto frontier graphs.