Investigating a citrus fruit supply chain network considering CO₂ emissions using meta-heuristic algorithms

According to the increasing carbon dioxide released through vehicles and the shortage of water resources, decision-makers decided to combine the environmental and economic effects in the Agri-Food Supply Chain Network (AFSCN) in developing countries. This paper focuses on the citrus fruit supply chain network. The novelty of this study is the proposal of a mathematical model for a three-echelon AFSCN considering simultaneously CO₂ emissions, coefficient water, and time window. Additionally, a bi-objective mixed-integer non-linear programming is formulated for production–distribution-inventory-allocation problem. The model seeks to minimise the total cost and CO⁺ emission simultaneously. To solve the multi-objective model in this paper, the Augmented Epsilon-constraint method is utilised for small- and medium-sized problems. The Augmented Epsilon-constraint method is not able to solve large-scale problems due to its high computational time. This method is a well-known approach to dealing with multi-objective problems. It allows for producing a set of Pareto solutions for multi-objective problems. Multi-Objective Ant Colony Optimisation, fast Pareto genetic algorithm, non-dominated sorting genetic algorithm II, and multi-objective simulated annealing are used to solve the model. Then, a hybrid meta-heuristic algorithm called Hybrid multi-objective Ant Colony Optimisation with multi-objective Simulated Annealing (HACO-SA) is developed to solve the model. In the HACO-SA algorithm, an initial temperature and temperature reduction rate is utilised to ensure a faster convergence rate and to optimise the ability of exploitation and exploration as input data of the SA algorithm. The computational results show the superiority of the Augmented Epsilon-constraint method in small-sized problems, while HACO-SA indicates that is better than the suggested original algorithms in the medium- and large-sized problems.