Efficient Algorithms on Multicommodity Flow over Time Problems with Partial Lane Reversals

Author:

Pyakurel Urmila1ORCID,Gupta Shiva Prakash2,Khanal Durga Prasad3,Dhamala Tanka Nath1ORCID

Affiliation:

1. Central Department of Mathematics, Tribhuvan University, P.O. Box 13143, Kathmandu, Nepal

2. Tribhuvan University, Tri-Chandra Multiple Campus, Kathmandu, Nepal

3. Tribhuvan University, Saraswati Multiple Campus, Kathmandu, Nepal

Abstract

The multicommodity flow problem arises when several different commodities are transshipped from specific supply nodes to the corresponding demand nodes through the arcs of an underlying capacity network. The maximum flow over time problem concerns to maximize the sum of commodity flows in a given time horizon. It becomes the earliest arrival flow problem if it maximizes the flow at each time step. The earliest arrival transshipment problem is the one that satisfies specified supplies and demands. These flow over time problems are computationally hard. By reverting the orientation of lanes towards the demand nodes, the outbound lane capacities can be increased. We introduce a partial lane reversal approach in the class of multicommodity flow problems. Moreover, a polynomial-time algorithm for the maximum static flow problem and pseudopolynomial algorithms for the earliest arrival transshipment and maximum dynamic flow problems are presented. Also, an approximation solution to the latter problem is obtained in polynomial-time.

Publisher

Hindawi Limited

Subject

Mathematics (miscellaneous)

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