{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,28]],"date-time":"2025-03-28T06:42:23Z","timestamp":1743144143514,"version":"3.40.3"},"publisher-location":"Boston, MA","reference-count":14,"publisher":"Springer US","isbn-type":[{"type":"print","value":"9780387747583"},{"type":"electronic","value":"9780387747590"}],"license":[{"start":{"date-parts":[[2008,1,1]],"date-time":"2008-01-01T00:00:00Z","timestamp":1199145600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2008,1,1]],"date-time":"2008-01-01T00:00:00Z","timestamp":1199145600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2008]]},"DOI":"10.1007\/978-0-387-74759-0_661","type":"book-chapter","created":{"date-parts":[[2008,8,25]],"date-time":"2008-08-25T11:08:03Z","timestamp":1219662483000},"page":"3797-3801","source":"Crossref","is-referenced-by-count":0,"title":["Stochastic Programs with Recourse: Upper Bounds"],"prefix":"10.1007","author":[{"given":"Stein W.","family":"Wallace","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chanaka","family":"Edirisinghe","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"661_CR1_661","doi-asserted-by":"publisher","first-page":"238","DOI":"10.1007\/BF01386316","volume":"4","author":"J.F. Benders","year":"1962","unstructured":"Benders JF (1962) Partitioning procedures for solving mixed-variables programming problems. Numerische Math 4:238\u2013252","journal-title":"Numerische Math."},{"key":"661_CR2_661","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1007\/BF02591859","volume":"31","author":"J.R. Birge","year":"1985","unstructured":"Birge JR (1985) Aggregation bounds in stochastic linear programming. Math Program 31:25\u201341","journal-title":"Math. Program."},{"key":"661_CR3_661","doi-asserted-by":"publisher","first-page":"725","DOI":"10.1137\/0326042","volume":"26","author":"J.R. Birge","year":"1988","unstructured":"Birge JR, Wallace SW (1988) A\u00a0separable piecewise linear upper bound for stochastic linear programs. SIAM J Control Optim 26:725\u2013739","journal-title":"SIAM J. Control Optim."},{"key":"661_CR4_661","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1007\/BF01582286","volume":"43","author":"J.R. Birge","year":"1989","unstructured":"Birge JR, Wets RJ-B (1989) Sublinear upper bounds for stochastic programs with recourse. Math Program 43:131\u2013149","journal-title":"Math. Program."},{"key":"661_CR5_661","doi-asserted-by":"publisher","first-page":"909","DOI":"10.1287\/opre.44.6.909","volume":"44","author":"N.C.P. Edirisinghe","year":"1996","unstructured":"Edirisinghe NCP (1996) New second-order bounds on the expectation of saddle functions with applications to stochastic linear programming. Oper Res 44:909\u2013922","journal-title":"Oper. Res."},{"key":"661_CR6_661","doi-asserted-by":"publisher","first-page":"660","DOI":"10.1287\/opre.40.4.660","volume":"40","author":"N.C.P. Edirisinghe","year":"1992","unstructured":"Edirisinghe NCP, Ziemba WT (1992) Tight bounds for stochastic convex programs. Oper Res 40:660\u2013677","journal-title":"Oper. Res."},{"key":"661_CR7_661","unstructured":"Edmundson HP (1957) Bounds on the expectation of a\u00a0convex function of a\u00a0random variable. Techn Report RAND Corp P-382"},{"key":"661_CR8_661","volume-title":"Stochastic programming","author":"P. Kall","year":"1994","unstructured":"Kall P, Wallace SW (1994) Stochastic programming. Wiley, New York"},{"key":"661_CR9_661","first-page":"743","volume":"30","author":"A. Madansky","year":"1959","unstructured":"Madansky A (1959) Bounds on the expectation of a\u00a0convex function of a\u00a0multivariate random variable. A-STAT 30:743\u2013746","journal-title":"A-STAT"},{"key":"661_CR10_661","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1287\/mnsc.6.2.197","volume":"6","author":"A. Madansky","year":"1960","unstructured":"Madansky A (1960) Inequalities for stochastic linear programming problems. Managem Sci 6:197\u2013204","journal-title":"Managem. Sci."},{"key":"661_CR11_661","doi-asserted-by":"publisher","first-page":"943","DOI":"10.1287\/opre.47.6.943","volume":"47","author":"D.P. Morton","year":"1999","unstructured":"Morton DP, Wood RK (1999) Restricted-recourse bounds for stochastic linear programming. Oper Res 47:943\u2013956","journal-title":"Oper. Res."},{"key":"661_CR12_661","doi-asserted-by":"publisher","first-page":"638","DOI":"10.1137\/0117061","volume":"17","author":"R.van Slyke","year":"1969","unstructured":"Slyke Rvan, Wets RJ-B (1969) L-shaped linear programs with applications to optimal control and stochastic programming. SIAM J Appl Math 17:638\u2013663","journal-title":"SIAM J. Appl. Math."},{"key":"661_CR13_661","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1007\/BF02604638","volume":"38","author":"S.W. Wallace","year":"1987","unstructured":"Wallace SW (1987) A\u00a0piecewise linear upper bound on the network recourse function. Math Program 38:133\u2013146","journal-title":"Math. Program."},{"issue":"1","key":"661_CR14_661","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1007\/BF01582142","volume":"61","author":"S.W. Wallace","year":"1993","unstructured":"Wallace SW, Yan T (1993) Bounding multistage stochastic linear programs from above. Math Program 61(1):111\u2013130","journal-title":"Math. Program."}],"container-title":["Encyclopedia of Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-0-387-74759-0_661","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,11]],"date-time":"2024-07-11T10:47:02Z","timestamp":1720694822000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-0-387-74759-0_661"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008]]},"ISBN":["9780387747583","9780387747590"],"references-count":14,"URL":"https:\/\/doi.org\/10.1007\/978-0-387-74759-0_661","relation":{},"subject":[],"published":{"date-parts":[[2008]]}}}