{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,9]],"date-time":"2026-02-09T23:31:31Z","timestamp":1770679891279,"version":"3.49.0"},"reference-count":44,"publisher":"Springer Science and Business Media LLC","issue":"3-4","license":[{"start":{"date-parts":[[2018,6,5]],"date-time":"2018-06-05T00:00:00Z","timestamp":1528156800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2018,6,5]],"date-time":"2018-06-05T00:00:00Z","timestamp":1528156800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","award":["FA9550-15-1-0267"],"award-info":[{"award-number":["FA9550-15-1-0267"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["ECCS 1548847"],"award-info":[{"award-number":["ECCS 1548847"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Manag Sci"],"published-print":{"date-parts":[[2018,10]]},"DOI":"10.1007\/s10287-018-0311-3","type":"journal-article","created":{"date-parts":[[2018,6,5]],"date-time":"2018-06-05T07:39:08Z","timestamp":1528184348000},"page":"501-540","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["A Progressive Hedging based branch-and-bound algorithm for mixed-integer stochastic programs"],"prefix":"10.1007","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9699-0314","authenticated-orcid":false,"given":"Semih","family":"Atakan","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6285-8833","authenticated-orcid":false,"given":"Suvrajeet","family":"Sen","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,6,5]]},"reference":[{"issue":"6","key":"311_CR1","doi-asserted-by":"publisher","first-page":"565","DOI":"10.1016\/j.orl.2013.07.009","volume":"41","author":"S Ahmed","year":"2013","unstructured":"Ahmed S (2013) A scenario decomposition algorithm for 0\u20131 stochastic programs. Oper Res Lett 41(6):565\u2013569","journal-title":"Oper Res Lett"},{"key":"311_CR2","unstructured":"Ahmed S, Garcia R, Kong N, Ntaimo L, Parija G, Qiu F, Sen S (2015) SIPLIB: a stochastic integer programming test problem library. \n                    http:\/\/www.isye.gatech.edu\/~sahmed\/siplib\n                    \n                  . Accessed 5 July 2017"},{"key":"311_CR3","unstructured":"Angulo G, Ahmed S, Dey SS (2014) Improving the integer L-shaped method. Technical report, School of Industrial and Systems Engineering, Georgia Institute of Technology"},{"issue":"1","key":"311_CR4","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1016\/j.orl.2016.11.006","volume":"45","author":"J Barnett","year":"2017","unstructured":"Barnett J, Watson J-P, Woodruff DL (2017) BBPH: using Progressive Hedging within branch and bound to solve multi-stage stochastic mixed integer programs. Oper Res Lett 45(1):34\u201339","journal-title":"Oper Res Lett"},{"issue":"5","key":"311_CR5","doi-asserted-by":"publisher","first-page":"989","DOI":"10.1287\/opre.33.5.989","volume":"33","author":"JR Birge","year":"1985","unstructured":"Birge JR (1985) Decomposition and partitioning methods for multistage stochastic linear programs. Oper Res 33(5):989\u20131007","journal-title":"Oper Res"},{"issue":"1","key":"311_CR6","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1287\/opre.50.1.3.17780","volume":"50","author":"RE Bixby","year":"2002","unstructured":"Bixby RE (2002) Solving real-world linear programs: a decade and more of progress. Oper Res 50(1):3\u201315","journal-title":"Oper Res"},{"key":"311_CR7","unstructured":"Boland N, Christiansen J, Dandurand B, Eberhard A, Linderoth J, Luedtke J, Oliveira F (2016) Combining Progressive Hedging with a Frank\u2013Wolfe method to compute Lagrangian dual bounds in stochastic mixed-integer programming. Technical report, Optimization Online"},{"issue":"2","key":"311_CR8","doi-asserted-by":"publisher","first-page":"491","DOI":"10.1007\/s10107-014-0763-3","volume":"150","author":"NL Boland","year":"2014","unstructured":"Boland NL, Eberhard AC (2014) On the augmented Lagrangian dual for integer programming. Math Program 150(2):491\u2013509","journal-title":"Math Program"},{"issue":"1","key":"311_CR9","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1561\/2200000016","volume":"3","author":"S Boyd","year":"2010","unstructured":"Boyd S (2010) Distributed optimization and statistical learning via the alternating direction method of multipliers. Found Trends Mach Learn 3(1):1\u2013122","journal-title":"Found Trends Mach Learn"},{"issue":"1\u20132","key":"311_CR10","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1016\/S0167-6377(98)00050-9","volume":"24","author":"CC Car\u00f8e","year":"1999","unstructured":"Car\u00f8e CC, Schultz R (1999) Dual decomposition in stochastic integer programming. Oper Res Lett 24(1\u20132):37\u201345","journal-title":"Oper Res Lett"},{"key":"311_CR11","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1007\/BF02680570","volume":"83","author":"CC Car\u00f8e","year":"1998","unstructured":"Car\u00f8e CC, Tind J (1998) L-shaped decomposition of two-stage stochastic programs with integer recourse. Math Program 83:451\u2013464","journal-title":"Math Program"},{"key":"311_CR12","doi-asserted-by":"publisher","first-page":"96","DOI":"10.1007\/s11750-009-0083-6","volume":"17","author":"LF Escudero","year":"2009","unstructured":"Escudero LF, Gar\u00edn A, Merino M, P\u00e9rez G (2009) BFC-MSMIP: an exact branch-and-fix coordination approach for solving multistage stochastic mixed 0\u20131 problems. Top 17:96\u2013122","journal-title":"Top"},{"key":"311_CR13","unstructured":"Feizollahi MJ, Ahmed S, Sun A (2015) Exact augmented Lagrangian duality for mixed integer linear programming. Technical report, School of Industrial and Systems Engineering, Georgia Institute of Technology"},{"issue":"1","key":"311_CR14","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1007\/s10107-016-1000-z","volume":"157","author":"D Gade","year":"2016","unstructured":"Gade D, Hackebeil G, Ryan SM, Roger J-PW, David JW (2016) Obtaining lower bounds from the Progressive Hedging algorithm for stochastic mixed-integer programs. Math Program 157(1):47\u201367","journal-title":"Math Program"},{"issue":"1\u20132","key":"311_CR15","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1007\/s10107-012-0615-y","volume":"144","author":"D Gade","year":"2014","unstructured":"Gade D, K\u00fc\u00e7\u00fckyavuz S, Sen S (2014) Decomposition algorithms with parametric Gomory cuts for two-stage stochastic integer programs. Math Program 144(1\u20132):39\u201364","journal-title":"Math Program"},{"issue":"2","key":"311_CR16","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1007\/BF02592954","volume":"39","author":"M Guignard","year":"1987","unstructured":"Guignard M, Kim S (1987) Lagrangean decomposition: a model yielding stronger Lagrangean bounds. Math Program 39(2):215\u2013228","journal-title":"Math Program"},{"issue":"3","key":"311_CR17","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1016\/j.orl.2015.03.008","volume":"43","author":"G Guo","year":"2015","unstructured":"Guo G, Hackebeil G, Ryan SM, Watson J-P, Woodruff DL (2015) Integration of Progressive Hedging and dual decomposition in stochastic integer programs. Oper Res Lett 43(3):311\u2013316","journal-title":"Oper Res Lett"},{"key":"311_CR18","volume-title":"Semidefinite programming for combinatorial optimization","author":"C Helmberg","year":"2000","unstructured":"Helmberg C (2000) Semidefinite programming for combinatorial optimization. Konrad-Zuse-Zentrum f\u00fcr Informationstechnik, Berlin"},{"issue":"2\u20133","key":"311_CR19","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1007\/s10107-002-0322-1","volume":"94","author":"R Hemmecke","year":"2003","unstructured":"Hemmecke R, Schultz R (2003) Decomposition of test sets in stochastic integer programming. Math Program 94(2\u20133):323\u2013341","journal-title":"Math Program"},{"issue":"1","key":"311_CR20","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1007\/s10479-006-6165-z","volume":"142","author":"JL Higle","year":"2006","unstructured":"Higle JL, Sen S (2006) Multistage stochastic convex programs: duality and its implications. Ann Oper Res 142(1):129\u2013146","journal-title":"Ann Oper Res"},{"key":"311_CR21","volume-title":"Global optimization: deterministic approaches","author":"R Horst","year":"2013","unstructured":"Horst R, Tuy H (2013) Global optimization: deterministic approaches. Springer, Berlin"},{"key":"311_CR22","unstructured":"J\u00f6rnsten K, N\u00e4sberg M, Smeds P (1985) Variable splitting: a new Lagrangean relaxation approach to some mathematical programming models. Technical report, Department of Mathematics, University of Link\u00f6ping"},{"issue":"3","key":"311_CR23","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1016\/0167-6377(93)90002-X","volume":"13","author":"G Laporte","year":"1993","unstructured":"Laporte G, Louveaux FV (1993) The integer L-shaped method for stochastic integer programs with complete recourse. Oper Res Lett 13(3):133\u2013142","journal-title":"Oper Res Lett"},{"issue":"2","key":"311_CR24","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1007\/BF00247208","volume":"2","author":"A L\u00f8kketangen","year":"1996","unstructured":"L\u00f8kketangen A, Woodruff DL (1996) Progressive Hedging and tabu search applied to mixed integer (0, 1) multistage stochastic programming. J Heuristics 2(2):111\u2013128","journal-title":"J Heuristics"},{"issue":"4","key":"311_CR25","doi-asserted-by":"publisher","first-page":"889","DOI":"10.1287\/opre.28.4.889","volume":"28","author":"FV Louveaux","year":"1980","unstructured":"Louveaux FV (1980) A solution method for multistage stochastic programs with recourse with application to an energy investment problem. Oper Res 28(4):889\u2013902","journal-title":"Oper Res"},{"issue":"3","key":"311_CR26","doi-asserted-by":"publisher","first-page":"252","DOI":"10.1016\/j.orl.2013.02.003","volume":"41","author":"M Lubin","year":"2013","unstructured":"Lubin M, Martin K, Petra CG, Sand\u0131k\u00e7\u0131 B (2013) On parallelizing dual decomposition in stochastic integer programming. Oper Res Lett 41(3):252\u2013258","journal-title":"Oper Res Lett"},{"issue":"6","key":"311_CR27","doi-asserted-by":"publisher","first-page":"786","DOI":"10.1287\/mnsc.1030.0164","volume":"50","author":"G Lulli","year":"2004","unstructured":"Lulli G, Sen S (2004) A branch-and-price algorithm for multistage stochastic integer programming with application to stochastic batch-sizing problems. Manag Sci 50(6):786\u2013796","journal-title":"Manag Sci"},{"issue":"1","key":"311_CR28","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1007\/BF02204860","volume":"31","author":"JM Mulvey","year":"1991","unstructured":"Mulvey JM, Vladimirou H (1991) Applying the Progressive Hedging algorithm to stochastic generalized networks. Ann Oper Res 31(1):399\u2013424","journal-title":"Ann Oper Res"},{"issue":"3","key":"311_CR29","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1287\/opre.43.3.477","volume":"43","author":"JR Mulvey","year":"1995","unstructured":"Mulvey JR, Ruszczy\u0144ski A (1995) A new scenario decomposition method for large-scale stochastic optimization. Oper Res 43(3):477\u2013490","journal-title":"Oper Res"},{"issue":"3","key":"311_CR30","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1007\/s10898-004-5910-6","volume":"32","author":"L Ntaimo","year":"2005","unstructured":"Ntaimo L, Sen S (2005) The million-variable \u201cmarch\u201d for stochastic combinatorial optimization. J Global Optim 32(3):385\u2013400","journal-title":"J Global Optim"},{"key":"311_CR31","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1016\/j.ejor.2015.01.004","volume":"244","author":"A Pages-Bernausa","year":"2015","unstructured":"Pages-Bernausa A, P\u00e9rez-Vald\u00e9s G, Tomasgard A (2015) A parallelised distributed implementation of a branch and fix coordination algorithm. Eur J Oper Res 244:77\u201385","journal-title":"Eur J Oper Res"},{"key":"311_CR32","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1007\/s10107-016-1006-6","volume":"161","author":"Y Qi","year":"2016","unstructured":"Qi Y, Sen S (2016) The ancestral Benders\u2019 cutting plane algorithm with multi-term disjunctions for mixed-integer recourse decisions in stochastic programming. Math Program 161:193\u2013235","journal-title":"Math Program"},{"key":"311_CR33","unstructured":"Ralphs T, Hassanzadeh A (2014) A generalization of Benders\u2019 algorithm for two-stage stochastic optimization problems with mixed integer recourse. Technical report, Laboratory for Computational Optimization at Lehigh (COR@L), Department of Industrial and Systems Engineering, Lehigh University"},{"issue":"5","key":"311_CR34","doi-asserted-by":"publisher","first-page":"877","DOI":"10.1137\/0314056","volume":"14","author":"RT Rockafellar","year":"1976","unstructured":"Rockafellar RT (1976) Monotone operators and the proximal point algorithm. SIAM J Control Optim 14(5):877\u2013898","journal-title":"SIAM J Control Optim"},{"issue":"1","key":"311_CR35","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1287\/moor.16.1.119","volume":"16","author":"RT Rockafellar","year":"1991","unstructured":"Rockafellar RT, Wets RJ-B (1991) Scenarios and policy aggregation in optimization under uncertainty. Math Oper Res 16(1):119\u2013147","journal-title":"Math Oper Res"},{"key":"311_CR36","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1007\/s10107-002-0337-7","volume":"93","author":"A Ruszczy\u0144ski","year":"2002","unstructured":"Ruszczy\u0144ski A (2002) Probabilistic programming with discrete distributions and precedence constrained knapsack polyhedra. Math Program 93:195\u2013215","journal-title":"Math Program"},{"key":"311_CR37","unstructured":"Ryan K, Ahmed S, Dey SS, Rajan D (2016) Optimization driven scenario grouping. Technical report, School of Industrial and Systems Engineering, Georgia Institute of Technology"},{"key":"311_CR38","doi-asserted-by":"crossref","unstructured":"Ryan SM, Wets RJB, Woodruff DL, Silva-Monroy C, Watson JP (2013) Toward scalable, parallel Progressive Hedging for stochastic unit commitment. In: Power and energy society general meeting (PES), 2013 IEEE, pp 1\u20135","DOI":"10.1109\/PESMG.2013.6673013"},{"issue":"1","key":"311_CR39","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10107-004-0566-z","volume":"104","author":"S Sen","year":"2005","unstructured":"Sen S, Higle JL (2005) The C3 theorem and a D2 algorithm for large scale stochastic mixed-integer programming: set convexification. Math Program 104(1):1\u201320","journal-title":"Math Program"},{"issue":"2","key":"311_CR40","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1007\/s10107-005-0592-5","volume":"106","author":"S Sen","year":"2006","unstructured":"Sen S, Sherali HD (2006) Decomposition with branch-and-cut approaches for two-stage stochastic mixed-integer programming. Math Program 106(2):203\u2013223","journal-title":"Math Program"},{"issue":"2","key":"311_CR41","doi-asserted-by":"publisher","first-page":"498","DOI":"10.1287\/opre.1120.1156","volume":"61","author":"AC Trapp","year":"2013","unstructured":"Trapp AC, Prokopyev OA, Schaefer AJ (2013) On a level-set characterization of the value function of an integer program and its application to stochastic programming. Oper Res 61(2):498\u2013511","journal-title":"Oper Res"},{"issue":"4","key":"311_CR42","doi-asserted-by":"publisher","first-page":"638","DOI":"10.1137\/0117061","volume":"17","author":"RM Van Slyke","year":"1969","unstructured":"Van Slyke RM, Wets R (1969) L-shaped linear programs with applications to optimal control and stochastic programming. SIAM J Appl Math 17(4):638\u2013663","journal-title":"SIAM J Appl Math"},{"issue":"4","key":"311_CR43","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1007\/s10287-010-0125-4","volume":"8","author":"J-P Watson","year":"2010","unstructured":"Watson J-P, Woodruff DL (2010) Progressive hedging innovations for a class of stochastic mixed-integer resource allocation problems. CMS 8(4):355\u2013370","journal-title":"CMS"},{"issue":"4","key":"311_CR44","doi-asserted-by":"publisher","first-page":"1933","DOI":"10.1137\/13092678X","volume":"24","author":"M Zhang","year":"2014","unstructured":"Zhang M, K\u00fc\u00e7\u00fckyavuz S (2014) Finitely convergent decomposition algorithms for two-stage stochastic pure integer programs. SIAM J Optim 24(4):1933\u20131951","journal-title":"SIAM J Optim"}],"container-title":["Computational Management Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10287-018-0311-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10287-018-0311-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10287-018-0311-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,16]],"date-time":"2020-05-16T17:02:28Z","timestamp":1589648548000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10287-018-0311-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6,5]]},"references-count":44,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2018,10]]}},"alternative-id":["311"],"URL":"https:\/\/doi.org\/10.1007\/s10287-018-0311-3","relation":{},"ISSN":["1619-697X","1619-6988"],"issn-type":[{"value":"1619-697X","type":"print"},{"value":"1619-6988","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,6,5]]},"assertion":[{"value":"27 September 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 May 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 June 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}