{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T19:48:53Z","timestamp":1780602533512,"version":"3.54.1"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2025,2,9]],"date-time":"2025-02-09T00:00:00Z","timestamp":1739059200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,2,9]],"date-time":"2025-02-09T00:00:00Z","timestamp":1739059200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["72002065"],"award-info":[{"award-number":["72002065"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Comb Optim"],"published-print":{"date-parts":[[2025,3]]},"DOI":"10.1007\/s10878-025-01260-z","type":"journal-article","created":{"date-parts":[[2025,2,9]],"date-time":"2025-02-09T18:45:01Z","timestamp":1739126701000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Solving the optimal order quantity with unknown parameters for products with stock-dependent demand and variable holding cost rate"],"prefix":"10.1007","volume":"49","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6562-0089","authenticated-orcid":false,"given":"Zhanbing","family":"Guo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yejie","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,2,9]]},"reference":[{"key":"1260_CR1","doi-asserted-by":"publisher","first-page":"170","DOI":"10.1016\/j.cie.2016.02.009","volume":"94","author":"HK Alfares","year":"2016","unstructured":"Alfares HK, Ghaithan AM (2016) Inventory and pricing model with price-dependent demand, time-varying holding cost, and quantity discounts. Comput Ind Eng 94:170\u2013177","journal-title":"Comput Ind Eng"},{"key":"1260_CR2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2023.113511","volume":"172","author":"J Andaluz","year":"2023","unstructured":"Andaluz J, Elsadany A, Jarne G (2023) Dynamic behavior in a cournot duopoly with social responsibility. Chaos Solitons Fractals 172:113511","journal-title":"Chaos Solitons Fractals"},{"key":"1260_CR3","volume":"432","author":"S Askar","year":"2022","unstructured":"Askar S (2022) On the dynamics of cournot duopoly game with private firms: investigations and analysis. Appl Math Comput 432:127354","journal-title":"Appl Math Comput"},{"issue":"9","key":"1260_CR4","doi-asserted-by":"publisher","first-page":"823","DOI":"10.1057\/jors.1988.142","volume":"39","author":"RC Baker","year":"1988","unstructured":"Baker RC, Urban TL (1988) A deterministic inventory system with an inventory-level-dependent demand rate. J Oper Res Soc 39(9):823\u2013831","journal-title":"J Oper Res Soc"},{"issue":"5","key":"1260_CR5","doi-asserted-by":"publisher","first-page":"630","DOI":"10.1287\/mnsc.1040.0228","volume":"50","author":"A Balakrishnan","year":"2004","unstructured":"Balakrishnan A, Pangburn MS, Stavrulaki E (2004) Stack them high, let \u2019em fly: lot-sizing policies when inventories stimulate demand. Manag Sci 50(5):630\u2013644","journal-title":"Manag Sci"},{"issue":"03","key":"1260_CR6","doi-asserted-by":"publisher","first-page":"2150035","DOI":"10.1142\/S0217595921500354","volume":"39","author":"Y Barron","year":"2022","unstructured":"Barron Y (2022) A replenishment inventory model with a stock-dependent demand and age-stock-dependent cost functions in a random environment. Asia-Pacific J Oper Res 39(03):2150035","journal-title":"Asia-Pacific J Oper Res"},{"issue":"3","key":"1260_CR7","doi-asserted-by":"publisher","first-page":"731","DOI":"10.1007\/s10479-024-06016-2","volume":"337","author":"GI Bischi","year":"2024","unstructured":"Bischi GI, Baiardi LC, Lamantia F, Radi D (2024) Nonlinear dynamics and game-theoretic modeling in economics and finance. Ann Oper Res 337(3):731\u2013737","journal-title":"Ann Oper Res"},{"issue":"3","key":"1260_CR8","doi-asserted-by":"publisher","first-page":"582","DOI":"10.1287\/msom.2018.0764","volume":"22","author":"P Boada-Collado","year":"2020","unstructured":"Boada-Collado P, Mart\u00ednez-de Alb\u00e9niz V (2020) Estimating and optimizing the impact of inventory on consumer choices in a fashion retail setting. Manuf Serv Oper Manag 22(3):582\u2013597","journal-title":"Manuf Serv Oper Manag"},{"key":"1260_CR9","doi-asserted-by":"publisher","first-page":"102","DOI":"10.1016\/j.cor.2019.04.019","volume":"109","author":"M Braglia","year":"2019","unstructured":"Braglia M, Castellano D, Marrazzini L, Song D (2019) A continuous review,(Q, r) inventory model for a deteriorating item with random demand and positive lead time. Comput Oper Res 109:102\u2013121","journal-title":"Comput Oper Res"},{"key":"1260_CR10","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ijpe.2014.07.002","volume":"155","author":"LE C\u00e1rdenas-Barr\u00f3n","year":"2014","unstructured":"C\u00e1rdenas-Barr\u00f3n LE, Chung K-J, Trevi\u00f1o-Garza G (2014) Celebrating a century of the economic order quantity model in honor of ford whitman harris. Int J Prod Econ 155:1\u20137","journal-title":"Int J Prod Econ"},{"issue":"2","key":"1260_CR11","doi-asserted-by":"publisher","first-page":"481","DOI":"10.1016\/j.ejor.2004.06.029","volume":"170","author":"H-C Chang","year":"2006","unstructured":"Chang H-C, Ouyang L-Y, Wu K-S, Ho C-H (2006) Integrated vendor-buyer cooperative inventory models with controllable lead time and ordering cost reduction. Eur J Oper Res 170(2):481\u2013495","journal-title":"Eur J Oper Res"},{"issue":"11","key":"1260_CR12","doi-asserted-by":"publisher","first-page":"5108","DOI":"10.1287\/mnsc.2019.3474","volume":"66","author":"B Chen","year":"2020","unstructured":"Chen B, Chao X (2020) Dynamic inventory control with stockout substitution and demand learning. Manag Sci 66(11):5108\u20135127","journal-title":"Manag Sci"},{"issue":"4","key":"1260_CR13","first-page":"1035","volume":"67","author":"B Chen","year":"2019","unstructured":"Chen B, Chao X, Ahn H-S (2019) Coordinating pricing and inventory replenishment with nonparametric demand learning. Oper Res 67(4):1035\u20131052","journal-title":"Oper Res"},{"key":"1260_CR14","doi-asserted-by":"publisher","first-page":"208","DOI":"10.1016\/j.ijpe.2018.11.013","volume":"208","author":"C-H Chuang","year":"2019","unstructured":"Chuang C-H, Zhao Y (2019) Demand stimulation in finished-goods inventory management: empirical evidence from general motors dealerships. Int J Prod Econ 208:208\u2013220","journal-title":"Int J Prod Econ"},{"key":"1260_CR15","volume":"374","author":"L Cui","year":"2020","unstructured":"Cui L, Deng J, Liu R, Xu D, Zhang Y, Xu M (2020) A stochastic multi-item replenishment and delivery problem with lead-time reduction initiatives and the solving methodologies. Appl Math Comput 374:125055","journal-title":"Appl Math Comput"},{"issue":"1","key":"1260_CR16","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1016\/j.ejor.2016.06.073","volume":"257","author":"G Dobson","year":"2017","unstructured":"Dobson G, Pinker EJ, Yildiz O (2017) An EOQ model for perishable goods with age-dependent demand rate. Eur J Oper Res 257(1):84\u201388","journal-title":"Eur J Oper Res"},{"issue":"3","key":"1260_CR17","doi-asserted-by":"publisher","first-page":"940","DOI":"10.1016\/j.ejor.2021.04.023","volume":"296","author":"L Feng","year":"2022","unstructured":"Feng L, Wang W-C, Teng J-T, C\u00e1rdenas-Barr\u00f3n LE (2022) Pricing and lot-sizing decision for fresh goods when demand depends on unit price, displaying stocks and product age under generalized payments. Eur J Oper Res 296(3):940\u2013952","journal-title":"Eur J Oper Res"},{"issue":"3","key":"1260_CR18","doi-asserted-by":"publisher","first-page":"467","DOI":"10.1016\/S0377-2217(97)00086-6","volume":"105","author":"B Giri","year":"1998","unstructured":"Giri B, Chaudhuri K (1998) Deterministic models of perishable inventory with stock-dependent demand rate and nonlinear holding cost. Eur J Oper Res 105(3):467\u2013474","journal-title":"Eur J Oper Res"},{"key":"1260_CR19","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2022.106080","volume":"150","author":"Z Guo","year":"2023","unstructured":"Guo Z, Wang H (2023) Implications on managing inventory systems for products with stock-dependent demand and nonlinear holding cost via the adaptive EOQ policy. Comput Oper Res 150:106080","journal-title":"Comput Oper Res"},{"issue":"1","key":"1260_CR20","first-page":"42","volume":"34","author":"S Khalilpourazari","year":"2017","unstructured":"Khalilpourazari S, Pasandideh SHR (2017) Multi-item EOQ model with nonlinear unit holding cost and partial backordering: moth-flame optimization algorithm. J Ind Prod Eng 34(1):42\u201351","journal-title":"J Ind Prod Eng"},{"issue":"2","key":"1260_CR21","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1016\/j.jretai.2008.04.003","volume":"84","author":"MA Koschat","year":"2008","unstructured":"Koschat MA (2008) Store inventory can affect demand: empirical evidence from magazine retailing. J Retail 84(2):165\u2013179","journal-title":"J Retail"},{"key":"1260_CR22","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2020.105078","volume":"124","author":"J Liu","year":"2020","unstructured":"Liu J, Pang Z, Qi L (2020) Dynamic pricing and inventory management with demand learning: a bayesian approach. Comput Oper Res 124:105078","journal-title":"Comput Oper Res"},{"key":"1260_CR23","doi-asserted-by":"publisher","first-page":"610","DOI":"10.1016\/j.apm.2022.07.002","volume":"111","author":"J Ma","year":"2022","unstructured":"Ma J, Wang Z (2022) Optimal pricing and complex analysis for low-carbon apparel supply chains. Appl Math Model 111:610\u2013629","journal-title":"Appl Math Model"},{"key":"1260_CR24","doi-asserted-by":"publisher","DOI":"10.1016\/j.dajour.2023.100288","volume":"8","author":"RK Mallick","year":"2023","unstructured":"Mallick RK, Patra K, Mondal SK (2023) A new economic order quantity model for deteriorated items under the joint effects of stock dependent demand and inflation. Decis Anal J 8:100288","journal-title":"Decis Anal J"},{"issue":"1","key":"1260_CR25","first-page":"2022808","volume":"10","author":"SH Nita","year":"2023","unstructured":"Nita SH, Rabari K, Patel E (2023) Greening efforts and deteriorating inventory policies for price-sensitive stock-dependent demand. Int J Syst Sci Oper Logist 10(1):2022808","journal-title":"Int J Syst Sci Oper Logist"},{"issue":"1","key":"1260_CR26","doi-asserted-by":"publisher","first-page":"294","DOI":"10.1016\/j.ijpe.2013.04.050","volume":"145","author":"V Pando","year":"2013","unstructured":"Pando V, San-Jos\u00e9 LA, Garc\u00eda-Laguna J, Sicilia J (2013) An economic lot-size model with non-linear holding cost hinging on time and quantity. Int J Prod Econ 145(1):294\u2013303","journal-title":"Int J Prod Econ"},{"key":"1260_CR27","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1016\/j.cie.2018.01.008","volume":"117","author":"V Pando","year":"2018","unstructured":"Pando V, San-Jos\u00e9 LA, Garc\u00eda-Laguna J, Sicilia J (2018) Optimal lot-size policy for deteriorating items with stock-dependent demand considering profit maximization. Comput Ind Eng 117:81\u201393","journal-title":"Comput Ind Eng"},{"key":"1260_CR28","doi-asserted-by":"publisher","first-page":"643","DOI":"10.1016\/j.apm.2018.10.007","volume":"66","author":"V Pando","year":"2019","unstructured":"Pando V, San-Jos\u00e9 LA, Sicilia J (2019) Profitability ratio maximization in an inventory model with stock-dependent demand rate and non-linear holding cost. Appl Math Model 66:643\u2013661","journal-title":"Appl Math Model"},{"key":"1260_CR29","doi-asserted-by":"publisher","DOI":"10.1016\/j.omega.2021.102481","volume":"104","author":"D Prak","year":"2021","unstructured":"Prak D, Teunter R, Babai MZ, Boylan JE, Syntetos A (2021) Robust compound poisson parameter estimation for inventory control. Omega 104:102481","journal-title":"Omega"},{"issue":"17","key":"1260_CR30","first-page":"8736","volume":"218","author":"SS Sana","year":"2012","unstructured":"Sana SS (2012) The EOQ model-A dynamical system. Appl Math Comput 218(17):8736\u20138749","journal-title":"Appl Math Comput"},{"key":"1260_CR31","doi-asserted-by":"publisher","first-page":"806","DOI":"10.1016\/j.apm.2017.02.024","volume":"48","author":"FZ Sargut","year":"2017","unstructured":"Sargut FZ, I\u015f\u0131k G (2017) Dynamic economic lot size model with perishable inventory and capacity constraints. Appl Math Model 48:806\u2013820","journal-title":"Appl Math Model"},{"key":"1260_CR32","doi-asserted-by":"publisher","first-page":"232","DOI":"10.1016\/j.tre.2016.04.011","volume":"93","author":"Z Sazvar","year":"2016","unstructured":"Sazvar Z, Hashem Mirzapour Al-e S, Govindan K, Bahli B (2016) A novel mathematical model for a multi-period, multi-product optimal ordering problem considering expiry dates in a FEFO system. Transp Res Part E Logist Transp Rev 93:232\u2013261","journal-title":"Transp Res Part E Logist Transp Rev"},{"key":"1260_CR33","volume-title":"Inventory control and management","author":"D Waters","year":"2003","unstructured":"Waters D (2003) Inventory control and management, 2nd edn. Wiley, Hoboken","edition":"2"},{"key":"1260_CR34","doi-asserted-by":"publisher","DOI":"10.1016\/j.tre.2020.101918","volume":"137","author":"Y Wei","year":"2020","unstructured":"Wei Y, Li F (2020) Omnichannel supply chain operations for luxury products with conspicuous consumers. Transp Res Part E Logist Transp Rev 137:101918","journal-title":"Transp Res Part E Logist Transp Rev"},{"key":"1260_CR35","doi-asserted-by":"publisher","first-page":"214","DOI":"10.1016\/j.ijpe.2014.01.016","volume":"155","author":"C-T Yang","year":"2014","unstructured":"Yang C-T (2014) An inventory model with both stock-dependent demand rate and stock-dependent holding cost rate. Int J Prod Econ 155:214\u2013221","journal-title":"Int J Prod Econ"},{"key":"1260_CR36","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2021.105898","volume":"101","author":"Y-L Zhu","year":"2021","unstructured":"Zhu Y-L, Zhou W, Chu T, Elsadany A (2021) Complex dynamical behavior and numerical simulation of a cournot-bertrand duopoly game with heterogeneous players. Commun Nonlinear Sci Numer Simul 101:105898","journal-title":"Commun Nonlinear Sci Numer Simul"}],"container-title":["Journal of Combinatorial Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-025-01260-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10878-025-01260-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-025-01260-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,13]],"date-time":"2025-03-13T21:07:09Z","timestamp":1741900029000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10878-025-01260-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,9]]},"references-count":36,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,3]]}},"alternative-id":["1260"],"URL":"https:\/\/doi.org\/10.1007\/s10878-025-01260-z","relation":{},"ISSN":["1382-6905","1573-2886"],"issn-type":[{"value":"1382-6905","type":"print"},{"value":"1573-2886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,2,9]]},"assertion":[{"value":"7 January 2025","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 February 2025","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"28"}}