Abstract
Node aggregation methods have been previously studied as a means for approximating large scale transportation problems. In this paper, we show how the approximations inherent in Benders' decomposition method can be combined with node aggregation in optimizing large scale capacitated plant location problems.
References
G.R. Bitran, V. Chandru, D.E. Sempolinski and J.F. Shapiro, “Inverse Optimization: An application to the capacitated plant location problem”,Management Science 27 (1981) 1120–1141.
A. Geoffrion, ‘Customer aggregation in distribution modeling’, Western Management Science Institute Working Paper No. 259, University of California at Los Angeles, 1976.
J.F. Shapiro, Mathematical programming: Structures and algorithms (Wiley, New York, 1979).
T.J. Van Roy, “Cross decomposition for mixed integer programming problems”,Mathematical Programming 25 (1983) 66–83.
P.H. Zipkin, “Bounds for aggregating nodes in network problems”,Mathematical Programming 19 (1980) 155–177.
P.H. Zipkin, “Aggregation and disaggregation in convex network problems”,Networks 12 (1982) 101–117.
P.H. Zipkin, “Exact and approximate cost functions for product aggregates”,Management Science 28 (1982) 1002–1012.
Author information
Authors and Affiliations
Additional information
This research was supported by the National Science Foundation under Grant No. ECS-8117105.
Rights and permissions
About this article
Cite this article
Shapiro, J.F. A note on node aggregation and Benders' decomposition. Mathematical Programming 29, 113–119 (1984). https://doi.org/10.1007/BF02591733
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02591733