Hybrid meta-heuristic algorithms for optimising a sustainable agricultural supply chain network considering CO2 emissions and water consumption

In this research, a new mixed-integer linear programming (MILP) formulation for the production-distribution-routing problem is developed in a sustainable agricultural product supply chain network (SAPSCN) considering CO2 emission. The objective functions of the SAPSCN model seek to minimise the economic effects containing total cost in SAPSCN and environmental impacts including production and operation emissions, water consumption in production, operational water consumption, and transportation emission, as well as to maximise social impacts including on the number of the created works. Due to the complexity and NP-hardness of the SAPSCN formulation, four multi-objective meta-heuristic algorithms were applied, and two new hybrid meta-heuristic algorithms were developed. To assess the efficiency of the suggested meta-heuristic algorithms, various test instances were used to solve the proposed model and comparisons and sensitivity analyses were carried out with various criteria. A real case study is provided to validate the mathematical model. Finally, the results of the hybrid simulated annealing and particle swarm optimisation algorithm emphasises that it is more robust than other proposed algorithms to solve the problem in a reasonable time.