Finding rectilinear least cost paths in the presence of convex polygonal congested regions

Authors:
Avijit Sarkar;Rajan Batta;Rakesh Nagi
Affiliations:
School of Business, University of Redlands, 1200 East Colton Avenue, Redlands, CA 92373, USA;Department of Industrial and Systems Engineering, 438 Bell Hall, University at Buffalo (SUNY), Buffalo, NY 14260, USA;Department of Industrial and Systems Engineering, 438 Bell Hall, University at Buffalo (SUNY), Buffalo, NY 14260, USA
Venue:
Computers and Operations Research
Year:
2009

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Abstract

This paper considers the problem of finding the least cost rectilinear distance path in the presence of convex polygonal congested regions. We demonstrate that there are a finite, though exponential number of potential staircase least cost paths between a specified pair of origin-destination points. An upper bound for the number of entry/exit points of a rectilinear path between two points specified a priori in the presence of a congested region is obtained. Based on this key finding, a ''memory-based probing algorithm'' is proposed for the problem and computational experience for various problem instances is reported. A special case where polynomial time solutions can be obtained has also been outlined.