{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T04:34:41Z","timestamp":1772771681758,"version":"3.50.1"},"reference-count":51,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2017,10,13]],"date-time":"2017-10-13T00:00:00Z","timestamp":1507852800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2019,2]]},"DOI":"10.1007\/s00500-017-2866-2","type":"journal-article","created":{"date-parts":[[2017,10,13]],"date-time":"2017-10-13T08:38:17Z","timestamp":1507883897000},"page":"1375-1391","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["A bi-objective fleet size and mix green inventory routing problem, model and solution method"],"prefix":"10.1007","volume":"23","author":[{"given":"Mehdi","family":"Alinaghian","sequence":"first","affiliation":[]},{"given":"Mohsen","family":"Zamani","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,10,13]]},"reference":[{"key":"2866_CR1","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1287\/ijoc.2013.0550","volume":"26","author":"Y Adulyasak","year":"2013","unstructured":"Adulyasak Y, Cordeau J-F, Jans R (2013) Formulations and branch-and-cut algorithms for multivehicle production and inventory routing problems. INFORMS J Comput 26:103\u2013120","journal-title":"INFORMS J Comput"},{"key":"2866_CR2","doi-asserted-by":"publisher","first-page":"582","DOI":"10.1016\/j.tre.2009.06.005","volume":"46","author":"Javid A Ahmadi","year":"2010","unstructured":"Ahmadi Javid A, Azad N (2010) Incorporating location, routing and inventory decisions in supply chain network design. Transp Res Part E Logist Transp Rev 46:582\u2013597","journal-title":"Transp Res Part E Logist Transp Rev"},{"key":"2866_CR3","first-page":"33","volume":"1","author":"M Alinaghian","year":"2012","unstructured":"Alinaghian M, Ghazanfari M, Salamatbakhsh A, Norouzi N (2012) A new competitive approach on multi-objective periodic vehicle routing problem. Int J Appl Oper Res 1:33\u201341","journal-title":"Int J Appl Oper Res"},{"key":"2866_CR4","doi-asserted-by":"publisher","first-page":"59","DOI":"10.5195\/EMAJ.2014.31","volume":"3","author":"N Ayd\u0131n","year":"2014","unstructured":"Ayd\u0131n N (2014) A genetic algorithm on inventory routing problem. EMAJ Emerg Mark J 3:59\u201366","journal-title":"EMAJ Emerg Mark J"},{"key":"2866_CR5","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1287\/inte.13.6.4","volume":"13","author":"WJ Bell","year":"1983","unstructured":"Bell WJ, Dalberto LM, Fisher ML, Greenfield AJ, Jaikumar R, Kedia P et al (1983) Improving the distribution of industrial gases with an on-line computerized routing and scheduling optimizer. Interfaces 13:4\u201323","journal-title":"Interfaces"},{"key":"2866_CR6","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1016\/j.trc.2011.06.003","volume":"27","author":"L Bertazzi","year":"2013","unstructured":"Bertazzi L, Bosco A, Guerriero F, Lagan\u00e0 D (2013) A stochastic inventory routing problem with stock-out. Transp Res Part C Emerg Technol 27:89\u2013107","journal-title":"Transp Res Part C Emerg Technol"},{"key":"2866_CR7","doi-asserted-by":"publisher","first-page":"488","DOI":"10.1287\/trsc.1030.0054","volume":"38","author":"AM Campbell","year":"2004","unstructured":"Campbell AM, Savelsbergh MW (2004) A decomposition approach for the inventory-routing problem. Transp Sci 38:488\u2013502","journal-title":"Transp Sci"},{"key":"2866_CR8","unstructured":"Chrysochoou EC, Ziliaskopoulos AK, Lois A (2015) An exact algorithm for the stochastic inventory routing problem with transhipment. In: Transportation research board 94th annual meeting"},{"key":"2866_CR9","volume-title":"Multiobjective programming and planning","author":"JL Cohon","year":"2013","unstructured":"Cohon JL (2013) Multiobjective programming and planning. Courier Corporation, North Chelmsford"},{"key":"2866_CR10","volume-title":"Search methodologies","author":"K Deb","year":"2014","unstructured":"Deb K (2014) Multi-objective optimization. In: Burke E, Kendall G (eds) Search methodologies. Springer, Boston, MA"},{"key":"2866_CR11","doi-asserted-by":"publisher","first-page":"182","DOI":"10.1109\/4235.996017","volume":"6","author":"K Deb","year":"2002","unstructured":"Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6:182\u2013197","journal-title":"IEEE Trans Evol Comput"},{"key":"2866_CR12","doi-asserted-by":"publisher","first-page":"464","DOI":"10.1016\/j.ejor.2013.08.002","volume":"232","author":"E Demir","year":"2014","unstructured":"Demir E, Bekta\u015f T, Laporte G (2014) The bi-objective pollution-routing problem. Eur J Oper Res 232:464\u2013478","journal-title":"Eur J Oper Res"},{"key":"2866_CR13","doi-asserted-by":"publisher","first-page":"701","DOI":"10.1007\/s00500-014-1294-9","volume":"19","author":"W Deng","year":"2015","unstructured":"Deng W, Zhao H, Liu J, Yan X, Li Y, Yin L et al (2015) An improved CACO algorithm based on adaptive method and multi-variant strategies. Soft Comput 19:701\u2013713","journal-title":"Soft Comput"},{"key":"2866_CR14","doi-asserted-by":"crossref","unstructured":"Deng W, Zhao H, Zou L, Li G, Yang X, Wu D (2017a) A novel collaborative optimization algorithm in solving complex optimization problems. Soft Comput 21:4387\u20134398","DOI":"10.1007\/s00500-016-2071-8"},{"key":"2866_CR15","doi-asserted-by":"crossref","unstructured":"Deng W, Zhao H, Yang X, Xiong J, Sun M, Li B (2017b) Study on an improved adaptive PSO algorithm for solving multi-objective gate assignment. Appl Soft Comput 59:288\u2013302","DOI":"10.1016\/j.asoc.2017.06.004"},{"key":"2866_CR16","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1016\/0305-0548(84)90007-8","volume":"11","author":"B Golden","year":"1984","unstructured":"Golden B, Assad A, Levy L, Gheysens F (1984) The fleet size and mix vehicle routing problem. Comput Oper Res 11:49\u201366","journal-title":"Comput Oper Res"},{"key":"2866_CR17","doi-asserted-by":"publisher","first-page":"1646","DOI":"10.1109\/TNNLS.2016.2544779","volume":"28","author":"B Gu","year":"2017","unstructured":"Gu B, Sun X, Sheng VS (2017) Structural minimax probability machine. IEEE Trans Neural Netw Learn Syst 28:1646\u20131656","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"2866_CR18","doi-asserted-by":"crossref","unstructured":"Halim H, Moin N (2014) Solving inventory routing problem with backordering using Artificial Bee Colony. In: International conference on industrial engineering and engineering management (IEEM), 2014 IEEE, pp 913\u2013917","DOI":"10.1109\/IEEM.2014.7058771"},{"key":"2866_CR19","doi-asserted-by":"publisher","first-page":"580","DOI":"10.1109\/TEVC.2002.804320","volume":"6","author":"K-H Han","year":"2002","unstructured":"Han K-H, Kim J-H (2002) Quantum-inspired evolutionary algorithm for a class of combinatorial optimization. IEEE Trans Evol Comput 6:580\u2013593","journal-title":"IEEE Trans Evol Comput"},{"key":"2866_CR20","doi-asserted-by":"publisher","first-page":"156","DOI":"10.1109\/TEVC.2004.823467","volume":"8","author":"K-H Han","year":"2004","unstructured":"Han K-H, Kim J-H (2004) Quantum-inspired evolutionary algorithms with a new termination criterion, Hε gate, and two-phase scheme. IEEE Trans Evol Comput 8:156\u2013169","journal-title":"IEEE Trans Evol Comput"},{"key":"2866_CR21","doi-asserted-by":"publisher","first-page":"598","DOI":"10.1016\/j.tre.2010.01.006","volume":"46","author":"S-H Huang","year":"2010","unstructured":"Huang S-H, Lin P-C (2010) A modified ant colony optimization algorithm for multi-item inventory routing problems with demand uncertainty. Transp Res Part E Logist Transp Rev 46:598\u2013611","journal-title":"Transp Res Part E Logist Transp Rev"},{"key":"2866_CR22","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1007\/s10845-009-0285-7","volume":"22","author":"F Jolai","year":"2011","unstructured":"Jolai F, Amalnick MS, Alinaghian M, Shakhsi-Niaei M, Omrani H (2011) A hybrid memetic algorithm for maximizing the weighted number of just-in-time jobs on unrelated parallel machines. J Intell Manuf 22:247\u2013261","journal-title":"J Intell Manuf"},{"key":"2866_CR23","volume-title":"An introduction to quantum computing","author":"P Kaye","year":"2007","unstructured":"Kaye P, Laflamme R, Mosca M (2007) An introduction to quantum computing. Oxford University Press, Oxford"},{"key":"2866_CR24","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1016\/j.trb.2014.09.008","volume":"70","author":"\u00c7 Ko\u00e7","year":"2014","unstructured":"Ko\u00e7 \u00c7, Bekta\u015f T, Jabali O, Laporte G (2014) The fleet size and mix pollution-routing problem. Transp Res Part B Methodol 70:239\u2013254","journal-title":"Transp Res Part B Methodol"},{"key":"2866_CR25","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1016\/j.knosys.2016.10.016","volume":"115","author":"Y Kong","year":"2017","unstructured":"Kong Y, Zhang M, Ye D (2017) A belief propagation-based method for task allocation in open and dynamic cloud environments. Knowl Based Syst 115:123\u2013132","journal-title":"Knowl Based Syst"},{"key":"2866_CR26","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1007\/978-3-642-35966-8_4","volume-title":"Dynamics in Logistics","author":"H Kopfer","year":"2013","unstructured":"Kopfer H (2013) Emissions minimization vehicle routing problem in dependence of different vehicle classes. In: Kreowski H-J, Scholz-Reiter B, Thoben K-D (eds) Dynamics in Logistics. Springer, Berlin, Heidelberg, pp 49\u201358"},{"key":"2866_CR27","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1016\/j.trd.2013.04.001","volume":"23","author":"YJ Kwon","year":"2013","unstructured":"Kwon YJ, Choi YJ, Lee DH (2013) Heterogeneous fixed fleet vehicle routing considering carbon emission. Transp Res Part D Transp Environ 23:81\u201389","journal-title":"Transp Res Part D Transp Environ"},{"key":"2866_CR28","first-page":"22","volume":"12","author":"HL Lee","year":"2008","unstructured":"Lee HL, Seungjin W (2008) The whose, where and how of inventory control design. Supply Chain Manag Rev 12:22\u201329","journal-title":"Supply Chain Manag Rev"},{"key":"2866_CR29","doi-asserted-by":"publisher","first-page":"4002","DOI":"10.1002\/sec.1582","volume":"9","author":"Q Liu","year":"2016","unstructured":"Liu Q, Cai W, Shen J, Fu Z, Liu X, Linge N (2016) A speculative approach to spatial-temporal efficiency with multi-objective optimization in a heterogeneous cloud environment. Secur Commun Netw 9:4002\u20134012","journal-title":"Secur Commun Netw"},{"key":"2866_CR30","first-page":"455","volume":"213","author":"G Mavrotas","year":"2009","unstructured":"Mavrotas G (2009) Effective implementation of the \n                    \n                      \n                    \n                    $$\\varepsilon $$\n                    \n                      \n                        \u03b5\n                      \n                    \n                  -constraint method in multi-objective mathematical programming problems. Appl Math Comput 213:455\u2013465","journal-title":"Appl Math Comput"},{"key":"2866_CR31","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1016\/j.ijpe.2013.09.005","volume":"157","author":"SMJ Mirzapour Al-e-hashem","year":"2014","unstructured":"Mirzapour Al-e-hashem SMJ, Rekik Y (2014) Multi-product multi-period Inventory Routing Problem with a transshipment option: a green approach. Int J Prod Econ 157:80\u201388","journal-title":"Int J Prod Econ"},{"key":"2866_CR32","doi-asserted-by":"publisher","first-page":"334","DOI":"10.1016\/j.ijpe.2010.06.012","volume":"133","author":"N Moin","year":"2011","unstructured":"Moin N, Salhi S, Aziz N (2011) An efficient hybrid genetic algorithm for the multi-product multi-period inventory routing problem. Int J Prod Econ 133:334\u2013343","journal-title":"Int J Prod Econ"},{"key":"2866_CR33","unstructured":"Montgomery DC (2017) Design and analysis of experiments. Wiley"},{"key":"2866_CR34","doi-asserted-by":"publisher","first-page":"74","DOI":"10.1016\/j.tre.2015.04.010","volume":"80","author":"F Niakan","year":"2015","unstructured":"Niakan F, Rahimi M (2015) A multi-objective healthcare inventory routing problem; a fuzzy possibilistic approach. Transp Res Part E Logist Transp Rev 80:74\u201394","journal-title":"Transp Res Part E Logist Transp Rev"},{"key":"2866_CR35","doi-asserted-by":"crossref","unstructured":"Platel MD, Schliebs S, Kasabov N (2007) A versatile quantum-inspired evolutionary algorithm. In: IEEE congress on evolutionary computation, 2007. CEC 2007, pp 423\u2013430","DOI":"10.1109\/CEC.2007.4424502"},{"key":"2866_CR36","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1016\/j.ijpe.2006.08.023","volume":"112","author":"B Raa","year":"2008","unstructured":"Raa B, Aghezzaf E-H (2008) Designing distribution patterns for long-term inventory routing with constant demand rates. Int J Prod Econ 112:255\u2013263","journal-title":"Int J Prod Econ"},{"key":"2866_CR37","doi-asserted-by":"publisher","first-page":"384","DOI":"10.1287\/trsc.2013.0503","volume":"49","author":"JG Rakke","year":"2014","unstructured":"Rakke JG, Andersson H, Christiansen M, Desaulniers G (2014) A new formulation based on customer delivery patterns for a maritime inventory routing problem. Transp Sci 49:384\u2013401","journal-title":"Transp Sci"},{"key":"2866_CR38","doi-asserted-by":"publisher","unstructured":"Rong H, Ma T, Tang M, Cao J (2017) A novel subgraph \n                    \n                      \n                    \n                    $$K^{+}$$\n                    \n                      \n                        \n                          K\n                          +\n                        \n                      \n                    \n                  -isomorphism method in social network based on graph similarity detection. Soft Comput. doi:\n                    10.1007\/s00500-017-2513-y","DOI":"10.1007\/s00500-017-2513-y"},{"key":"2866_CR39","doi-asserted-by":"publisher","first-page":"1744","DOI":"10.1016\/j.cor.2005.05.036","volume":"34","author":"M Savelsbergh","year":"2007","unstructured":"Savelsbergh M, Song J-H (2007) Inventory routing with continuous moves. Comput Oper Res 34:1744\u20131763","journal-title":"Comput Oper Res"},{"key":"2866_CR40","doi-asserted-by":"crossref","unstructured":"Sbihi A, Eglese RW (2007) Combinatorial optimization and green logistics. 4OR Q J Oper Res 5:99\u2013116","DOI":"10.1007\/s10288-007-0047-3"},{"key":"2866_CR41","unstructured":"Schott JR (1995) Fault tolerant design using single and multicriteria genetic algorithm optimization, TIC Document1995"},{"key":"2866_CR42","unstructured":"Shao S, Huang GQ (2014) A SHIP inventory routing problem with heterogeneous vehicles under order-up-to level policies. In: Proceedings of IIE annual conference, p 1106"},{"key":"2866_CR43","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1287\/trsc.37.1.40.12823","volume":"37","author":"Z-JM Shen","year":"2003","unstructured":"Shen Z-JM, Coullard C, Daskin MS (2003) A joint location-inventory model. Transp Sci 37:40\u201355","journal-title":"Transp Sci"},{"key":"2866_CR44","doi-asserted-by":"publisher","first-page":"118","DOI":"10.1016\/j.ijpe.2015.03.008","volume":"164","author":"M Soysal","year":"2015","unstructured":"Soysal M, Bloemhof-Ruwaard JM, Haijema R, van der Vorst JG (2015) Modeling an Inventory Routing Problem for perishable products with environmental considerations and demand uncertainty. Int J Prod Econ 164:118\u2013133","journal-title":"Int J Prod Econ"},{"key":"2866_CR45","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1287\/trsc.26.3.171","volume":"26","author":"P Trudeau","year":"1992","unstructured":"Trudeau P, Dror M (1992) Stochastic inventory routing: route design with stockouts and route failures. Transp Sci 26:171\u2013184","journal-title":"Transp Sci"},{"key":"2866_CR46","doi-asserted-by":"publisher","unstructured":"Xue Y, Jiang J, Zhao B, Ma T (2017) A self-adaptive artificial bee colony algorithm based on global best for global optimization. Soft Comput. doi:\n                    10.1007\/s00500-017-2547-1","DOI":"10.1007\/s00500-017-2547-1"},{"key":"2866_CR47","doi-asserted-by":"publisher","first-page":"570","DOI":"10.1016\/S0377-2217(01)00345-9","volume":"143","author":"P-C Yang","year":"2002","unstructured":"Yang P-C, Wee H-M (2002) A single-vendor and multiple-buyers production-inventory policy for a deteriorating item. Eur J Oper Res 143:570\u2013581","journal-title":"Eur J Oper Res"},{"key":"2866_CR48","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1007\/s10732-010-9136-0","volume":"17","author":"G Zhang","year":"2011","unstructured":"Zhang G (2011) Quantum-inspired evolutionary algorithms: a survey and empirical study. J Heuristics 17:303\u2013351","journal-title":"J Heuristics"},{"key":"2866_CR49","first-page":"1","volume":"2012","author":"J Zhang","year":"2012","unstructured":"Zhang J, Wang W, Zhao Y, Cattani C (2012) Multiobjective quantum evolutionary algorithm for the vehicle routing problem with customer satisfaction. Math Probl Eng 2012:1\u201319","journal-title":"Math Probl Eng"},{"key":"2866_CR50","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1016\/j.swevo.2011.03.001","volume":"1","author":"A Zhou","year":"2011","unstructured":"Zhou A, Qu B-Y, Li H, Zhao S-Z, Suganthan PN, Zhang Q (2011) Multiobjective evolutionary algorithms: a survey of the state of the art. Swarm Evol Comput 1:32\u201349","journal-title":"Swarm Evol Comput"},{"key":"2866_CR51","unstructured":"Zitzler E, Thiele L (1998) Multi-objective optimization using evolutionary algorithms\u2014a comparative case study. In: International conference on parallel problem solving from nature. Springer, Berlin, Heidelberg, pp 292\u2013301"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00500-017-2866-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-017-2866-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-017-2866-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,2,6]],"date-time":"2019-02-06T01:07:39Z","timestamp":1549415259000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00500-017-2866-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,10,13]]},"references-count":51,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2019,2]]}},"alternative-id":["2866"],"URL":"https:\/\/doi.org\/10.1007\/s00500-017-2866-2","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,10,13]]},"assertion":[{"value":"13 October 2017","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"The authors declare that there is no conflict of interests regarding the publication of this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This article does not contain any studies with human participants or animals performed by any of the authors.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}}]}}