{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,28]],"date-time":"2025-11-28T12:39:24Z","timestamp":1764333564718,"version":"build-2065373602"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2025,6,4]],"date-time":"2025-06-04T00:00:00Z","timestamp":1748995200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,6,4]],"date-time":"2025-06-04T00:00:00Z","timestamp":1748995200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Oper. Res. Forum"],"DOI":"10.1007\/s43069-025-00454-9","type":"journal-article","created":{"date-parts":[[2025,6,4]],"date-time":"2025-06-04T13:41:27Z","timestamp":1749044487000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Fractional Programming-Based Heuristic: An Efficient Method for Marine Inventory Routing Problem"],"prefix":"10.1007","volume":"6","author":[{"given":"Mohammad Nasir","family":"Yarahmadi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Seyed Ali","family":"MirHassani","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Farnaz","family":"Hooshmand","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,6,4]]},"reference":[{"issue":"5","key":"454_CR1","doi-asserted-by":"publisher","first-page":"1019","DOI":"10.1287\/opre.32.5.1019","volume":"32","author":"A Federgruen","year":"1984","unstructured":"Federgruen A, Zipkin P (1984) A combined vehicle routing and inventory. Oper Res 32(5):1019\u20131036","journal-title":"Oper Res"},{"issue":"2\u20133","key":"454_CR2","first-page":"181","volume":"7","author":"B Golden","year":"1984","unstructured":"Golden B, Assad A, Dahl R (1984) Analysis of a large scale vehicle routing problem with an inventory component. Large Scale Syst 7(2\u20133):181\u2013190","journal-title":"Large Scale Syst"},{"key":"454_CR3","doi-asserted-by":"publisher","first-page":"1157","DOI":"10.1007\/s12351-020-00593-3","volume":"22","author":"AS Nikkhah-Qamsari","year":"2022","unstructured":"Nikkhah-Qamsari AS, Hosseini-Motlagh SM, Ghannadpour SF (2022) A column generation approach for an inventory routing problem with fuzzy time windows. Oper Res Int Journal 22:1157\u20131207","journal-title":"Oper Res Int Journal"},{"key":"454_CR4","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1016\/S0377-2217(87)80005-X","volume":"32","author":"DM Miller","year":"1987","unstructured":"Miller DM (1987) An interactive, computer-aided ship scheduling system. Eur J Oper Res 32:363\u2013379","journal-title":"Eur J Oper Res"},{"issue":"1","key":"454_CR5","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1287\/trsc.33.1.3","volume":"33","author":"M Christiansen","year":"1999","unstructured":"Christiansen M (1999) Decomposition of a combined inventory and time constrained ship routing problem. Transp Sci 33(1):3\u201316","journal-title":"Transp Sci"},{"issue":"1","key":"454_CR6","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1016\/j.ejor.2005.06.047","volume":"176","author":"F Al-Khayyal","year":"2007","unstructured":"Al-Khayyal F, Hwang S (2007) Inventory constrained maritime routing and scheduling for multi-commodity liquid bulk, part I: applications and model. Eur J Oper Res 176(1):106\u2013130","journal-title":"Eur J Oper Res"},{"issue":"2","key":"454_CR7","doi-asserted-by":"publisher","first-page":"555","DOI":"10.1016\/j.ijpe.2006.11.008","volume":"107","author":"B Bilgen","year":"2007","unstructured":"Bilgen B, Ozkarahan I (2007) A mixed-integer linear programming model for bulk grain blending and shipping. Int J Prod Econ 107(2):555\u2013571","journal-title":"Int J Prod Econ"},{"issue":"4","key":"454_CR8","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1002\/net.21518","volume":"62","author":"A Agra","year":"2013","unstructured":"Agra A, Andersson H, Christiansen M, Wolsey L (2013) A maritime inventory routing problem: discrete time formulations and valid inequalities. Networks 62(4):297\u2013314","journal-title":"Networks"},{"key":"454_CR9","doi-asserted-by":"publisher","first-page":"350","DOI":"10.1016\/j.ejor.2013.12.013","volume":"235","author":"DJ Papageorgiou","year":"2014","unstructured":"Papageorgiou DJ, Nemhauser GL, Sokol J (2014) MIRPLib \u2013 a library of maritime inventory routing problem instances: survey, core model, and benchmark results. Eur J Oper Res 235:350\u2013366","journal-title":"Eur J Oper Res"},{"key":"454_CR10","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1016\/j.compchemeng.2015.03.005","volume":"77","author":"Y Jiang","year":"2015","unstructured":"Jiang Y, Grossmann IE (2015) Alternative mixed-integer linear programming models of a maritime inventory routing problem. Comput Chem Eng 77:147\u2013161","journal-title":"Comput Chem Eng"},{"key":"454_CR11","doi-asserted-by":"crossref","unstructured":"Sacramento D, Solnon C, and\u00a0 Pisinger D (2020) Constraint programming and local search heuristic: A matheuristic approach for routing and scheduling feeder vessels in multi-terminal ports. In SN Operations Research Forum Vol. 1, p 1-33","DOI":"10.1007\/s43069-020-00036-x"},{"key":"454_CR12","doi-asserted-by":"crossref","unstructured":"Charalambopoulos N, and Nearchou AC (2021) Ship routing using genetic algorithms. In Operations Research Forum Vol. 2, p 1-26","DOI":"10.1007\/s43069-021-00093-w"},{"key":"454_CR13","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1016\/j.cor.2015.01.008","volume":"61","author":"A Agostinho","year":"2015","unstructured":"Agostinho A, Marielle C, Alexandrino D, Lars Magnus H (2015) A maritime inventory routing problem with stochastic sailing and port times. Comput Oper Res 61:18\u201330","journal-title":"Comput Oper Res"},{"key":"454_CR14","doi-asserted-by":"publisher","first-page":"107307","DOI":"10.1016\/j.compchemeng.2021.107307","volume":"149","author":"B Liu","year":"2021","unstructured":"Liu B, Zhang Q, Yuan Z (2021) Two-stage distributionally robust optimization for maritime inventory routing. Comput Chem Eng 149:107307","journal-title":"Comput Chem Eng"},{"issue":"4","key":"454_CR15","doi-asserted-by":"publisher","first-page":"937","DOI":"10.1007\/s11081-018-9383-8","volume":"19","author":"Y Dong","year":"2018","unstructured":"Dong Y, Maravelias CT, Jerome NF (2018) Reoptimization framework and policy analysis for maritime inventory routing under uncertainty. Optim Eng 19(4):937\u2013976","journal-title":"Optim Eng"},{"issue":"1","key":"454_CR16","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1287\/opre.1110.0997","volume":"60","author":"FG Engineer","year":"2012","unstructured":"Engineer FG, Furman KC, Nemhauser GL (2012) A branch-price-and-cut algorithm for single-product maritime inventory routing. Oper Res 60(1):106\u2013122","journal-title":"Oper Res"},{"issue":"2","key":"454_CR17","first-page":"355","volume":"21","author":"KT Uggen","year":"2013","unstructured":"Uggen KT, Fodstan M, Norstebo VS (2013) Using and extending fix-and-relax to solve maritime routing problems. Off J Spanish Soc Stat Oper Res 21(2):355\u2013377","journal-title":"Off J Spanish Soc Stat Oper Res"},{"issue":"4","key":"454_CR18","doi-asserted-by":"publisher","first-page":"825","DOI":"10.1287\/ijoc.2014.0601","volume":"26","author":"DJ Papageorgiou","year":"2014","unstructured":"Papageorgiou DJ, Keha AB, Nemhauser GL, Sokol J (2014) Two-stage decomposition algorithms for single product maritime inventory routing. INFORMS J Comput 26(4):825\u2013847","journal-title":"INFORMS J Comput"},{"issue":"4","key":"454_CR19","doi-asserted-by":"publisher","first-page":"870","DOI":"10.1287\/trsc.2014.0542","volume":"49","author":"DJ Papageorgiou","year":"2015","unstructured":"Papageorgiou DJ, Cheon MS, Nemhauser GL, Sokol J (2015) Approximate dynamic programming for a class of long-horizon maritime inventory routing problems. Transp Sci 49(4):870\u2013885","journal-title":"Transp Sci"},{"key":"454_CR20","doi-asserted-by":"publisher","first-page":"p31","DOI":"10.3390\/systems4030031","volume":"4","author":"VP Rodrigues","year":"2016","unstructured":"Rodrigues VP, Morabito R, Yamashita D, Da Silva JV, Ribas PC (2016) Ship routing with pickup and delivery for a maritime oil transportation system: MIP model and heuristics. Systems 4:p31","journal-title":"Systems"},{"key":"454_CR21","doi-asserted-by":"crossref","unstructured":"Friske MW, and Buriol LS (2017) A relax-and-fix algorithm for a maritime inventory routing problem. In Computational Logistics: 8th International Conference, ICCL 2017, Southampton, UK, October 18-20, Proceedings 8 pp 270-284","DOI":"10.1007\/978-3-319-68496-3_18"},{"issue":"46","key":"454_CR22","doi-asserted-by":"publisher","first-page":"20394","DOI":"10.1021\/acs.iecr.0c03186","volume":"59","author":"S Misra","year":"2020","unstructured":"Misra S, Kapadi M, Gudi RD (2020) Hybrid time-based framework for maritime inventory routing problem. Ind Eng Chem Res 59(46):20394\u201320409","journal-title":"Ind Eng Chem Res"},{"key":"454_CR23","doi-asserted-by":"publisher","first-page":"105051","DOI":"10.1016\/j.cor.2020.105051","volume":"123","author":"L Eide","year":"2020","unstructured":"Eide L, \u00c5rdal GC, Evsikova N, Hvattum LM, Urrutia S (2020) Load-dependent speed optimization in maritime inventory routing. Comput Oper Res 123:105051","journal-title":"Comput Oper Res"},{"key":"454_CR24","doi-asserted-by":"crossref","unstructured":"Friske, MW,\u00a0 and Buriol LS (2020) A multi-start algorithm and a large neighborhood search for a maritime inventory routing problem. In 2020 IEEE congress on evolutionary computation CEC p 1-8","DOI":"10.1109\/CEC48606.2020.9185499"},{"key":"454_CR25","doi-asserted-by":"publisher","first-page":"105520","DOI":"10.1016\/j.cor.2021.105520","volume":"137","author":"MW Friske","year":"2022","unstructured":"Friske MW, Buriol LS, Camponogara E (2022) A relax-and-fix and fix-and-optimize algorithm for a maritime inventory routing problem. Comput Oper Res 137:105520","journal-title":"Comput Oper Res"},{"key":"454_CR26","doi-asserted-by":"publisher","first-page":"106214","DOI":"10.1016\/j.cor.2023.106214","volume":"154","author":"H Shaabani","year":"2023","unstructured":"Shaabani H, Hoff A, Hvattum LM, Laporte G (2023) A matheuristic for the multi-product maritime inventory routing problem. Comput Oper Res 154:106214","journal-title":"Comput Oper Res"},{"key":"454_CR27","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1016\/j.ejor.2017.05.003","volume":"263","author":"CE Andrade","year":"2017","unstructured":"Andrade CE, Ahmed S, Nemhauser GL (2017) A hybrid primal heuristic for finding feasible solutions to mixed integer programs. Eur J Oper Res 263:62\u201371","journal-title":"Eur J Oper Res"},{"key":"454_CR28","doi-asserted-by":"publisher","first-page":"501","DOI":"10.1007\/s10898-017-0560-7","volume":"71","author":"S Cafieri","year":"2018","unstructured":"Cafieri S, D\u2019ambrosio C (2018) Feasibility pump for aircraft deconfliction with speed regulation. J Global Optim 71:501\u2013515","journal-title":"J Global Optim"},{"key":"454_CR29","doi-asserted-by":"publisher","first-page":"105175","DOI":"10.1016\/j.cor.2020.105175","volume":"128","author":"L Assuncao","year":"2021","unstructured":"Assuncao L, Mateus GR (2021) Coupling feasibility pump and large neighborhood search to solve the steiner team orienteering problem. Comput Oper Res 128:105175","journal-title":"Comput Oper Res"},{"key":"454_CR30","doi-asserted-by":"crossref","unstructured":"Yarahmadi MN, MirHassani, SA, and Hooshmand F (2023) A heuristic method to find a quick feasible solution based on the ratio programming. Operational Research, 23:(3):41","DOI":"10.1007\/s12351-023-00777-7"},{"key":"454_CR31","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1007\/s10107-004-0518-7","volume":"102","author":"E Danna","year":"2005","unstructured":"Danna E, Rothberg E, Le Pape C (2005) Exploring relaxation induced neighborhoods to improve MIP solutions. Math Program 102:71\u201390","journal-title":"Math Program"},{"key":"454_CR32","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1007\/s10107-003-0395-5","volume":"98","author":"M Fischetti","year":"2003","unstructured":"Fischetti M, Lodi A (2003) Local branching. Math Program 98:23\u201347","journal-title":"Math Program"},{"key":"454_CR33","first-page":"653","volume":"29","author":"F Glover","year":"2000","unstructured":"Glover F, Laguna M (2000) Fundamentals of scatter search and path relinking. Control Cybern 29:653\u2013684","journal-title":"Control Cybern"},{"issue":"1","key":"454_CR34","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1007\/s10107-004-0570-3","volume":"104","author":"M Fischetti","year":"2005","unstructured":"Fischetti M, Glover F, Lodi A (2005) The feasibility pump. Math Program 104(1):91\u2013104","journal-title":"Math Program"},{"issue":"1","key":"454_CR35","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1016\/j.disopt.2006.10.001","volume":"4","author":"L Bertacco","year":"2007","unstructured":"Bertacco L, Fischetti M, Lodi A (2007) A feasibility pump heuristic for general mixed-integer problems. Discret Optim 4(1):63\u201376","journal-title":"Discret Optim"},{"issue":"1","key":"454_CR36","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1016\/j.disopt.2006.10.004","volume":"4","author":"T Achterberg","year":"2007","unstructured":"Achterberg T, Berthold T (2007) Improving the feasibility pump. Discret Optim 4(1):77\u201386","journal-title":"Discret Optim"},{"issue":"2","key":"454_CR37","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1007\/s12532-009-0007-3","volume":"1","author":"M Fischetti","year":"2009","unstructured":"Fischetti M, Salvagnin D (2009) Feasibility pump 2.0. Math Program Comput 1(2):201\u2013222","journal-title":"Math Program Comput"},{"key":"454_CR38","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1016\/j.cor.2013.09.008","volume":"43","author":"J Naoum-Sawaya","year":"2014","unstructured":"Naoum-Sawaya J (2014) Recursive central rounding for mixed integer programs. Comput Oper Res 43:191\u2013200","journal-title":"Comput Oper Res"},{"key":"454_CR39","doi-asserted-by":"publisher","first-page":"971","DOI":"10.1007\/s13226-021-00102-y","volume":"52","author":"YJ Kim","year":"2021","unstructured":"Kim YJ, Jong YC, Yu JW (2021) A parametric solution method for a generalized fractional programming problem. Indian J Pure Appl Math 52:971\u2013989","journal-title":"Indian J Pure Appl Math"}],"container-title":["Operations Research Forum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s43069-025-00454-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s43069-025-00454-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s43069-025-00454-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T15:57:59Z","timestamp":1760457479000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s43069-025-00454-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,4]]},"references-count":39,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,6]]}},"alternative-id":["454"],"URL":"https:\/\/doi.org\/10.1007\/s43069-025-00454-9","relation":{},"ISSN":["2662-2556"],"issn-type":[{"type":"electronic","value":"2662-2556"}],"subject":[],"published":{"date-parts":[[2025,6,4]]},"assertion":[{"value":"19 September 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 April 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 June 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"78"}}