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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 CO\n                    <jats:sub>2<\/jats:sub>\n                    emissions, coefficient water, and time window. Additionally, a bi-objective mixed-integer non-linear programming is formulated for production\u2013distribution-inventory-allocation problem. The model seeks to minimise the total cost and CO\n                    <jats:sup>+<\/jats:sup>\n                    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.\n                  <\/jats:p>","DOI":"10.1007\/s10479-022-05005-7","type":"journal-article","created":{"date-parts":[[2022,10,13]],"date-time":"2022-10-13T06:02:39Z","timestamp":1665640959000},"page":"547-603","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Investigating a citrus fruit supply chain network considering CO2 emissions using meta-heuristic algorithms"],"prefix":"10.1007","volume":"354","author":[{"given":"Fariba","family":"Goodarzian","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8062-7123","authenticated-orcid":false,"given":"Vikas","family":"Kumar","sequence":"additional","affiliation":[]},{"given":"Peiman","family":"Ghasemi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,10,13]]},"reference":[{"key":"5005_CR1","doi-asserted-by":"publisher","first-page":"158","DOI":"10.1016\/j.jclepro.2015.06.082","volume":"112","author":"R Accorsi","year":"2016","unstructured":"Accorsi, R., Cholette, S., Manzini, R., Pini, C., & Penazzi, S. 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