{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T18:47:12Z","timestamp":1776106032822,"version":"3.50.1"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2020,2,26]],"date-time":"2020-02-26T00:00:00Z","timestamp":1582675200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,2,26]],"date-time":"2020-02-26T00:00:00Z","timestamp":1582675200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100003407","name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","doi-asserted-by":"publisher","award":["TESUN-83486178370409"],"award-info":[{"award-number":["TESUN-83486178370409"]}],"id":[{"id":"10.13039\/501100003407","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2020,9]]},"DOI":"10.1007\/s10107-020-01482-5","type":"journal-article","created":{"date-parts":[[2020,2,26]],"date-time":"2020-02-26T03:03:01Z","timestamp":1582686181000},"page":"249-281","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["An exact approach for the bilevel knapsack problem with interdiction constraints and extensions"],"prefix":"10.1007","volume":"183","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2897-183X","authenticated-orcid":false,"given":"Federico","family":"Della\u00a0Croce","sequence":"first","affiliation":[]},{"given":"Rosario","family":"Scatamacchia","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,2,26]]},"reference":[{"key":"1482_CR1","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1016\/j.ejor.2008.09.012","volume":"197","author":"H Aissi","year":"2009","unstructured":"Aissi, H., Bazgan, C., Vanderpooten, D.: Minmax and minmax regret versions of combinatorial optimization problems: a survey. Eur. J. Oper. Res. 197, 427\u2013438 (2009)","journal-title":"Eur. J. Oper. Res."},{"key":"1482_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.disopt.2012.09.001","volume":"10","author":"L Brotcorne","year":"2013","unstructured":"Brotcorne, L., Hanafi, S., Mansi, R.: One-level reformulation of the bilevel knapsack problem using dynamic programming. Discrete Optim. 10, 1\u201310 (2013)","journal-title":"Discrete Optim."},{"key":"1482_CR3","doi-asserted-by":"crossref","unstructured":"Caprara, A., Carvalho, M., Lodi, A., Woeginger, G.: A Complexity and approximability study of the bilevel knapsack problem. In: Proceedings of IPCO 2013. LNCS, vol. 7801, pp. 98\u2013109 (2013)","DOI":"10.1007\/978-3-642-36694-9_9"},{"key":"1482_CR4","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1287\/ijoc.2015.0676","volume":"28","author":"A Caprara","year":"2016","unstructured":"Caprara, A., Carvalho, M., Lodi, A., Woeginger, G.: Bilevel knapsack with interdiction constraints. INFORMS J. Comput. 28, 319\u2013333 (2016)","journal-title":"INFORMS J. Comput."},{"key":"1482_CR5","doi-asserted-by":"publisher","first-page":"1447","DOI":"10.1007\/s11590-015-0872-9","volume":"9","author":"M Caramia","year":"2015","unstructured":"Caramia, M., Mari, R.: Enhanced exact algorithms for discrete bilevel linear problems. Optim. Lett. 9, 1447\u20131468 (2015)","journal-title":"Optim. Lett."},{"key":"1482_CR6","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1016\/j.orl.2017.12.009","volume":"46","author":"M Carvalho","year":"2018","unstructured":"Carvalho, M., Lodi, A., Marcotte, P.: A polynomial algorithm for a continuous bilevel knapsack problem. Oper. Res. Lett. 46, 185\u2013188 (2018)","journal-title":"Oper. Res. Lett."},{"key":"1482_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.tcs.2012.08.008","volume":"497","author":"L Chen","year":"2013","unstructured":"Chen, L., Zhang, G.: Approximation algorithms for a bi-level knapsack problem. Theor. Comput. Sci. 497, 1\u201312 (2013)","journal-title":"Theor. Comput. Sci."},{"issue":"4","key":"1482_CR8","doi-asserted-by":"publisher","first-page":"691","DOI":"10.1007\/s11590-017-1227-5","volume":"12","author":"C D\u2019Ambrosio","year":"2018","unstructured":"D\u2019Ambrosio, C., Furini, F., Monaci, M., Traversi, E.: On the product knapsack problem. Optim. Lett. 12(4), 691\u2013712 (2018)","journal-title":"Optim. Lett."},{"key":"1482_CR9","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1016\/j.disopt.2010.03.008","volume":"7","author":"VG Deineko","year":"2010","unstructured":"Deineko, V.G., Woeginger, G.: Pinpointing the complexity of the interval min\u2013max regret knapsack problem. Discrete Optim. 7, 191\u2013196 (2010)","journal-title":"Discrete Optim."},{"key":"1482_CR10","doi-asserted-by":"publisher","first-page":"122","DOI":"10.1016\/j.dam.2017.11.023","volume":"253","author":"F Della Croce","year":"2019","unstructured":"Della Croce, F., Pferschy, U., Scatamacchia, R.: New exact approaches and approximation results for the penalized knapsack problem. Discrete Appl. Math. 253, 122\u2013135 (2019)","journal-title":"Discrete Appl. Math."},{"key":"1482_CR11","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1016\/j.cor.2016.11.015","volume":"80","author":"F Della Croce","year":"2019","unstructured":"Della Croce, F., Salassa, F., Scatamacchia, R.: An exact approach for the 0\u20131 knapsack problem with setups. Comput. Oper. Res. 80, 61\u201367 (2019)","journal-title":"Comput. Oper. Res."},{"key":"1482_CR12","doi-asserted-by":"publisher","first-page":"56","DOI":"10.1016\/j.ejor.2016.12.009","volume":"260","author":"F Della Croce","year":"2017","unstructured":"Della Croce, F., Salassa, F., Scatamacchia, R.: A new exact approach for the 0\u20131 collapsing knapsack problem. Eur. J. Oper. Res. 260, 56\u201369 (2017)","journal-title":"Eur. J. Oper. Res."},{"key":"1482_CR13","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1007\/978-3-030-17953-3_12","volume-title":"Integer Programming and Combinatorial Optimization","author":"F Della Croce","year":"2019","unstructured":"Della Croce, F., Scatamacchia, R.: Lower bounds and a new exact approach for the bilevel knapsack with interdiction constraints. In: Lodi, A., Nagarajan, V. (eds.) Integer Programming and Combinatorial Optimization, vol. 11480, pp. 155\u2013167. Springer, Berlin (2019)"},{"key":"1482_CR14","unstructured":"DeNegre, S.: Interdiction and discrete bilevel linear programming. PhD thesis, Lehigh University (2011)"},{"key":"1482_CR15","doi-asserted-by":"crossref","unstructured":"DeNegre, S., Ralphs, T.K.: A branch-and-cut algorithm for integer bilevel linear programs. In: Operations Research and Cyber-Infrastructure, Volume 47 of Operations Research\/Computer Science Interfaces, pp. 65\u201378 (2009)","DOI":"10.1007\/978-0-387-88843-9_4"},{"key":"1482_CR16","doi-asserted-by":"publisher","first-page":"1615","DOI":"10.1287\/opre.2017.1650","volume":"65","author":"M Fischetti","year":"2017","unstructured":"Fischetti, M., Ljubi\u0107, I., Monaci, M., Sinnl, M.: A new general-purpose algorithm for mixed-integer bilevel linear programs. Oper. Res. 65, 1615\u20131637 (2017)","journal-title":"Oper. Res."},{"issue":"2","key":"1482_CR17","doi-asserted-by":"publisher","first-page":"390","DOI":"10.1287\/ijoc.2018.0831","volume":"31","author":"M Fischetti","year":"2019","unstructured":"Fischetti, M., Ljubi\u0107, I., Monaci, M., Sinnl, M.: Interdiction games and monotonicity, with application to knapsack problems. INFORMS J. Comput. 31(2), 390\u2013410 (2019)","journal-title":"INFORMS J. Comput."},{"key":"1482_CR18","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1007\/s10107-017-1189-5","volume":"172","author":"M Fischetti","year":"2018","unstructured":"Fischetti, M., Ljubi\u0107, I., Monaci, M., Sinnl, M.: On the use of intersection cuts for bilevel optimization. Math. Program. 172, 77\u2013103 (2018)","journal-title":"Math. Program."},{"key":"1482_CR19","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1016\/j.ejor.2017.11.043","volume":"267","author":"M Fischetti","year":"2018","unstructured":"Fischetti, M., Monaci, M., Sinnl, M.: A dynamic reformulation heuristic for generalized interdiction problems. Eur. J. Oper. Res. 267, 40\u201351 (2018)","journal-title":"Eur. J. Oper. Res."},{"key":"1482_CR20","doi-asserted-by":"publisher","first-page":"392","DOI":"10.1287\/ijoc.2014.0632","volume":"27","author":"F Furini","year":"2015","unstructured":"Furini, F., Iori, M., Martello, S., Yagiura, M.: Heuristic and exact algorithms for the interval min\u2013max regret knapsack problem. INFORMS J. Comput. 27, 392\u2013405 (2015)","journal-title":"INFORMS J. Comput."},{"key":"1482_CR21","doi-asserted-by":"publisher","first-page":"208","DOI":"10.1016\/j.cor.2017.09.019","volume":"90","author":"F Furini","year":"2018","unstructured":"Furini, F., Monaci, M., Traversi, E.: Exact approaches for the knapsack problem with setups. Comput. Oper. Res. 90, 208\u2013220 (2018)","journal-title":"Comput. Oper. Res."},{"key":"1482_CR22","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1007\/BF01586088","volume":"32","author":"R Jeroslow","year":"1985","unstructured":"Jeroslow, R.: The polynomial hierarchy and a simple model for competitive analysis. Math. Program. 32, 146\u2013164 (1985)","journal-title":"Math. Program."},{"key":"1482_CR23","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-24777-7","volume-title":"Knapsack Problems","author":"H Kellerer","year":"2004","unstructured":"Kellerer, H., Pferschy, U., Pisinger, D.: Knapsack Problems. Springer, New York (2004)"},{"key":"1482_CR24","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2620-6","volume-title":"Robust Discrete Optimization and its Applications","author":"P Kouvelis","year":"1997","unstructured":"Kouvelis, P., Yu, G.: Robust Discrete Optimization and its Applications. Kluwer Academic Publishers, Boston (1997)"},{"key":"1482_CR25","doi-asserted-by":"publisher","first-page":"414","DOI":"10.1287\/mnsc.45.3.414","volume":"45","author":"S Martello","year":"1999","unstructured":"Martello, S., Pisinger, D., Toth, P.: Dynamic programming and strong bounds for the 0\u20131 knapsack problem. Manag. Sci. 45, 414\u2013424 (1999)","journal-title":"Manag. Sci."},{"key":"1482_CR26","volume-title":"Knapsack Problems: Algorithms and Computer Implementations","author":"S Martello","year":"1990","unstructured":"Martello, S., Toth, P.: Knapsack Problems: Algorithms and Computer Implementations. Wiley, New York (1990)"},{"key":"1482_CR27","doi-asserted-by":"publisher","first-page":"911","DOI":"10.1287\/opre.38.5.911","volume":"38","author":"JT Moore","year":"1990","unstructured":"Moore, J.T., Bard, J.F.: The mixed integer linear bilevel programming problem. Oper. Res. 38, 911\u2013921 (1990)","journal-title":"Oper. Res."},{"key":"1482_CR28","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1016\/j.tcs.2019.10.007","volume":"799","author":"U Pferschy","year":"2019","unstructured":"Pferschy, U., Nicosia, G., Pacifici, A.: A Stackelberg knapsack game with weight control. Theor. Comput. Sci. 799, 149\u2013159 (2019)","journal-title":"Theor. Comput. Sci."},{"key":"1482_CR29","doi-asserted-by":"publisher","first-page":"667","DOI":"10.1111\/itor.12381","volume":"25","author":"U Pferschy","year":"2018","unstructured":"Pferschy, U., Scatamacchia, R.: Improved dynamic programming and approximation results for the knapsack problem with setups. Int. Trans. Oper. Res. 25, 667\u2013682 (2018)","journal-title":"Int. Trans. Oper. Res."},{"key":"1482_CR30","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1016\/S0166-218X(98)00127-9","volume":"89","author":"D Pisinger","year":"1998","unstructured":"Pisinger, D.: A fast algorithm for strongly correlated knapsack problems. Discrete Appl. Math. 89, 197\u2013212 (1998)","journal-title":"Discrete Appl. Math."},{"key":"1482_CR31","doi-asserted-by":"publisher","first-page":"758","DOI":"10.1287\/opre.45.5.758","volume":"45","author":"D Pisinger","year":"1997","unstructured":"Pisinger, D.: A minimal algorithm for the 0\u20131 knapsack problem. Oper. Res. 45, 758\u2013767 (1997)","journal-title":"Oper. Res."},{"key":"1482_CR32","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1006\/jagm.1999.1034","volume":"33","author":"D Pisinger","year":"1999","unstructured":"Pisinger, D.: Linear time algorithms for knapsack problems with bounded weights. J. Algorithms 33, 1\u201314 (1999)","journal-title":"J. Algorithms"},{"key":"1482_CR33","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1016\/j.tcs.2015.06.027","volume":"595","author":"X Qiu","year":"2015","unstructured":"Qiu, X., Kern, W.: Improved approximation algorithms for a bilevel knapsack problem. Theor. Comput. Sci. 595, 120\u2013129 (2015)","journal-title":"Theor. Comput. Sci."},{"key":"1482_CR34","volume-title":"The Theory of the Market Economy","author":"HV Stackelberg","year":"1952","unstructured":"Stackelberg, H.V.: The Theory of the Market Economy. Oxford University Press, Oxford (1952)"},{"issue":"2","key":"1482_CR35","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1007\/s10898-015-0274-7","volume":"66","author":"Y Tang","year":"2016","unstructured":"Tang, Y., Richard, J.P.P., Smith, J.C.: A class of algorithms for mixed-integer bilevel min\u2013max optimization. J. Global Optim. 66(2), 225\u2013262 (2016)","journal-title":"J. Global Optim."},{"issue":"3","key":"1482_CR36","doi-asserted-by":"publisher","first-page":"1403","DOI":"10.1137\/15M1051592","volume":"27","author":"L Wang","year":"2017","unstructured":"Wang, L., Xu, P.: The watermelon algorithm for the bilevel integer linear programming problem. SIAM J. Optim. 27(3), 1403\u20131430 (2017)","journal-title":"SIAM J. Optim."},{"key":"1482_CR37","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1016\/j.cor.2013.07.016","volume":"41","author":"P Xu","year":"2014","unstructured":"Xu, P., Wang, L.: An exact algorithm for the bilevel mixed integer linear programming problem under three simplifying assumptions. Comput. Oper. Res. 41, 309\u2013318 (2014)","journal-title":"Comput. Oper. Res."}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-020-01482-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-020-01482-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-020-01482-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,25]],"date-time":"2021-02-25T00:22:10Z","timestamp":1614212530000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-020-01482-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,26]]},"references-count":37,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2020,9]]}},"alternative-id":["1482"],"URL":"https:\/\/doi.org\/10.1007\/s10107-020-01482-5","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,2,26]]},"assertion":[{"value":"31 May 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 February 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 February 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}