Addressing a set of meta-heuristics to solve a multi-objective model for closed-loop citrus supply chain considering CO2 emissions

Abstract Nowadays, the agricultural supply chain as one of the key fields of food production is considered which has recently attracted much attention from researchers. This paper focuses on optimizing a closed-loop citrus supply chain. To this end, a multi-objective mathematical model is formulated that it attempts to minimize total costs, to maximize demands' responsiveness, and to minimize CO2 emissions as environmental damages. To solve the proposed model, five meta-heuristic algorithms include a multi-objective version of the recently published algorithm called tree growth algorithm (MOTGA) and four well-known algorithms called NSGA-II, NRGA, MOKA, and MOSA are utilized. It should be noted that these algorithms are tuned using the Taguchi method to achieve better performance and these are validated using the e-constraint method in small size examples. It shows that the e-constraint cannot solve the large size problems and it implies the NP-hardness of the problem. Moreover, the MOTGA is selected as the best approach with the least distance from the ideal point. Finally, to more measurement, a sensitivity analysis is performed and the results confirmed the efficiency of the proposed algorithms. Based on the results, it is shown that multiple transportation vehicles can reduce CO2 emissions and improved all objective functions’ values. In addition, considering multiple vehicles improved responsiveness by about 14%. So, considering two new assumptions include CO2 emissions and multiple vehicles in this model, can lead to improve demand responsiveness and emissions reductions.