{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T13:30:42Z","timestamp":1775050242547,"version":"3.50.1"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2020,2,24]],"date-time":"2020-02-24T00:00:00Z","timestamp":1582502400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,2,24]],"date-time":"2020-02-24T00:00:00Z","timestamp":1582502400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100009153","name":"University of Portsmouth","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100009153","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":[[2020,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Finite horizon periodic review backlog models are considered in this paper for an inventory system that remanufactures two types of cores: buyback cores and normal cores. Returns of used products as buyback cores are modelled to depend on past demands and past sales. We derive an optimal inventory policy for the model in which returns are forecast to depend on past demands, and analyze properties of the optimal cost and optimal policy we derived. As the structure of the optimal inventory policy for the model in which returns are forecast from past sales is unlikely to be tractable, we instead consider a feasible inventory policy with a nice structure for this model. We investigate how close this policy is to optimality and find that in the worst case, the difference in system costs between the feasible policy and the optimal inventory policy is bounded by a constant that is dependent only on cost parameters, mean demands and a discount factor, and is independent of the planning horizon and initial inventories. We also perform numerical experiments to study the difference between system costs under the feasible policy and those under the optimal policy.<\/jats:p>","DOI":"10.1007\/s10479-020-03545-4","type":"journal-article","created":{"date-parts":[[2020,2,24]],"date-time":"2020-02-24T21:04:17Z","timestamp":1582578257000},"page":"137-180","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Policies for inventory models with product returns forecast from past demands and past sales"],"prefix":"10.1007","volume":"288","author":[{"given":"Mabel C.","family":"Chou","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0696-4698","authenticated-orcid":false,"given":"Chee-Khian","family":"Sim","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1575-0130","authenticated-orcid":false,"given":"Xue-Ming","family":"Yuan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,2,24]]},"reference":[{"key":"3545_CR1","doi-asserted-by":"publisher","first-page":"2373","DOI":"10.1080\/00207541003692021","volume":"49","author":"E Ak\u00e7ali","year":"2011","unstructured":"Ak\u00e7ali, E., & \u00c7etinkaya, S. (2011). Quantitative models for inventory and production planning in closed-loop supply chains. International Journal of Production Research, 49, 2373\u20132407.","journal-title":"International Journal of Production Research"},{"key":"3545_CR2","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1287\/inte.1040.0098","volume":"34","author":"M Bayiz","year":"2004","unstructured":"Bayiz, M., & Tang, C. S. (2004). An integrated planning system for managing the refurbishment of thermoluminescent badges. Interface, 34, 383\u2013393.","journal-title":"Interface"},{"key":"3545_CR3","volume-title":"Dynamic programming and optimal control","author":"DP Bertsekas","year":"2005","unstructured":"Bertsekas, D. P. (2005). Dynamic programming and optimal control (3rd ed., Vol. 1). Belmont, MA: Athena Scientific.","edition":"3"},{"key":"3545_CR4","doi-asserted-by":"publisher","first-page":"589","DOI":"10.1111\/j.1540-5915.2012.00362.x","volume":"43","author":"T Clottey","year":"2012","unstructured":"Clottey, T., Benton, W. C, Jr., & Srivastava, R. (2012). Forecasting product returns for remanufacturing operations. Decision Science, 43, 589\u2013614.","journal-title":"Decision Science"},{"key":"3545_CR5","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1016\/j.ejor.2007.11.063","volume":"194","author":"MP de Brito","year":"2009","unstructured":"de Brito, M. P., & van der Laan, E. A. (2009). Inventory control with product returns: The impact of imperfect information. European Journal of Operational Research, 194, 85\u2013101.","journal-title":"European Journal of Operational Research"},{"key":"3545_CR6","doi-asserted-by":"publisher","first-page":"532","DOI":"10.1287\/opre.1060.0290","volume":"54","author":"GA DeCroix","year":"2006","unstructured":"DeCroix, G. A. (2006). Optimal policy for a multiechelon inventory system with remanufacturing. Operations Research, 54, 532\u2013543.","journal-title":"Operations Research"},{"key":"3545_CR7","doi-asserted-by":"publisher","first-page":"1250","DOI":"10.1287\/mnsc.1050.0394","volume":"51","author":"GA DeCroix","year":"2005","unstructured":"DeCroix, G. A., & Zipkin, P. H. (2005). Inventory management for an assembly system with product or component returns. Management Science, 51, 1250\u20131265.","journal-title":"Management Science"},{"key":"3545_CR8","doi-asserted-by":"publisher","first-page":"42","DOI":"10.1080\/07408178608975328","volume":"18","author":"TN Goh","year":"1986","unstructured":"Goh, T. N., & Varaprasad, N. (1986). A statistical methodology for the analysis of the life-cycle of reusable containers. IIE Transactions, 18, 42\u201347.","journal-title":"IIE Transactions"},{"key":"3545_CR9","doi-asserted-by":"publisher","first-page":"603","DOI":"10.1287\/opre.2013.1168","volume":"61","author":"X Gong","year":"2013","unstructured":"Gong, X., & Chao, X. (2013). Optimal control policy for capacitated inventory systems with remanufacturing. Operations Research, 61, 603\u2013611.","journal-title":"Operations Research"},{"key":"3545_CR10","doi-asserted-by":"publisher","first-page":"580","DOI":"10.1016\/j.ejor.2013.09.042","volume":"233","author":"S Guo","year":"2014","unstructured":"Guo, S., Aydin, G., & Souza, G. C. (2014). Dismantle or remanufacture? European Journal of Operational Research, 233, 580\u2013583.","journal-title":"European Journal of Operational Research"},{"key":"3545_CR11","doi-asserted-by":"publisher","first-page":"645","DOI":"10.1016\/j.ijpe.2011.05.007","volume":"133","author":"C-F Hsueh","year":"2011","unstructured":"Hsueh, C.-F. (2011). An inventory control model with consideration of remanufacturing and product life cycle. International Journal of Production Economics, 133, 645\u2013652.","journal-title":"International Journal of Production Economics"},{"key":"3545_CR12","doi-asserted-by":"publisher","first-page":"284","DOI":"10.1287\/mnsc.15.5.284","volume":"15","author":"E Ignall","year":"1969","unstructured":"Ignall, E., & Veinott, A. F, Jr. (1969). Optimality of myopic inventory policies for several substitute products. Management Science, 15, 284\u2013304.","journal-title":"Management Science"},{"key":"3545_CR13","doi-asserted-by":"publisher","first-page":"1958","DOI":"10.1111\/poms.12598","volume":"25","author":"J Jia","year":"2016","unstructured":"Jia, J., Xu, S. H., & Guide, V. D. R, Jr. (2016). Addressing supply-demand imbalance: Designing efficient remanufacturing strategies. Production and Operations Management, 25, 1958\u20131967.","journal-title":"Production and Operations Management"},{"key":"3545_CR14","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1007\/978-981-4451-48-2_97","volume-title":"Re-engineering manufacturing for sustainability","author":"L Jing","year":"2013","unstructured":"Jing, L., & Huang, B. (2013). Jointly consider acquisition price, trade in rebate and selling price in remanufacturing. In A. Nee, B. Song, & S. K. Ong (Eds.), Re-engineering manufacturing for sustainability (pp. 597\u2013602). Singapore: Springer."},{"key":"3545_CR15","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-015-1998-y","author":"MN Katehakis","year":"2015","unstructured":"Katehakis, M. N., Melamed, B., & Shi, J. J. (2015). Optimal replenishment rate for inventory systems with compound Poisson demands and lost sales: A direct treatment of time-average cost. Annals of Operations Research,. https:\/\/doi.org\/10.1007\/s10479-015-1998-y.","journal-title":"Annals of Operations Research"},{"key":"3545_CR16","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1016\/S0272-6963(89)80003-8","volume":"8","author":"P Kelle","year":"1989","unstructured":"Kelle, P., & Silver, E. A. (1989a). Forecasting the returns of reusable containers. Journal of Operations Management, 8, 17\u201335.","journal-title":"Journal of Operations Management"},{"key":"3545_CR17","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1080\/07408178908966241","volume":"21","author":"P Kelle","year":"1989","unstructured":"Kelle, P., & Silver, E. A. (1989b). Purchasing policy of new containers considering the random returns of previously issued containers. IIE Transactions, 21, 349\u2013354.","journal-title":"IIE Transactions"},{"key":"3545_CR18","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1111\/j.1937-5956.2006.tb00253.x","volume":"15","author":"ME Ketzenberg","year":"2006","unstructured":"Ketzenberg, M. E., van der Laan, E., & Teunter, R. H. (2006). Value of information in closed loop supply chains. Production and Operations Management, 15, 393\u2013406.","journal-title":"Production and Operations Management"},{"key":"3545_CR19","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1287\/inte.1070.0299","volume":"37","author":"J Khawan","year":"2007","unstructured":"Khawan, J., Hausman, W. H., & Cheng, D. W. (2007). Warranty inventory optimization for Hitachi Global Storage Technologies, Inc. Interfaces, 37, 455\u2013471.","journal-title":"Interfaces"},{"key":"3545_CR20","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1016\/S0925-5273(00)00080-3","volume":"72","author":"GP Kiesm\u00fcller","year":"2001","unstructured":"Kiesm\u00fcller, G. P., & van der Laan, E. (2001). An inventory model with dependent product demands and returns. International Journal of Production Economics, 72, 73\u201387.","journal-title":"International Journal of Production Economics"},{"issue":"4","key":"3545_CR21","first-page":"107","volume":"3","author":"OR Koppius","year":"2004","unstructured":"Koppius, O. R., Akyildirim, \u00d6. \u00d6., & van der Laan, E. (2004). Business value from closed-loop supply chains. International Journal of Supply Chain Management, 3(4), 107\u2013120.","journal-title":"International Journal of Supply Chain Management"},{"key":"3545_CR22","doi-asserted-by":"publisher","first-page":"3657","DOI":"10.1080\/00207540701837029","volume":"47","author":"C Li","year":"2009","unstructured":"Li, C., Liu, F., Cao, H., & Wang, Q. (2009). A stochastic dynamic programming based model for uncertain production planning for re-manufacturing system. International Journal of Production Research, 47, 3657\u20133668.","journal-title":"International Journal of Production Research"},{"issue":"5","key":"3545_CR23","doi-asserted-by":"publisher","first-page":"744","DOI":"10.1111\/poms.12070","volume":"23","author":"A Ovchinnikov","year":"2014","unstructured":"Ovchinnikov, A., Blass, V., & Raz, G. (2014). Economic and environmental assessment of remanufacturing strategies for product + service firms. Production and Operations Management, 23(5), 744\u2013761.","journal-title":"Production and Operations Management"},{"issue":"9","key":"3545_CR24","doi-asserted-by":"publisher","first-page":"1561","DOI":"10.1111\/poms.12176","volume":"23","author":"M Pourakbar","year":"2014","unstructured":"Pourakbar, M., van der Laan, E. A., & Dekker, R. (2014). End-of-life inventory problem with phaseout returns. Production and Operations Management, 23(9), 1561\u20131576.","journal-title":"Production and Operations Management"},{"key":"3545_CR25","doi-asserted-by":"publisher","first-page":"447","DOI":"10.1007\/s10479-014-1542-5","volume":"217","author":"KS Puranam","year":"2014","unstructured":"Puranam, K. S., & Katehakis, M. N. (2014). On optimal bidding and inventory control in sequential procurement auctions: The multi period case. Annals of Operations Research, 217, 447\u2013462.","journal-title":"Annals of Operations Research"},{"key":"3545_CR26","doi-asserted-by":"publisher","DOI":"10.1515\/9781400873173","volume-title":"Convex analysis","author":"RT Rockafellar","year":"1970","unstructured":"Rockafellar, R. T. (1970). Convex analysis. New Jersey: Princeton University Press."},{"key":"3545_CR27","doi-asserted-by":"publisher","first-page":"1048","DOI":"10.1287\/opre.2014.1299","volume":"62","author":"JJ Shi","year":"2014","unstructured":"Shi, J. J., Katehakis, M. N., Melamed, B., & Xia, Y. (2014). Production-inventory systems with lost sales and compound Poisson demands. Operations Research, 62, 1048\u20131063.","journal-title":"Operations Research"},{"key":"3545_CR28","doi-asserted-by":"publisher","first-page":"270","DOI":"10.1287\/opre.26.2.270","volume":"26","author":"VP Simpson","year":"1978","unstructured":"Simpson, V. P. (1978). Optimum solution structure for a repairable inventory problem. Operations Research, 26, 270\u2013281.","journal-title":"Operations Research"},{"issue":"1","key":"3545_CR29","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1111\/j.1540-5915.2012.00394.x","volume":"44","author":"GC Souza","year":"2013","unstructured":"Souza, G. C. (2013). Closed-loop supply chains: A critical review, and future research. Decision Sciences, 44(1), 7\u201338.","journal-title":"Decision Sciences"},{"key":"3545_CR30","doi-asserted-by":"publisher","first-page":"1179","DOI":"10.1287\/moor.2014.0647","volume":"39","author":"Z Tao","year":"2014","unstructured":"Tao, Z., & Zhou, S. X. (2014). Approximation balancing policies for inventory systems with remanufacturing. Mathematics of Operations Research, 39, 1179\u20131197.","journal-title":"Mathematics of Operations Research"},{"key":"3545_CR31","doi-asserted-by":"publisher","first-page":"797","DOI":"10.1111\/j.1937-5956.2011.01313.x","volume":"21","author":"Z Tao","year":"2012","unstructured":"Tao, Z., Zhou, S. X., & Tang, C. S. (2012). Managing a remanufacturing system with random yield: Properties, observations, and heuristics. Production and Operations Management, 21, 797\u2013813.","journal-title":"Production and Operations Management"},{"key":"3545_CR32","volume-title":"Reverse logistics: Quantitative methods for closed- loop supply chains","author":"LB Toktay","year":"2004","unstructured":"Toktay, L. B., van der Laan, E. A., & de Brito, M. P. (2004). Managing product returns: Informational issues and forecasting methods. In R. Dekker, M. Fleischmann, K. Inderfurth, & L. N. Van Wassenhove (Eds.), Reverse logistics: Quantitative methods for closed- loop supply chains. Berlin: Springer."},{"key":"3545_CR33","doi-asserted-by":"publisher","first-page":"1412","DOI":"10.1287\/mnsc.46.11.1412.12082","volume":"46","author":"LB Toktay","year":"2000","unstructured":"Toktay, L. B., Wein, L. M., & Zenios, S. A. (2000). Inventory management of remanufacturable products. Management Science, 46, 1412\u20131426.","journal-title":"Management Science"},{"key":"3545_CR34","doi-asserted-by":"publisher","first-page":"264","DOI":"10.1016\/S0377-2217(97)00108-2","volume":"102","author":"E van der Laan","year":"1997","unstructured":"van der Laan, E., & Salomon, M. (1997). Production planning and inventory control with remanufacturing and disposal. European Journal of Operational Research, 102, 264\u2013278.","journal-title":"European Journal of Operational Research"},{"issue":"1","key":"3545_CR35","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1016\/j.ejor.2007.11.063","volume":"194","author":"EA van der Laan","year":"2009","unstructured":"van der Laan, E. A., & de Brito, M. P. (2009). Inventory control with product returns: The impact of imperfect information. European Journal of Operational Research, 194(1), 85\u2013101.","journal-title":"European Journal of Operational Research"},{"key":"3545_CR36","doi-asserted-by":"publisher","first-page":"1084","DOI":"10.1016\/j.ejor.2005.06.030","volume":"175","author":"EA van der Laan","year":"2006","unstructured":"van der Laan, E. A., & Teunter, R. H. (2006). Simple heuristics for push and pull remanufacturing policies. European Journal of Operational Research, 175, 1084\u20131102.","journal-title":"European Journal of Operational Research"},{"key":"3545_CR37","doi-asserted-by":"publisher","first-page":"486","DOI":"10.1109\/TR.2015.2417536","volume":"65","author":"W Xie","year":"2016","unstructured":"Xie, W., & Ye, Z. S. (2016). Aggregate discounted warranty cost forecast for a new product considering stochastic sales. IEEE Transactions on Reliability, 65, 486\u2013497.","journal-title":"IEEE Transactions on Reliability"},{"issue":"2","key":"3545_CR38","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1080\/0740817X.2012.677573","volume":"45","author":"ZS Ye","year":"2013","unstructured":"Ye, Z. S., Murthy, D. N. P., Xie, M., & Tang, L. C. (2013). Optimal burn-in for repairable products sold with a two-dimensional warranty. IIE Transactions, 45(2), 164\u2013176.","journal-title":"IIE Transactions"},{"key":"3545_CR39","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1287\/msom.1100.0298","volume":"13","author":"SX Zhou","year":"2011","unstructured":"Zhou, S. X., Tao, Z., & Chao, X. (2011). Optimal control of inventory systems with multiple types of remanufacturing products. Manufacturing & Service Operations Management, 13, 20\u201334.","journal-title":"Manufacturing & Service Operations Management"},{"key":"3545_CR40","doi-asserted-by":"publisher","first-page":"514","DOI":"10.1287\/opre.1100.0898","volume":"59","author":"SX Zhou","year":"2011","unstructured":"Zhou, S. X., & Yu, Y. (2011). Optimal product acquisition, pricing, and inventory management for systems with remanufacturing. Operations Research, 59, 514\u2013521.","journal-title":"Operations Research"}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-020-03545-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10479-020-03545-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-020-03545-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,23]],"date-time":"2021-02-23T00:51:48Z","timestamp":1614041508000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10479-020-03545-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,24]]},"references-count":40,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,5]]}},"alternative-id":["3545"],"URL":"https:\/\/doi.org\/10.1007\/s10479-020-03545-4","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"value":"0254-5330","type":"print"},{"value":"1572-9338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,2,24]]},"assertion":[{"value":"24 February 2020","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}