{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T05:25:17Z","timestamp":1769750717880,"version":"3.49.0"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[2012,8]]},"DOI":"10.1007\/s10479-010-0772-4","type":"journal-article","created":{"date-parts":[[2010,7,20]],"date-time":"2010-07-20T19:10:53Z","timestamp":1279653053000},"page":"135-158","source":"Crossref","is-referenced-by-count":57,"title":["Large scale stochastic inventory routing problems with\u00a0split delivery and service level constraints"],"prefix":"10.1007","volume":"197","author":[{"given":"Yugang","family":"Yu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chengbin","family":"Chu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haoxun","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Feng","family":"Chu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2010,7,21]]},"reference":[{"issue":"4","key":"772_CR1","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1287\/opre.1040.0114","volume":"52","author":"D. Adelman","year":"2004","unstructured":"Adelman, D. (2004). A price-directed approach to stochastic inventory\/routing. Operations Research, 52(4), 499\u2013514.","journal-title":"Operations Research"},{"issue":"2","key":"772_CR2","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1287\/trsc.1050.0117","volume":"40","author":"C. Archetti","year":"2006","unstructured":"Archetti, C., Savelsbergh, M. W. P., & Speranza, M. G. (2006). Worst-case analysis for split delivery vehicle routing problems. Transportation Science, 40(2), 226\u2013234.","journal-title":"Transportation Science"},{"issue":"1","key":"772_CR3","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1287\/trsc.1070.0204","volume":"42","author":"C. Archetti","year":"2008","unstructured":"Archetti, C., Speranza, M. G., & Savelsbergh, M. W. P. (2008). An optimization-based heuristic for the split delivery vehicle routing problem. Transportation Science, 42(1), 22\u201331.","journal-title":"Transportation Science"},{"issue":"5","key":"772_CR4","doi-asserted-by":"crossref","first-page":"801","DOI":"10.1287\/opre.48.5.801.12407","volume":"48","author":"J. M. Belenguer","year":"2000","unstructured":"Belenguer, J. M., Martinez, M. C., & Mota, E. (2000). A lower bound for the split delivery vehicle routing problem. Operations Research, 48(5), 801\u2013810.","journal-title":"Operations Research"},{"issue":"6","key":"772_CR5","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1287\/inte.13.6.4","volume":"13","author":"W. J. Bell","year":"1983","unstructured":"Bell, W. J., Dalberto, L. M., Fisher, M. L., Greenfield, A. J., Jaikumar, R., Kedia, P., Mack, R. G., & Prutzman, P. J. (1983). Improving the distribution of industrial gases with an on-line computerized routing and scheduling optimizer. Interfaces, 13(6), 4\u201323.","journal-title":"Interfaces"},{"issue":"4","key":"772_CR6","doi-asserted-by":"crossref","first-page":"370","DOI":"10.1504\/EJIE.2007.015390","volume":"1","author":"H. Chen","year":"2007","unstructured":"Chen, H. (2007). A Lagrangian relaxation approach for production planning with demand uncertainty. European Journal of Industrial Engineering, 1(4), 370\u2013390.","journal-title":"European Journal of Industrial Engineering"},{"issue":"4","key":"772_CR7","doi-asserted-by":"crossref","first-page":"318","DOI":"10.1002\/net.20181","volume":"49","author":"S. Chen","year":"2007","unstructured":"Chen, S., Golden, B., & Wasil, E. (2007). The split delivery vehicle routing problem: applications, algorithms, test problems, and computational results. Networks, 49(4), 318\u2013329.","journal-title":"Networks"},{"issue":"4","key":"772_CR8","first-page":"1169","volume":"34","author":"L. Ciupala","year":"2005","unstructured":"Ciupala, L. (2005). A scaling out-of-kilter algorithm for minimum cost flow. Control and Cybernetics, 34(4), 1169\u20131174.","journal-title":"Control and Cybernetics"},{"issue":"6","key":"772_CR9","doi-asserted-by":"crossref","first-page":"891","DOI":"10.1002\/1520-6750(198712)34:6<891::AID-NAV3220340613>3.0.CO;2-J","volume":"34","author":"M. Dror","year":"1987","unstructured":"Dror, M., & Ball, M. (1987). Inventory\/routing: reduction from an annual to a short period problem. Naval Research Logistics Quarterly, 34(6), 891\u2013905.","journal-title":"Naval Research Logistics Quarterly"},{"key":"772_CR10","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1002\/nav.3800370304","volume":"37","author":"M. Dror","year":"1990","unstructured":"Dror, M., & Trudeau, P. (1990). Split delivery routing. Naval Research Logistics, 37, 383\u2013402.","journal-title":"Naval Research Logistics"},{"issue":"3","key":"772_CR11","doi-asserted-by":"crossref","first-page":"504","DOI":"10.1016\/0377-2217(94)00205-3","volume":"88","author":"M. Dror","year":"1996","unstructured":"Dror, M., & Trudeau, P. (1996). Cash flow optimization in delivery scheduling. European Journal of Operational Research, 88(3), 504\u2013515.","journal-title":"European Journal of Operational Research"},{"key":"772_CR12","doi-asserted-by":"crossref","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 allocation problem. Operation Research, 32, 1019\u20131037.","journal-title":"Operation Research"},{"issue":"3","key":"772_CR13","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1287\/trsc.33.3.330","volume":"33","author":"F. Fumero","year":"1999","unstructured":"Fumero, F., & Vercellis, C. (1999). Synchronized development of production, inventory, and distribution schedules. Transportation Science, 33(3), 330\u2013340.","journal-title":"Transportation Science"},{"issue":"2","key":"772_CR14","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1287\/ijoc.1080.0291","volume":"21","author":"L. M. Hvattum","year":"2009","unstructured":"Hvattum, L. M., Lokketangen, A., & Laporte, G. (2009). Scenario tree-based heuristics for stochastic inventory-routing problems. Informs Journal on Computing, 21(2), 268\u2013285.","journal-title":"Informs Journal on Computing"},{"issue":"3","key":"772_CR15","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1287\/trsc.36.3.292.7829","volume":"36","author":"P. Jaillet","year":"2002","unstructured":"Jaillet, P., Bard, J. F., Huang, L., & Dror, M. (2002). Delivery cost approximations for inventory routing problems in a rolling horizon framework. Transportation Science, 36(3), 292\u2013300.","journal-title":"Transportation Science"},{"issue":"1","key":"772_CR16","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1016\/j.ijpe.2006.04.014","volume":"105","author":"M. Z. Jin","year":"2007","unstructured":"Jin, M. Z., Liu, K., & Bowden, R. O. (2007). A two-stage algorithm with valid inequalities for the split delivery vehicle routing problem. International Journal of Production Economics, 105(1), 228\u2013242.","journal-title":"International Journal of Production Economics"},{"issue":"1","key":"772_CR17","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1287\/trsc.36.1.94.574","volume":"36","author":"A. J. Kleywegt","year":"2002","unstructured":"Kleywegt, A. J., Nori, V. S., & Savelsbergh, M. W. P. (2002). The stochastic inventory routing problem with direct deliveries. Transportation Science, 36(1), 94\u2013118.","journal-title":"Transportation Science"},{"issue":"1","key":"772_CR18","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1287\/trsc.1030.0041","volume":"38","author":"A. J. Kleywegt","year":"2004","unstructured":"Kleywegt, A. J., Nori, V. S., & Savelsbergh, M. W. P. (2004). Dynamic programming approximations for a stochastic inventory routing problem. Transportation Science, 38(1), 42\u201370.","journal-title":"Transportation Science"},{"issue":"1","key":"772_CR19","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1142\/S0219622009003259","volume":"8","author":"M. Koksalan","year":"2009","unstructured":"Koksalan, M., & Tuncer, C. (2009). A DEA-based approach to ranking multi-criteria alternatives. International Journal of Information Technology & Decision Making, 8(1), 29\u201354.","journal-title":"International Journal of Information Technology & Decision Making"},{"issue":"2","key":"772_CR20","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1287\/opre.1060.0356","volume":"55","author":"MA Lejeune","year":"2007","unstructured":"Lejeune, MA, & Ruszczynski, A. (2007). An efficient trajectory method for probabilistic production-inventory-distribution problems. Operations Research, 55(2), 378\u2013394.","journal-title":"Operations Research"},{"issue":"2","key":"772_CR21","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1142\/S0219622008002922","volume":"7","author":"H. L. Li","year":"2008","unstructured":"Li, H. L., & Ma, L. C. (2008). Ranking decision alternatives by integrated DEA, AHP and Gower plot techniques. International Journal of Information Technology & Decision Making, 7(2), 241\u2013258.","journal-title":"International Journal of Information Technology & Decision Making"},{"issue":"2","key":"772_CR22","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/BF00939668","volume":"78","author":"M. Patriksson","year":"1993","unstructured":"Patriksson, M. (1993). Partial linearization methods in nonlinear-programming. Journal of Optimization Theory and Applications, 78(2), 227\u2013246.","journal-title":"Journal of Optimization Theory and Applications"},{"issue":"4","key":"772_CR23","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1142\/S0219622008003204","volume":"7","author":"Y. Peng","year":"2008","unstructured":"Peng, Y., Kou, G., Shi, Y., & Chen, Z. X. (2008). A descriptive framework for the field of data mining and knowledge discovery. International Journal of Information Technology & Decision Making, 7(4), 639\u2013682.","journal-title":"International Journal of Information Technology & Decision Making"},{"issue":"3","key":"772_CR24","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1287\/msom.1060.0111","volume":"8","author":"L. Schwarz","year":"2006","unstructured":"Schwarz, L., Ward, J., & Zhai, X. (2006). On the interactions between routing and inventory-management policies in a one-warehouse n-retailer distribution system. Manufacturing & Service Operations Management, 8(3), 253\u2013272.","journal-title":"Manufacturing & Service Operations Management"},{"issue":"1","key":"772_CR25","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1142\/S0219622009003272","volume":"8","author":"A. P. Tchangani","year":"2009","unstructured":"Tchangani, A. P. (2009). Evaluation model for multiattributes-multiagents decision making: satisfying game approach. International Journal of Information Technology & Decision Making, 8(1), 73\u201391.","journal-title":"International Journal of Information Technology & Decision Making"},{"issue":"3","key":"772_CR26","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1287\/trsc.26.3.171","volume":"26","author":"P. Trudeau","year":"1992","unstructured":"Trudeau, P., & Dror, M. (1992). Stochastic inventory routing: route design with stockouts and route failures. Transportation Science, 26(3), 171\u2013184.","journal-title":"Transportation Science"},{"key":"772_CR27","unstructured":"Wolfram. Mathematica 6.0: Wolfram Research, Inc. 2007."},{"key":"772_CR28","first-page":"38","volume-title":"Integer programming","author":"L. A. Wolsey","year":"1998","unstructured":"Wolsey, L. A. (1998). Integer programming (pp. 38\u201340). New York: Wiley."},{"key":"772_CR29","unstructured":"Yu, Y., Chen, H., & Chu, F. (2005). Large scale inventory routing problem with split delivery: a new model and Lagrangian relaxation approach. In: 2005 IEEE international conference on service operations and logistics, and informatics, Beijing, China."},{"issue":"1","key":"772_CR30","doi-asserted-by":"crossref","first-page":"626","DOI":"10.1016\/j.ejor.2005.09.045","volume":"177","author":"Y. Yu","year":"2007","unstructured":"Yu, Y., Chu, F., & Chen, H. (2007). A note on coordination of production and distribution planning. European Journal of Operational Research, 177(1), 626\u2013629.","journal-title":"European Journal of Operational Research"},{"issue":"3","key":"772_CR31","doi-asserted-by":"crossref","first-page":"1022","DOI":"10.1016\/j.ejor.2007.02.061","volume":"189","author":"Y. Yu","year":"2008","unstructured":"Yu, Y., Chen, H., & Chu, F. (2008). A new model and hybrid approach for large scale inventory routing problems. European Journal of Operational Research, 189(3), 1022\u20131040.","journal-title":"European Journal of Operational Research"},{"issue":"3","key":"772_CR32","doi-asserted-by":"crossref","first-page":"929","DOI":"10.1016\/j.ejor.2007.10.016","volume":"192","author":"Y. Yu","year":"2009","unstructured":"Yu, Y., Chu, F., & Chen, H. (2009a). A Stackelberg game and its improvement in a VMI system with a manufacturing vendor. European Journal of Operational Research, 192(3), 929\u2013948.","journal-title":"European Journal of Operational Research"},{"issue":"1","key":"772_CR33","first-page":"368","volume":"57","author":"Y. Yu","year":"2009","unstructured":"Yu, Y., Huang, G. Q., & Liang, L. (2009b). Stackelberg game theory model for optimizing advertising, pricing and inventory policies in vendor managed inventory (VMI) supply chains. Computers & Industrial. Engineering, 57(1), 368\u2013382.","journal-title":"Engineering"}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.springerlink.com\/index\/pdf\/10.1007\/s10479-010-0772-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,3,2]],"date-time":"2019-03-02T09:20:35Z","timestamp":1551518435000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10479-010-0772-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,7,21]]},"references-count":33,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,8]]}},"alternative-id":["772"],"URL":"https:\/\/doi.org\/10.1007\/s10479-010-0772-4","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"value":"0254-5330","type":"print"},{"value":"1572-9338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,7,21]]}}}