{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T13:12:18Z","timestamp":1762521138083},"reference-count":21,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":4546,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1994,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper, we study a special class of stochastic programs where the recourse problem consists of trees with random arc capacities, which we call tree recourse. We develop an efficient procedure to obtain the expected recourse function exactly for single\u2010stage problems. This procedure is used in a backward recursion to find the exact expected recourse function for multistage trees. We show that for large trees <jats:italic>n<\/jats:italic>\u2010stage networks can be solved more easily than can a single\u2010stage network with <jats:italic>n<\/jats:italic>\u2010levels. We also show that the expected recourse functions for single\u2010stage and <jats:italic>n<\/jats:italic>\u2010stage formulations of the same network can be quite similar. Finally, we illustrate the potential of using the tree recourse problems in a more general stochastic network problem. \u00a9 1994 by John Wiley &amp; Sons, Inc.<\/jats:p>","DOI":"10.1002\/net.3230240304","type":"journal-article","created":{"date-parts":[[2007,5,12]],"date-time":"2007-05-12T18:18:21Z","timestamp":1178993901000},"page":"161-175","source":"Crossref","is-referenced-by-count":19,"title":["Stochastic programs over trees with random arc capacities"],"prefix":"10.1002","volume":"24","author":[{"given":"Warren B.","family":"Powell","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Raymond K.","family":"Cheung","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230140307"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1080\/17442508308833246"},{"key":"e_1_2_1_4_2","unstructured":"L. F.FrantzeskakisandW. B.Powell Development and evaluation of a successive linear approximation procedure for stochastic dynamic networks. Technical Report SOR\u201088\u201013 Dept. of Civil Engineering and Operations Research. Princeton University (1988)."},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1287\/trsc.24.1.40"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0167-6377(91)90005-A"},{"key":"e_1_2_1_7_2","unstructured":"J. L.Higle Private communication."},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1287\/moor.16.3.650"},{"key":"e_1_2_1_9_2","volume-title":"Combinatorial Optimization: Networks and Matroids","author":"Lawler E. L.","year":"1976"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1287\/opre.39.5.757"},{"key":"e_1_2_1_11_2","volume-title":"Numerical Techniques for Stochastic Optimization","author":"Nazareth J. 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