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Bounds for aggregated solid transportation problem and an improved disaggregation method. (English) Zbl 0661.90060

The present article deals with a solid transportation (classical three- index) problem of very large dimension which cannot be solved directly with the help of computers, despite developments in hardware and software. The authors propose for its solution the following approach: An arbitrary group of nodes in the original transportation problem is replaced by aggregate nodes and a corresponding aggregated solid transportation problem is solved (by a new method, the so-called disaggregation method). From its solution an approximative solution of the original transportation problem is recovered by a simple transformation. The difference between the cost of this approximative solution and the optimal objective value of the original transportation problem can be estimated from the a priori and a posteriori bounds. If the error is too large, then the authors suggest a heuristic approach for choosing new groups of nodes for an aggregation and a new aggregated solid transportation problem is solved.
Reviewer: L.Grygarova

MSC:

90C08 Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.)
90C06 Large-scale problems in mathematical programming
65K05 Numerical mathematical programming methods
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