Two level hierarchical time minimizing transportation problem |
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Authors: | Sonia Munish C Puri |
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Institution: | (1) Department of Mathematics, Indian Institute of Technology, Delhi, Hauz-Khas, 110016 New Delhi, India |
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Abstract: | A two level hierarchical balanced time minimizing transportation problem is considered in this paper. The whole set of source-destination
links consists of two disjoint partitions namely Level-I links and Level-II links. Some quantity of a homogeneous product
is first shipped from sources to destinations by Level-I decision maker using only Level-I links, and on its completion the
Level-II decision maker transports the remaining quantity of the product in an optimal fashion using only Level-II links.
Transportation is assumed to be done in parallel in both the levels. The aim is to find that feasible solution for Level-I
decision maker corresponding to which the optimal feasible solution for Level-II decision maker is such that the sum of shipment
times in Level-I and Level-II is the least. To obtain the global optimal feasible solution of this non-convex optimization
problem, related balanced time minimizing transportation problems are defined. Based upon the optimal feasible solutions of
these related problems, standard cost minimizing transportation problems are constructed whose optimal feasible solutions
provide various pairs for shipment times for Level-I and Level-II decision makers. The best out of these pairs is finally
selected. Being dependent upon solutions of a finite number of balanced time minimizing and cost minimizing transportation
problems, the proposed algorithm is a polynomial bound algorithm. The developed algorithm has been implemented and tested
on a variety of test problems and performance is found to be quite encouraging. |
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Keywords: | Global optimization concave minimization problem time minimizing transportation problem hierarchical optimization |
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