On solving stochastic production planning problems via scenario modelling |
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Authors: | L F Escudero P V Kamesam |
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Institution: | (1) Dept. of Statistics and Operations Research, Universidad Complutense de Madrid, Madrid, Spain;(2) IBM T.J. Watson Research Center, 10598 Yorktown Heights, New York |
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Abstract: | Summary Linear Porgramming models for stochastic planning problems and a methodology for solving them are proposed. A production planning
problem with uncertainty in demand is used as a test case, but the methodology presented here is applicable to other types
of problems as well. In these models, uncertainty in demand is characterized via scenarios. Solutions are obtained for each
scenario and then these individual scenario solutions are aggregated to yield an implementable non-anticipative policy. Such
an approach makes it possible to model correlated and nonstationary demand as well as a variety of recourse decision types.
For computational purposes, two alternative representations are proposed. A compact approach that is suitable for the Simplex
method and a splitting variable approach that is suitable for the Interior Point Methods. A crash procedure that generates
an advanced starting solution for the Simplex method is developed. Computational results are reported with both the representations.
Although some of the models presented here are very large (over 25000 constraints and 75000 variables), our computational
experience with these problems is quite encouraging. |
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Keywords: | production planning scenario tree compact representation splitting variable representation nonanticipativity |
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