Use of continuous approximations within discrete algorithms for routing vehicles: Experimental results and interpretation

Abstract

This paper creates and tests a vehicle routing heuristic that combines features of continuous space modeling and discrete modeling. The goals of the paper were (1) to determine whether exploiting continuous space approximations in the formation of an initial partition of customers into districts produces significant improvements in solution quality and (2) to test the validity of Daganzo's route-length approximation in cases where shipment sizes are either identical or variable. The initial partition is created by dividing the service region into multiple annuli and then partitioning the annuli with a modified sweep algorithm. The initial solution is iteratively updated with a generalized assignment algorithm, which employs a new method for approximating the cost of inserting a stop into a tour. Computational tests have been systematically performed on over 500 sample problems with up to 170 stops and 70 districts. Unlike prior research, sample problems are sufficiently large to exhibit the multiple-annuli phenomenon studied in Daganzo's work. Results show that continuous space models can provide substantial improvements in the initial customer partition compared to single-annulus methods. However, after repeated application of a generalized assignment algorithm, the initial advantage of the continuous space solution tends to evaporate. Results also show that Daganzo's model provides accurate predictions of average distance between stops, especially on large problems with identical shipment sizes. © 1994 by John Wiley & Sons, Inc.