{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:06:58Z","timestamp":1760144818806,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,5,24]],"date-time":"2024-05-24T00:00:00Z","timestamp":1716508800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"project AI4Life","award":["DSAIPA\/DS\/0054\/2019"],"award-info":[{"award-number":["DSAIPA\/DS\/0054\/2019"]}]},{"name":"projects LAETA Base Funding","award":["DSAIPA\/DS\/0054\/2019"],"award-info":[{"award-number":["DSAIPA\/DS\/0054\/2019"]}]},{"name":"LAETA Programatic Funding","award":["DSAIPA\/DS\/0054\/2019"],"award-info":[{"award-number":["DSAIPA\/DS\/0054\/2019"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics"],"abstract":"<jats:p>This paper proposes a novel approach to the fuzzy newsvendor problem for inventory management applications. The main contributions of the paper are the following: a new credibility estimation is proposed, to explore the neighborhood around the most impactful demand scenarios; a simulation procedure was designed for the different demand scenarios, which allows comparison of the proposed approach with classical and fuzzy multi-item newsvendor problems; a modified genetic algorithm (GA) is introduced to ameliorate previous genetic algorithms in both the generation and evaluation of solutions. The new formulation of the fuzzy newsvendor problem, together with the modified GA, were shown to improve the average profit by up to 55% in problems with low-budget scenarios.<\/jats:p>","DOI":"10.3390\/math12111652","type":"journal-article","created":{"date-parts":[[2024,5,24]],"date-time":"2024-05-24T08:30:22Z","timestamp":1716539422000},"page":"1652","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Fuzzy Multi-Item Newsvendor Problem: An Application to Inventory Management"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8030-4746","authenticated-orcid":false,"given":"Jo\u00e3o M. C.","family":"Sousa","sequence":"first","affiliation":[{"name":"IDMEC, Instituto Superior T\u00e9cnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-3100-3021","authenticated-orcid":false,"given":"Rodrigo","family":"Lu\u00eds","sequence":"additional","affiliation":[{"name":"IDMEC, Instituto Superior T\u00e9cnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal"}]},{"given":"Rui Mirra","family":"Santos","sequence":"additional","affiliation":[{"name":"IDMEC, Instituto Superior T\u00e9cnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5053-8077","authenticated-orcid":false,"given":"Lu\u00eds","family":"Mendon\u00e7a","sequence":"additional","affiliation":[{"name":"IDMEC, Escola Superior N\u00e1utica Infante D. Henrique (ENIDH), 2770-058 Pa\u00e7o de Arcos, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7961-1004","authenticated-orcid":false,"given":"Susana M.","family":"Vieira","sequence":"additional","affiliation":[{"name":"IDMEC, Instituto Superior T\u00e9cnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2024,5,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Choi, T.M. (2012). Handbook of Newsvendor Problems. International Series in Operations Research & Management Science, Springer.","DOI":"10.1007\/978-1-4614-3600-3"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1187","DOI":"10.1111\/risa.13988","article-title":"Medical capacity investment for epidemic disease: The effects of policymaker\u2019s confidence and public trust","volume":"43","author":"Chen","year":"2023","journal-title":"Risk Anal."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1126\/science.42.1077.248","article-title":"The Mathematical Theory of Investment","volume":"42","author":"Wilson","year":"1888","journal-title":"Science"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Mu, M., Chen, J., Yang, Y., and Guo, J. (2019, January 28\u201330). The Multi\u2013product Newsvendor Problem: Review and Extensions. Proceedings of the 2019 6th International Conference on Behavioral, Economic and Socio-Cultural Computing, Beijing, China.","DOI":"10.1109\/BESC48373.2019.8962977"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/0272-6963(95)00019-O","article-title":"The multi-product multi-constraint newsboy problem: Applications, formulation and solution","volume":"13","author":"Lau","year":"1995","journal-title":"J. Oper. Manag."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/0377-2217(95)00192-1","article-title":"The newsstand problem: A capacitated multiple-product single-period inventory problem","volume":"94","author":"Lau","year":"1996","journal-title":"Eur. J. Oper. Res."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3001","DOI":"10.1016\/j.apm.2010.12.018","article-title":"Jointly pricing and ordering for a multi\u2013product multi\u2013constraint newsvendor problem with supplier quantity discounts","volume":"35","author":"Shi","year":"2011","journal-title":"Appl. Math. Model."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"7674027","DOI":"10.1155\/2016\/7674027","article-title":"Multiproduct multiperiod newsvendor problem with dynamic market efforts","volume":"2016","author":"Shi","year":"2016","journal-title":"Discret. Dyn. Nat. Soc."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1016\/0925-5273(96)00014-X","article-title":"Fuzzy models for the newsboy problem","volume":"45","year":"1996","journal-title":"Int. J. Prod. Econ."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/j.amc.2005.11.123","article-title":"Fuzzy multi\u2013product constraint newsboy problem","volume":"180","author":"Shao","year":"2006","journal-title":"Appl. Math. Comput."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1273","DOI":"10.1016\/j.mcm.2011.03.038","article-title":"Meta-heuristic algorithms for solving a fuzzy single-period problem","volume":"54","author":"Taleizadeh","year":"2011","journal-title":"Math. Comput. Model."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Sousa, J.M.C., and Kaymak, U. (2002). Fuzzy Decision Making in Modeling and Control, World Scientific Inc.","DOI":"10.1142\/9789812777911"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/S0377-2217(97)00173-2","article-title":"A stochastic inventory problem with fuzzy shortage cost","volume":"106","author":"Ishii","year":"1998","journal-title":"Eur. J. Oper. Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/S0165-0114(02)00104-5","article-title":"Fuzzy models for single-period inventory problem","volume":"132","author":"Li","year":"2002","journal-title":"Fuzzy Sets Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"915","DOI":"10.1016\/j.mcm.2004.08.007","article-title":"A single-period inventory model with fuzzy random variable demand","volume":"41","author":"Dutta","year":"2005","journal-title":"Math. Comput. Model."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1502","DOI":"10.1016\/j.camwa.2006.04.029","article-title":"An inventory model for single-period products with reordering opportunities under fuzzy demand","volume":"53","author":"Dutta","year":"2007","journal-title":"Comput. Math. Appl."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"588","DOI":"10.1016\/j.asoc.2017.01.013","article-title":"Fuzzy inventory models: A comprehensive review","volume":"55","author":"Shekarian","year":"2017","journal-title":"Appl. Soft Comput."},{"key":"ref_18","first-page":"200","article-title":"A distribution-free newsboy problem with fuzzy-random demand","volume":"13","author":"Adhikary","year":"2018","journal-title":"Int. J. Manag. Sci. Eng. Manag."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1007\/s41066-019-00186-2","article-title":"Single stage fuzzy supply chain model with Weibull distributed demand for milk commodities","volume":"6","author":"Bhosale","year":"2021","journal-title":"Granul. Comput."},{"key":"ref_20","first-page":"39","article-title":"Single cycle supply chain coordination model for fuzzy stochastic demand of perishable items","volume":"17","author":"Latpate","year":"2020","journal-title":"Iran. J. Fuzzy Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2341","DOI":"10.1287\/mnsc.2015.2248","article-title":"Supply chain contract design under financial constraints and bankruptcy costs","volume":"62","author":"Kouvelis","year":"2016","journal-title":"Manag. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1235","DOI":"10.1287\/mnsc.2015.2173","article-title":"The impact of demand uncertainty on consumer subsidies for green technology adoption","volume":"62","author":"Cohen","year":"2016","journal-title":"Manag. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1287\/opre.2018.1757","article-title":"The big Data newsvendor: Practical insights from machine learning","volume":"67","author":"Ban","year":"2019","journal-title":"Oper. Res."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Levine, S.D., and Chen, K.Y. (2018, January 8\u201313). Neural Network Modeling of Gist and Verbatim in Business Decision Making. Proceedings of the International Joint Conference on Neural Networks (IJCNN), Rio de Janeiro, Brazil.","DOI":"10.1109\/IJCNN.2018.8489065"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1287\/msom.2017.0669","article-title":"Who should finance the supply chain? Impact of credit ratings on supply chain decisions","volume":"20","author":"Kouvelis","year":"2018","journal-title":"Manuf. Serv. Oper. Manag."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"159","DOI":"10.25103\/jestr.105.20","article-title":"Recent trends of the most used metaheuristic techniques for distribution network reconfiguration","volume":"10","author":"Candelo","year":"2017","journal-title":"J. Eng. Sci. Technol. Rev."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Liu, B. (2002). Theory and Practice of Uncertain Programming. Studies in Fuzziness and Soft Computing, Springer.","DOI":"10.1007\/978-3-7908-1781-2"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Liu, B. (2004). Uncertainty Theory. Studies in Fuzziness and Soft Computing, Springer.","DOI":"10.1007\/978-3-540-39987-2"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1109\/TFUZZ.2002.800692","article-title":"Expected value of fuzzy variable and fuzzy expected value models","volume":"10","author":"Liu","year":"2002","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/j.ijpe.2003.09.004","article-title":"Exact, approximate, and generic iterative models for the multi-product Newsboy problem with budget constraint","volume":"91","author":"Montanari","year":"2004","journal-title":"Int. J. Prod. Econ."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"283","DOI":"10.2307\/2282878","article-title":"Analysis of Inventory Systems","volume":"59","author":"Hadley","year":"1964","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1145\/321127.321128","article-title":"Outline for a Logical Theory of Adaptive Systems","volume":"9","author":"Holland","year":"1962","journal-title":"J. ACM (JACM)"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1016\/j.ijpe.2004.08.008","article-title":"An analysis of the multi-product newsboy problem with a budget constraint","volume":"97","author":"Montanari","year":"2005","journal-title":"Int. J. Prod. Econ."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Jang, J., Sun, C., and Mizutani, E. (1997). Neuro-Fuzzy and Soft Computing-A Computational Approach to Learning and Machine Intelligence, Prentice Hall.","DOI":"10.1109\/TAC.1997.633847"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1016\/0377-2217(92)90210-Z","article-title":"Reformulating nonlinear combinatorial optimization problems for higher computational efficiency","volume":"58","author":"Oral","year":"1992","journal-title":"Eur. J. Oper. Res."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"870","DOI":"10.1134\/S1995080217050031","article-title":"Numerical solution of huge-scale quasiseparable optimization problems","volume":"38","author":"Andrianov","year":"2017","journal-title":"Lobachevskii J. Math."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2923","DOI":"10.1016\/j.ins.2011.02.022","article-title":"A note on Z\u2013numbers","volume":"181","author":"Zadeh","year":"2011","journal-title":"Inf. Sci."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"27","DOI":"10.11648\/j.ijmfs.20190501.15","article-title":"G-Numbers: Importance-necessity concept in uncertain environment","volume":"5","author":"Ghoushchi","year":"2019","journal-title":"Int. J. Manag. Fuzzy Syst."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1016\/j.ins.2019.01.006","article-title":"R-numbers, a new risk modeling associated with fuzzy numbers and its application to decision making","volume":"483","author":"Seiti","year":"2019","journal-title":"Inf. Sci."}],"container-title":["Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2227-7390\/12\/11\/1652\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:48:08Z","timestamp":1760107688000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2227-7390\/12\/11\/1652"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,24]]},"references-count":39,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2024,6]]}},"alternative-id":["math12111652"],"URL":"https:\/\/doi.org\/10.3390\/math12111652","relation":{},"ISSN":["2227-7390"],"issn-type":[{"type":"electronic","value":"2227-7390"}],"subject":[],"published":{"date-parts":[[2024,5,24]]}}}