{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,9]],"date-time":"2026-02-09T12:20:06Z","timestamp":1770639606865,"version":"3.49.0"},"reference-count":48,"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":[[2013,3]]},"DOI":"10.1007\/s10479-011-0915-2","type":"journal-article","created":{"date-parts":[[2011,7,8]],"date-time":"2011-07-08T19:37:40Z","timestamp":1310153860000},"page":"55-80","source":"Crossref","is-referenced-by-count":78,"title":["A Lagrangian relaxation approach to simultaneous strategic and tactical planning in supply chain design"],"prefix":"10.1007","volume":"203","author":[{"given":"Ali","family":"Diabat","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jean-Philippe","family":"Richard","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Craig W.","family":"Codrington","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2011,7,9]]},"reference":[{"key":"915_CR1","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1016\/j.ejor.2004.09.018","volume":"171","author":"A. Amiri","year":"2006","unstructured":"Amiri, A. (2006). Designing a distribution network in a supply chain system: Formulation and efficient solution procedure. European Journal of Operational Research, 171, 567\u2013576.","journal-title":"European Journal of Operational Research"},{"key":"915_CR2","first-page":"661","volume":"29","author":"S. Axs\u00e4ter","year":"2004","unstructured":"Axs\u00e4ter, S. (2004). Simple evaluation of echelon stock (R,Q) policies for two-level inventory systems. IIE Transactions, 29, 661\u2013669.","journal-title":"IIE Transactions"},{"key":"915_CR3","first-page":"101","volume":"83","author":"F. Barahona","year":"1998","unstructured":"Barahona, F., & Jensen, D. (1998). Plant location with minimum inventory. Mathematical Programming, 83, 101\u2013111.","journal-title":"Mathematical Programming"},{"issue":"2","key":"915_CR4","first-page":"285","volume":"13","author":"J. L. Cavinato","year":"1992","unstructured":"Cavinato, J. L. (1992). A\u00a0total cost\/value model for supply chain competitiveness. Journal of Business Logistics, 13(2), 285\u2013291.","journal-title":"Journal of Business Logistics"},{"issue":"4","key":"915_CR5","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1016\/j.omega.2004.05.004","volume":"33","author":"F. T. S. Chan","year":"2005","unstructured":"Chan, F. T. S., Chung, S. H., & Wadhwa, S. (2005). A\u00a0hybrid genetic algorithm for production and distribution. Omega, 33(4), 345\u2013355.","journal-title":"Omega"},{"issue":"1","key":"915_CR6","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1007\/s11518-006-0123-9","volume":"12","author":"H. Chen","year":"2003","unstructured":"Chen, H., & Chu, C. (2003). A\u00a0Lagrangian relaxation approach for supply chain planning with order\/setup costs and capacity constraints. Journal of Systems Science and Systems Engineering, 12(1), 98\u2013110.","journal-title":"Journal of Systems Science and Systems Engineering"},{"key":"915_CR7","volume-title":"Supply chain management: strategy, planning, & operations","author":"S. Chopra","year":"2006","unstructured":"Chopra, S., & Meindl, P. (2006). Supply chain management: strategy, planning, & operations (3rd ed.). New York: Prentice-Hall.","edition":"3"},{"issue":"4","key":"915_CR8","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1287\/mnsc.6.4.475","volume":"6","author":"A. J. Clark","year":"1960","unstructured":"Clark, A. J., & Scarf, H. (1960). Optimal policies for a multi-echelon inventory problem. Management Science, 6(4), 475\u2013490.","journal-title":"Management Science"},{"key":"915_CR9","doi-asserted-by":"crossref","DOI":"10.1002\/9781118032343","volume-title":"Network and discrete location: models, algorithms, and applications","author":"M. S. Daskin","year":"1995","unstructured":"Daskin, M. S. (1995). Network and discrete location: models, algorithms, and applications. New York: Wiley."},{"key":"915_CR10","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1023\/A:1020763400324","volume":"110","author":"M. S. Daskin","year":"2002","unstructured":"Daskin, M. S., Coullard, C. R., & Shen, Z.-J. M. (2002). An inventory-location model: formulation, solution algorithm and computational results. Annals of Operations Research, 110, 83\u2013106.","journal-title":"Annals of Operations Research"},{"key":"915_CR11","volume-title":"Facility location in supply chain design","author":"M. S. Daskin","year":"2005","unstructured":"Daskin, M. S., Snyder, L. V., & Berger, R. T. (2005). Facility location in supply chain design. New York: Springer."},{"issue":"5","key":"915_CR12","doi-asserted-by":"crossref","first-page":"498","DOI":"10.1287\/mnsc.25.5.498","volume":"25","author":"G. D. Eppen","year":"1979","unstructured":"Eppen, G. D. (1979). Effects of centralization on expected costs in a multi-location newsboy problem. Management Science, 25(5), 498\u2013501.","journal-title":"Management Science"},{"key":"915_CR13","first-page":"155","volume":"32","author":"S. J. Erlebacher","year":"2000","unstructured":"Erlebacher, S. J., & Meller, R. D. (2000). The interaction of location and inventory in designing distribution systems. IIE Transactions, 32, 155\u2013166.","journal-title":"IIE Transactions"},{"issue":"1","key":"915_CR14","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1016\/j.ejor.2003.11.029","volume":"165","author":"E. Eskigun","year":"2005","unstructured":"Eskigun, E., Uzsoy, R., Preckel, P. V., Beaujon, G., Krishnan, S., & Tew, J. D. (2005). Outbound supply chain network design with mode selection, lead times and capacitated vehicle distribution centers. European Journal of Operational Research, 165(1), 182\u2013206.","journal-title":"European Journal of Operational Research"},{"issue":"1","key":"915_CR15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1287\/mnsc.27.1.1","volume":"27","author":"M. L. Fisher","year":"1981","unstructured":"Fisher, M. L. (1981). The Lagrangian relaxation method for solving integer programming problems. Management Science, 27(1), 1\u201318.","journal-title":"Management Science"},{"key":"915_CR16","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1287\/inte.15.2.10","volume":"15","author":"M. L. Fisher","year":"1985","unstructured":"Fisher, M. L. (1985). An applications-oriented guide to Lagrangian relaxation. Interfaces, 15, 10\u201321.","journal-title":"Interfaces"},{"issue":"1\/2","key":"915_CR17","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1108\/01443570110358468","volume":"21","author":"A. Gunasekaran","year":"2001","unstructured":"Gunasekaran, A., Patel, C., & Tirtiroglu, E. (2001). Performance measures and metrics in a supply chain environment. International Journal of Operations & Production Management, 21(1\/2), 71\u201387.","journal-title":"International Journal of Operations & Production Management"},{"key":"915_CR18","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/j.ijpe.2003.08.003","volume":"87","author":"A. Gunasekaran","year":"2004","unstructured":"Gunasekaran, A., Patel, C., & McGaughey, R. E. (2004). A framework for supply chain performance measurement. International Journal of Production Economics, 87, 333\u2013347.","journal-title":"International Journal of Production Economics"},{"key":"915_CR19","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1057\/palgrave.jors.2600698","volume":"50","author":"K. S. Hindi","year":"1999","unstructured":"Hindi, K. S., & Pienkosz, K. (1999). Efficient solution of large scale, single-source, capacitated plant location problems. Journal of the Operational Research Society, 50, 268\u2013274.","journal-title":"Journal of the Operational Research Society"},{"key":"915_CR20","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1016\/S0377-2217(00)00033-3","volume":"133","author":"V. Jayaraman","year":"2001","unstructured":"Jayaraman, V., & Pirkul, H. (2001). Planning and coordination of production and distribution facilities for multiple commodities. European Journal of Operational Research, 133, 394\u2013408.","journal-title":"European Journal of Operational Research"},{"issue":"3","key":"915_CR21","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1016\/S0377-2217(02)00153-4","volume":"144","author":"V. Jayaraman","year":"2003","unstructured":"Jayaraman, V., & Ross, A. (2003). A simulated annealing methodology to distribution network design and management. European Journal of Operational Research, 144(3), 629\u2013645.","journal-title":"European Journal of Operational Research"},{"key":"915_CR22","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1108\/eb014655","volume":"17","author":"T. C. Jones","year":"1987","unstructured":"Jones, T. C., & Riley, D. W. (1987). Using inventory for competitive advantage through supply chain management. International Journal of Physical Distribution & Logistics Management, 17, 94\u2013104.","journal-title":"International Journal of Physical Distribution & Logistics Management"},{"issue":"4","key":"915_CR23","doi-asserted-by":"crossref","first-page":"382","DOI":"10.1504\/IJLSM.2005.006292","volume":"1","author":"H. Min","year":"2005","unstructured":"Min, H., Ko, H. J., & Park, B. I. (2005). A\u00a0Lagrangian relaxation heuristic for solving the multi-echelon, multi-commodity, close-loop supply chain network design problem. International Journal of Logistics Systems and Management, 1(4), 382\u2013404.","journal-title":"International Journal of Logistics Systems and Management"},{"issue":"1","key":"915_CR24","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1007\/s11067-006-7684-5","volume":"6","author":"P. A. Miranda","year":"2006","unstructured":"Miranda, P. A., & Garrido, R. A. (2006). A\u00a0simultaneous inventory control and facility location model with stochastic capacity constraints. Networks and Spatial Economics, 6(1), 39\u201353.","journal-title":"Networks and Spatial Economics"},{"issue":"12","key":"915_CR25","doi-asserted-by":"crossref","first-page":"1613","DOI":"10.1287\/mnsc.33.12.1613","volume":"33","author":"J. A. Muckstadt","year":"1987","unstructured":"Muckstadt, J. A., & Roundy, R. O. (1987). Multi-item, one-warehouse, multi-retailer distribution systems. Management Science, 33(12), 1613\u20131621.","journal-title":"Management Science"},{"key":"915_CR26","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1002\/nav.20282","volume":"55","author":"L. Ozsen","year":"2008","unstructured":"Ozsen, L., Coullard, C. R., & Daskin, M. S. (2008). Capacitated warehouse location model with risk pooling. Naval Research Logistics, 55, 295\u2013312.","journal-title":"Naval Research Logistics"},{"key":"915_CR27","doi-asserted-by":"crossref","first-page":"869","DOI":"10.1016\/S0305-0548(97)00096-8","volume":"25","author":"H. Pirkul","year":"1998","unstructured":"Pirkul, H., & Jayaraman, V. (1998). A\u00a0multi-commodity, multi-plant, capacitated facility location problem: formulation and efficient heuristic solution. Computers & Operations Research, 25, 869\u2013878.","journal-title":"Computers & Operations Research"},{"key":"915_CR28","unstructured":"Putz, P. (2007). Subgradient optimization based Lagrangian relaxation and relax-and-cut approaches for the bounded-diameter minimum spanning tree problem. Master\u2019s thesis, Technical University of Vienna, October."},{"key":"915_CR29","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1016\/j.ejor.2006.02.016","volume":"178","author":"H. E. Romeijn","year":"2007","unstructured":"Romeijn, H. E., Shu, J., Teo, C.-P. (2007). Designing two-echelon supply networks. European Journal of Operations Research, 178, 449\u2013462.","journal-title":"European Journal of Operations Research"},{"issue":"11","key":"915_CR30","doi-asserted-by":"crossref","first-page":"1416","DOI":"10.1287\/mnsc.31.11.1416","volume":"31","author":"R. Roundy","year":"1985","unstructured":"Roundy, R. (1985). 98%-Effective integer-ratio lot-sizing for one-warehouse multi-retailer systems. Management Science, 31(11), 1416\u20131430.","journal-title":"Management Science"},{"issue":"5","key":"915_CR31","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1287\/mnsc.19.5.555","volume":"19","author":"L. B. Schwarz","year":"1973","unstructured":"Schwarz, L. B. (1973). A simple continuous review deterministic one-warehouse n-retailer inventory problem. Management Science, 19(5), 555\u2013566.","journal-title":"Management Science"},{"key":"915_CR32","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1287\/trsc.37.1.40.12823","volume":"37","author":"Z.-J. M. Shen","year":"2003","unstructured":"Shen, Z.-J. M., Coullard, C. R., & Daskin, M. S. (2003). A joint location-inventory model. Transportation Science, 37, 40\u201355.","journal-title":"Transportation Science"},{"issue":"2","key":"915_CR33","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1111\/j.1475-3995.2009.00741.x","volume":"17","author":"A. Shiguemoto","year":"2010","unstructured":"Shiguemoto, A., & Armentano, V. A. (2010). A tabu search procedure for coordinating production, inventory and distribution routing problems. International Transactions in Operational Research, 17(2), 179\u2013195.","journal-title":"International Transactions in Operational Research"},{"issue":"2","key":"915_CR34","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1287\/trsc.1090.0302","volume":"44","author":"J. Shu","year":"2010","unstructured":"Shu, J. (2010). An efficient greedy heuristic for warehouse retailer network design optimization. Transportation Science, 44(2), 183\u2013192.","journal-title":"Transportation Science"},{"issue":"1","key":"915_CR35","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1287\/opre.1040.0140","volume":"53","author":"J. Shu","year":"2005","unstructured":"Shu, J., Teo, C.-P., & Shen, Z.-J. M. (2005). Stochastic transportation-inventory network design problem. Operations Research, 53(1), 48\u201360.","journal-title":"Operations Research"},{"key":"915_CR36","volume-title":"Inventory management and production planning and scheduling","author":"E. A. Silver","year":"1998","unstructured":"Silver, E. A., Pyke, D. F., & Peterson, R. (1998). Inventory management and production planning and scheduling (3rd ed.). New York: Wiley.","edition":"3"},{"key":"915_CR37","volume-title":"Designing & managing the supply chain","author":"D. Simchi-Levi","year":"2007","unstructured":"Simchi-Levi, D., Kaminsky, P., & Simchi-Levi, E. (2007). Designing & managing the supply chain (3rd ed.). New York: McGraw-Hill\/Irwin.","edition":"3"},{"key":"915_CR38","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1080\/07408170600941631","volume":"39","author":"K. Sourirajan","year":"2007","unstructured":"Sourirajan, K., Ozsen, L., & Uzsoy, R. (2007). A\u00a0single-product network design model with lead time and safety stock considerations. IIE Transactions, 39, 411\u2013424.","journal-title":"IIE Transactions"},{"key":"915_CR39","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1016\/j.ejor.2008.07.038","volume":"197","author":"K. Sourirajan","year":"2009","unstructured":"Sourirajan, K., Ozsen, L., & Uzsoy, R. (2009). A\u00a0genetic algorithm for a single product network design model with lead time and safety stock considerations. European Journal of Operational Research, 197, 599\u2013608.","journal-title":"European Journal of Operational Research"},{"issue":"8","key":"915_CR40","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1108\/EUM0000000000329","volume":"19","author":"G. C. Stevens","year":"1993","unstructured":"Stevens, G. C. (1993). Integrating the supply chain. International Journal of Physical Distribution & Logistics Management, 19(8), 3\u20138.","journal-title":"International Journal of Physical Distribution & Logistics Management"},{"issue":"1","key":"915_CR41","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1287\/mnsc.37.1.68","volume":"37","author":"A. Svoronos","year":"1991","unstructured":"Svoronos, A., & Zipkin, P. (1991). Evaluation of one-for-one replenishment policies for multiechelon inventory systems. Management Science, 37(1), 68\u201383.","journal-title":"Management Science"},{"issue":"4","key":"915_CR42","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1109\/TASE.2008.917156","volume":"5","author":"G.-A. Tanonkou","year":"2008","unstructured":"Tanonkou, G.-A., Benyoucef, L., & Xie, X. (2008). Design of Stochastic distribution networks using Lagrangian relaxation. IEEE Transactions on Automation Science and Engineering, 5(4), 597\u2013608.","journal-title":"IEEE Transactions on Automation Science and Engineering"},{"issue":"3","key":"915_CR43","doi-asserted-by":"crossref","first-page":"396","DOI":"10.1287\/opre.1030.0096","volume":"52","author":"C.-P. Teo","year":"2004","unstructured":"Teo, C.-P., & Shu, J. (2004). Warehouse-retailer network design problem. Operations Research, 52(3), 396\u2013408.","journal-title":"Operations Research"},{"key":"915_CR44","first-page":"99","volume":"33","author":"C.-P. Teo","year":"2001","unstructured":"Teo, C.-P., Ou, J., & Goh, M. (2001). Impact on inventory costs with consolidation of distribution centers. IIE Transactions, 33, 99\u2013110.","journal-title":"IIE Transactions"},{"key":"915_CR45","doi-asserted-by":"crossref","first-page":"3585","DOI":"10.1021\/ie0100030","volume":"40","author":"P. Tsiakis","year":"2001","unstructured":"Tsiakis, P., Shah, N., & Pantelides, C. C. (2001). Design of multi-echelon supply chain networks under demand uncertainty. Industrial & Engineering Chemistry Research, 40, 3585\u20133604.","journal-title":"Industrial & Engineering Chemistry Research"},{"issue":"3","key":"915_CR46","doi-asserted-by":"crossref","first-page":"626","DOI":"10.1016\/S0377-2217(03)00383-7","volume":"158","author":"H. M. Wee","year":"2004","unstructured":"Wee, H. M., & Yang, P. C. (2004). The optimal and heuristic solutions of a distribution network. European Journal of Operational Research, 158(3), 626\u2013632.","journal-title":"European Journal of Operational Research"},{"key":"915_CR47","doi-asserted-by":"crossref","first-page":"7802","DOI":"10.1021\/ie800257x","volume":"47","author":"F. You","year":"2008","unstructured":"You, F., & Grossman, I. E. (2008). Mixed-integer nonlinear programming models and algorithms for large-scale supply chain design with stochastic inventory management. Industrial & Engineering Chemistry Research, 47, 7802\u20137817.","journal-title":"Industrial & Engineering Chemistry Research"},{"issue":"2","key":"915_CR48","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1002\/aic.12010","volume":"56","author":"F. You","year":"2010","unstructured":"You, F., & Grossman, I. E. (2010). Integrated multi-echelon supply chain design with inventories under uncertainty: MINLP models, computational strategies. AIChE Journal, 56(2), 419\u2013440.","journal-title":"AIChE Journal"}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-011-0915-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,8]],"date-time":"2024-04-08T15:23:15Z","timestamp":1712589795000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10479-011-0915-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,7,9]]},"references-count":48,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2013,3]]}},"alternative-id":["915"],"URL":"https:\/\/doi.org\/10.1007\/s10479-011-0915-2","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"value":"0254-5330","type":"print"},{"value":"1572-9338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,7,9]]}}}