{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T16:27:49Z","timestamp":1776270469531,"version":"3.50.1"},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2021,10,6]],"date-time":"2021-10-06T00:00:00Z","timestamp":1633478400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2021,10,6]],"date-time":"2021-10-06T00:00:00Z","timestamp":1633478400000},"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":["71573177"],"award-info":[{"award-number":["71573177"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100016780","name":"Chaoyang University of Technology","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100016780","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[2021,12]]},"DOI":"10.1007\/s10479-021-04272-0","type":"journal-article","created":{"date-parts":[[2021,10,6]],"date-time":"2021-10-06T13:20:40Z","timestamp":1633526440000},"page":"303-328","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Lot-sizing and pricing decisions for perishable products under three-echelon supply chains when demand depends on price and stock-age"],"prefix":"10.1007","volume":"307","author":[{"given":"Ruihai","family":"Li","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2935-2758","authenticated-orcid":false,"given":"Jinn-Tsair","family":"Teng","sequence":"additional","affiliation":[]},{"given":"Chun-Tao","family":"Chang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,10,6]]},"reference":[{"issue":"2","key":"4272_CR1","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1016\/j.ejor.2012.03.004","volume":"221","author":"M Bakker","year":"2012","unstructured":"Bakker, M., Riezebos, J., & Teunter, R. H. (2012). Review of inventory systems with deterioration since 2001. European Journal of Operational Research, 221(2), 275\u2013284.","journal-title":"European Journal of Operational Research"},{"key":"4272_CR2","volume-title":"Generalized convexity and optimization: Theory and application","author":"A Cambini","year":"2009","unstructured":"Cambini, A., & Martein, L. (2009). Generalized convexity and optimization: Theory and application. Springer."},{"key":"4272_CR3","doi-asserted-by":"crossref","unstructured":"C\u00e1rdenas-Barr\u00f3n, L. E., Shaikh, A. A., Tiwari, S., & Trevi\u00f1o-Garza, G. (2020). An EOQ inventory model with nonlinear stock dependent holding cost, nonlinear stock dependent demand and trade credit. Computers and Industrial Engineering, 139, 105557.","DOI":"10.1016\/j.cie.2018.12.004"},{"issue":"1\u20132","key":"4272_CR4","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1016\/j.ijpe.2019.04.039","volume":"218","author":"CT Chang","year":"2019","unstructured":"Chang, C. T., Ouyang, L. Y., Teng, J. T., Lai, K. K., & C\u00e1rdenas-Barr\u00f3n, L. E. (2019). Manufacturer\u2019s pricing and lot-sizing decisions for perishable goods under various payment terms by a discounted cash flow analysis. International Journal of Production Economics, 218(1\u20132), 83\u201395.","journal-title":"International Journal of Production Economics"},{"issue":"15\u201316","key":"4272_CR5","doi-asserted-by":"publisher","first-page":"4049","DOI":"10.1016\/j.apm.2013.11.056","volume":"38","author":"SC Chen","year":"2014","unstructured":"Chen, S. C., & Teng, J. T. (2014). Retailer\u2019s optimal ordering policy for deteriorating items with maximum lifetime under supplier\u2019s trade credit financing. Applied Mathematical Modelling, 38(15\u201316), 4049\u20134061.","journal-title":"Applied Mathematical Modelling"},{"issue":"2","key":"4272_CR6","doi-asserted-by":"publisher","first-page":"566","DOI":"10.1016\/j.ejor.2014.12.007","volume":"243","author":"SC Chen","year":"2015","unstructured":"Chen, S. C., & Teng, J. T. (2015). Inventory and credit decisions for time-varying deteriorating items with up-stream and down-stream trade credit financing by discounted cash-flow analysis. European Journal of Operational Research, 243(2), 566\u2013575.","journal-title":"European Journal of Operational Research"},{"key":"4272_CR7","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1016\/j.cie.2016.11.018","volume":"103","author":"K Chen","year":"2017","unstructured":"Chen, K., & Xiao, T. (2017). Pricing and replenishment policies in a supply chain with competing retailers under different retail behaviors. Computers and Industrial Engineering, 103, 145\u2013157.","journal-title":"Computers and Industrial Engineering"},{"issue":"6","key":"4272_CR8","doi-asserted-by":"publisher","first-page":"884","DOI":"10.1057\/jors.2015.100","volume":"67","author":"SC Chen","year":"2016","unstructured":"Chen, S. C., Min, J., Teng, J. T., & Li, F. (2016). Inventory and shelf-space management for fresh produce with freshness-and-stock dependent demand and expiration date. Journal of the Operational Research Society, 67(6), 884\u2013896.","journal-title":"Journal of the Operational Research Society"},{"issue":"3","key":"4272_CR9","doi-asserted-by":"publisher","first-page":"868","DOI":"10.1016\/j.ejor.2014.06.037","volume":"239","author":"CY Dye","year":"2014","unstructured":"Dye, C. Y., Yang, C. T., & Kung, F. C. (2014). A note on: Seller\u2019s optimal credit period and cycle time in a supply chain for deteriorating items with maximum lifetime. European Journal of Operational Research, 239(3), 868\u2013871.","journal-title":"European Journal of Operational Research"},{"issue":"3","key":"4272_CR10","doi-asserted-by":"publisher","first-page":"905","DOI":"10.1016\/j.ejor.2018.07.003","volume":"272","author":"L Feng","year":"2019","unstructured":"Feng, L., & Chan, Y. L. (2019). Joint pricing and production decisions for new products with learning curve effects under upstream and downstream trade credits. European Journal of Operational Research, 272(3), 905\u2013913.","journal-title":"European Journal of Operational Research"},{"issue":"3","key":"4272_CR11","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1016\/j.ijpe.2016.12.017","volume":"185","author":"L Feng","year":"2017","unstructured":"Feng, L., Chan, Y. L., & C\u00e1rdenas-Barr\u00f3n, L. E. (2017). Pricing and lot-sizing polices for perishable goods when the demand depends on selling price, displayed stocks, and expiration date. International Journal of Production Economics, 185(3), 11\u201320.","journal-title":"International Journal of Production Economics"},{"key":"4272_CR12","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-020-03761-y","author":"L Feng","year":"2020","unstructured":"Feng, L., Skouri, K., Wang, W. C., & Teng, J. T. (2020). Optimal selling price, replenishment cycle and payment time among advance, cash, and credit payments from the seller\u2019s perspective. Annals of Operations Research. https:\/\/doi.org\/10.1007\/s10479-020-03761-y","journal-title":"Annals of Operations Research"},{"key":"4272_CR13","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1007\/s10479-020-03673-x","volume":"295","author":"M Gupta","year":"2020","unstructured":"Gupta, M., Tiwari, S., & Jaggi, C. K. (2020). Retailer\u2019s ordering policies for time-varying deteriorating items with partial backlogging and permissible delay in payments in a two-warehouse environment. Annals of Operations Research, 295, 139\u2013161.","journal-title":"Annals of Operations Research"},{"key":"4272_CR14","unstructured":"Harris, F. W. (1913). How many parts to make at once. Factory, The Magazine of Management, 10(2), 135\u2013136 and 152."},{"issue":"1\u20132","key":"4272_CR15","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1007\/s10479-018-2925-9","volume":"274","author":"CK Jaggi","year":"2019","unstructured":"Jaggi, C. K., Gupta, M., Kausar, A., & Tiwari, S. (2019). Inventory and credit decisions for deteriorating items with displayed stock dependent demand in two-echelon supply chain using Stackelberg and Nash equilibrium solution. Annals of Operations Research, 274(1\u20132), 309\u2013329.","journal-title":"Annals of Operations Research"},{"issue":"3","key":"4272_CR16","doi-asserted-by":"publisher","first-page":"1099","DOI":"10.1016\/j.ejor.2018.04.029","volume":"270","author":"R Li","year":"2018","unstructured":"Li, R., & Teng, J. T. (2018). Pricing and lot-sizing decisions for perishable goods when demand depends on selling price, reference price, product freshness, and displayed stocks. European Journal of Operational Research, 270(3), 1099\u20131108.","journal-title":"European Journal of Operational Research"},{"issue":"11","key":"4272_CR17","doi-asserted-by":"publisher","first-page":"578","DOI":"10.1016\/j.ijpe.2017.08.020","volume":"193","author":"R Li","year":"2017","unstructured":"Li, R., Chan, Y. L., Chang, C. T., & C\u00e1rdenas-Barr\u00f3n, L. E. (2017). Pricing and lot-sizing policies for perishable products with advance-cash-credit payments by a discounted cash-flow analysis. International Journal of Production Economics, 193(11), 578\u2013589.","journal-title":"International Journal of Production Economics"},{"issue":"1","key":"4272_CR18","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1016\/j.ijpe.2017.12.015","volume":"197","author":"R Li","year":"2018","unstructured":"Li, R., Skouri, K., Teng, J. T., & Yang, W. G. (2018). Seller\u2019s optimal replenishment policy and payment term among advance, cash, and credit payments. International Journal of Production Economics, 197(1), 35\u201342.","journal-title":"International Journal of Production Economics"},{"issue":"1","key":"4272_CR19","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1016\/j.ejor.2019.04.033","volume":"278","author":"R Li","year":"2019","unstructured":"Li, R., Liu, Y., Teng, J. T., & Tsao, Y. C. (2019a). Optimal pricing, lot-sizing and backordering decisions when a seller demands for an advance-cash-credit payment scheme. European Journal of Operational Research, 278(1), 283\u2013295.","journal-title":"European Journal of Operational Research"},{"issue":"1\u20132","key":"4272_CR20","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1007\/s10479-019-03310-2","volume":"280","author":"R Li","year":"2019","unstructured":"Li, R., Teng, J. T., & Zheng, Y. (2019b). Optimal credit term, order quantity and pricing policies for perishable products when demand depends on price, expiration date, and credit period. Annals of Operations Research, 280(1\u20132), 377\u2013405.","journal-title":"Annals of Operations Research"},{"issue":"1\u20132","key":"4272_CR21","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1007\/s10479-017-2419-1","volume":"254","author":"U Mishra","year":"2017","unstructured":"Mishra, U., C\u00e1rdenas-Barr\u00f3n, L. E., Tiwari, S., Shaikh, A. A., & Trevi\u00f1o-Garza, G. (2017). An inventory model under price and stock dependent demand for controllable deterioration rate with shortages and preservation technology investment. Annals of Operations Research, 254(1\u20132), 165\u2013190.","journal-title":"Annals of Operations Research"},{"key":"4272_CR22","doi-asserted-by":"crossref","unstructured":"Mishra, U., Tijerina-Aguilera, J., Tiwari, S., & C\u00e1rdenas-Barr\u00f3n, L. E. (2018). Retailer's joint ordering, pricingand preservation technology investment policies for a deteriorating item under permissible delay inpayments. Mathematical Problems in Engineering, Volume 2018, Article ID 6962417.","DOI":"10.1155\/2018\/6962417"},{"issue":"1","key":"4272_CR23","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1016\/j.ejor.2018.05.067","volume":"272","author":"NM Modak","year":"2019","unstructured":"Modak, N. M., & Kelle, P. (2019). Managing a dual-channel supply chain under price and delivery-time dependent stochastic demand. European Journal of Operational Research, 272(1), 147\u2013161.","journal-title":"European Journal of Operational Research"},{"issue":"3","key":"4272_CR24","doi-asserted-by":"publisher","first-page":"654","DOI":"10.1016\/j.ejor.2014.01.060","volume":"238","author":"J Pahl","year":"2014","unstructured":"Pahl, J., & Vo\u00df, S. (2014). Integrating deterioration and lifetime constraints in production and supply chain planning: A survey. European Journal of Operational Research, 238(3), 654\u2013674.","journal-title":"European Journal of Operational Research"},{"issue":"3\u20134","key":"4272_CR25","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1016\/j.mcm.2011.08.009","volume":"55","author":"B Sarkar","year":"2012","unstructured":"Sarkar, B. (2012). An EOQ model with delay in payments and time varying deterioration rate. Mathematical and Computer Modelling, 55(3\u20134), 367\u2013377.","journal-title":"Mathematical and Computer Modelling"},{"issue":"2","key":"4272_CR26","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1016\/j.ejor.2013.03.016","volume":"231","author":"D Seifert","year":"2013","unstructured":"Seifert, D., Seifert, R. W., & Protopappa-Sieke, M. (2013). A review of trade credit literature: Opportunity for research in operations. European Journal of Operational Research, 231(2), 245\u2013256.","journal-title":"European Journal of Operational Research"},{"key":"4272_CR27","doi-asserted-by":"crossref","unstructured":"Shi, Y., Zhang, Z., Chen, S. H., C\u00e1rdenas-Barr\u00f3n, L. E., Skouri, K. (2020). Optimal replenishment decisionsfor perishable products under cash, advance, and credit payments considering carbon tax regulations. International Journal of Production Economics, 223, 107514.","DOI":"10.1016\/j.ijpe.2019.09.035"},{"key":"4272_CR28","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1016\/j.ijpe.2014.01.023","volume":"155","author":"AA Taleizadeh","year":"2014","unstructured":"Taleizadeh, A. A. (2014). An EOQ model with partial backordering and advance payments for an evaporating item. International Journal of Production Economics, 155, 185\u2013193.","journal-title":"International Journal of Production Economics"},{"issue":"8","key":"4272_CR29","doi-asserted-by":"publisher","first-page":"915","DOI":"10.1057\/palgrave.jors.2601410","volume":"53","author":"JT Teng","year":"2002","unstructured":"Teng, J. T. (2002). On the economic order quantity under conditions of permissible delay in payments. Journal of the Operational Research Society, 53(8), 915\u2013918.","journal-title":"Journal of the Operational Research Society"},{"issue":"2","key":"4272_CR30","doi-asserted-by":"publisher","first-page":"415","DOI":"10.1016\/j.ijpe.2009.04.004","volume":"119","author":"JT Teng","year":"2009","unstructured":"Teng, J. T. (2009). Optimal ordering policies for a retailer who offers distinct trade credits to its good and bad credit customers. International Journal of Production Economics, 119(2), 415\u2013423.","journal-title":"International Journal of Production Economics"},{"issue":"19\u201320","key":"4272_CR31","doi-asserted-by":"publisher","first-page":"8605","DOI":"10.1016\/j.apm.2016.05.022","volume":"40","author":"JT Teng","year":"2016","unstructured":"Teng, J. T., C\u00e1rdenas-Barr\u00f3n, L. E., Chang, H. J., Wu, J., & Hu, Y. (2016). Inventory lot-size policies for deteriorating items with expiration dates and advance payments. Applied Mathematical Modelling, 40(19\u201320), 8605\u20138616.","journal-title":"Applied Mathematical Modelling"},{"issue":"1\u20132","key":"4272_CR32","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1007\/s10479-017-2492-5","volume":"254","author":"S Tiwari","year":"2017","unstructured":"Tiwari, S., Jaggi, C. K., Bhunia, A. K., Shaikh, A. A., & Goh, M. (2017). Two-warehouse inventory model for non-instantaneous deteriorating items with stock-dependent demand and inflation using particle swarm optimization. Annals of Operations Research, 254(1\u20132), 401\u2013423.","journal-title":"Annals of Operations Research"},{"key":"4272_CR33","doi-asserted-by":"crossref","unstructured":"Tiwari, S., C\u00e1rdenas-Barr\u00f3n, L. E., Shaikh, A. A., Goh, M. (2020). Retailer's optimal ordering policy for deteriorating items under order-size dependent trade credit and complete backlogging. Computers and Industrial Engineering, 139, 105559.","DOI":"10.1016\/j.cie.2018.12.006"},{"key":"4272_CR34","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1016\/j.cie.2014.09.005","volume":"77","author":"C Wang","year":"2014","unstructured":"Wang, C., & Huang, R. (2014). Pricing for seasonal deteriorating products with price- and ramp-type time-dependent demand. Computers and Industrial Engineering, 77, 29\u201334.","journal-title":"Computers and Industrial Engineering"},{"issue":"2","key":"4272_CR35","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1016\/j.ejor.2013.06.027","volume":"232","author":"WC Wang","year":"2014","unstructured":"Wang, W. C., Teng, J. T., & Lou, K. R. (2014). Seller\u2019s optimal credit period and cycle time in a supply chain for deteriorating items with maximum lifetime. European Journal of Operational Research, 232(2), 315\u2013321.","journal-title":"European Journal of Operational Research"},{"issue":"3","key":"4272_CR36","doi-asserted-by":"publisher","first-page":"898","DOI":"10.1016\/j.ejor.2014.03.009","volume":"237","author":"J Wu","year":"2014","unstructured":"Wu, J., Ouyang, L. Y., C\u00e1rdenas-Barr\u00f3n, L. E., & Goyal, S. K. (2014). Optimal credit period and lot size for deteriorating items with expiration dates under two-level trade credit financing. European Journal of Operational Research, 237(3), 898\u2013908.","journal-title":"European Journal of Operational Research"},{"issue":"3","key":"4272_CR37","first-page":"138","volume":"3","author":"J Wu","year":"2016","unstructured":"Wu, J., Chang, C. T., Cheng, M. C., Teng, J. T., & Al-khateeb, F. B. (2016). Inventory management for fresh produce when the time-varying demand depends on product freshness, stock level and expiration date. International Journal of Systems Science: Operations and Logistics, 3(3), 138\u2013147.","journal-title":"International Journal of Systems Science: Operations and Logistics"},{"issue":"4","key":"4272_CR38","first-page":"310","volume":"5","author":"J Wu","year":"2018","unstructured":"Wu, J., Teng, J. T., & Chan, Y. L. (2018a). Inventory policies for perishable products with expiration dates and advance-instant-delayed payment schemes. International Journal of Systems Science: Operations and Logistics, 5(4), 310\u2013326.","journal-title":"International Journal of Systems Science: Operations and Logistics"},{"key":"4272_CR39","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1007\/s10479-017-2673-2","volume":"264","author":"J Wu","year":"2018","unstructured":"Wu, J., Teng, J. T., & Skouri, K. (2018b). Optimal inventory policies for deteriorating items with trapezoidal-type demand patterns and maximum lifetimes under upstream and downstream trade credits. Annals of Operations Research, 264, 459\u2013476.","journal-title":"Annals of Operations Research"},{"key":"4272_CR40","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1007\/s10479-021-03943-2","volume":"300","author":"Y Xie","year":"2021","unstructured":"Xie, Y., Tai, A. H., Ching, W. K., Kuo, Y. H., & Song, N. (2021). Joint inspection and inventory control for deteriorating items with time-dependent demand and deteriorating rate. Annals of Operations Research, 300, 225\u2013265.","journal-title":"Annals of Operations Research"},{"issue":"5","key":"4272_CR41","doi-asserted-by":"publisher","first-page":"577","DOI":"10.1016\/0305-0483(96)00023-0","volume":"24","author":"AX Zhang","year":"1996","unstructured":"Zhang, A. X. (1996). Optimal advance payment scheme involving fixed pre-payment costs. Omega, 24(5), 577\u2013582.","journal-title":"Omega"},{"issue":"24","key":"4272_CR42","doi-asserted-by":"publisher","first-page":"5910","DOI":"10.1016\/j.apm.2014.04.040","volume":"38","author":"Q Zhang","year":"2014","unstructured":"Zhang, Q., Tsao, Y. C., & Chen, T. H. (2014). Economic order quantity under advance payment. Applied Mathematical Modelling, 38(24), 5910\u20135921.","journal-title":"Applied Mathematical Modelling"}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-021-04272-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10479-021-04272-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-021-04272-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,8]],"date-time":"2025-04-08T23:08:54Z","timestamp":1744153734000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10479-021-04272-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,6]]},"references-count":42,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2021,12]]}},"alternative-id":["4272"],"URL":"https:\/\/doi.org\/10.1007\/s10479-021-04272-0","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"value":"0254-5330","type":"print"},{"value":"1572-9338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,10,6]]},"assertion":[{"value":"14 September 2021","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 October 2021","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}