A heuristic procedure for stochastic integer programs with complete recourse |
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| Affiliation: | 1. Dipartimento di Matematica Pura ed Applicata, Università di Padova, 35123 Padova, Italy;2. Department of Systems and Industrial Engineering, University of Arizona, Tucson, AZ 85721 USA;1. Vilnius Gediminas Technical University, Sauletekio st 11, Vilnius, Lithuania;2. DIKU - Department of Computer Science, University of Copenhagen, Universitetsparken 1, DK-2100 Copenhagen, Denmark;1. Otto-von-Guericke-University Magdeburg, Faculty of Economics and Management, Management Science, P.O. Box 4120, 39016 Magdeburg, Germany;2. Department of Industrial & Systems Engineering, University of Florida, 303 West Hall, Gainesville, FL 32611-6595, USA;3. Department of Industrial Engineering, Bogaziçi University, 34342, Bebek-Istanbul, Turkey;4. Koç University, Department of Industrial Engineering, 34450 Sariyer-Istanbul, Turkey;5. University of Vienna, Department of Management Science, Bruenner Strasse 72, 1210 Vienna, Austria;1. Otto-von-Guericke University, Magdeburg, Germany;2. Shippensburg University, Shippensburg, PA, USA;3. Kuehne Logistics University, Hamburg, Germany;1. Department of Applied Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran;2. Centro de Matemática Aplicaçõoes Fundamentais e Investigação Operacional, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal;1. Centro de Matemática Aplicações Fundamentais e Investigação Operacional, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal;2. Department of Applied Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran;1. Department of Precision Machinery and Instrumentation, University of Science and Technology of China, Hefei, Anhui 230026, China;2. Department of Industrial and Manufacturing Systems Engineering, The University of Texas at Arlington, 500 West First Street, P.O. Box 19017, Arlington, TX 76019, USA;1. Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, United States;2. Industrial and Systems Engineering, and Public Policy, University of Southern California, Los Angeles, CA, United States;3. Mechanical Engineering and Engineering Science, University of North Carolina at Charlotte, Charlotte, NC, United States |
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| Abstract: | In this paper, we propose a successive approximation heuristic which solves large stochastic mixed-integer programming problem with complete fixed recourse. We refer to this method as the Scenario Updating Method, since it solves the problem by considering only a subset of scenarios which is updated at each iteration. Only those scenarios which imply a significant change in the objective function are added. The algorithm is terminated when no such scenarios are available to enter in the current scenario subtree. Several rules to select scenarios are discussed. Bounds on heuristic solutions are computed by relaxing some of the non-anticipativity constraints. The proposed procedure is tested on a multistage stochastic batch-sizing problem. |
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