The first <i>K</i> minimum cost paths in a time-schedule network

Chen, Yen-Liang; Rinks, Dan B.; Tang, Kwei

doi:10.1057/palgrave.jors.2601028

Cited by 8 publications

(8 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Their approach is heuristic in the sense that eventually only j(<k) of the k-shortest looping paths are identified, without specifying how close is j to k. Other relevant work in this field relates to the k-shortest path problem on networks with time-invariant cost attributes, where either the departure or the arrival at any node is time constrained. In particular, Chen et al (2001) studied the k-minimum cost paths problem in a time-schedule network. The objective of their formulation is to determine k-minimum cost paths with total travel time less than a threshold value s. The corresponding network involves arcs with time-invariant travel times and non-negative cost attributes while the departure from any node is allowed only at specified discrete points in time.…”

Section: Previous Related Work On the K-shortest Path Problemmentioning

confidence: 99%

Solving the bicriterion routing and scheduling problem for hazardous materials distribution

Androutsopoulos

Zografos

2010

Transportation Research Part C: Emerging Technologies

View full text Add to dashboard Cite

Hazardous materials routing and scheduling decisions involve the determination of the minimum cost and/or risk routes for servicing the demand of a given set of customers. This paper addresses the bicriterion routing and scheduling problem arising in hazardous materials distribution planning. Under the assumption that the cost and risk attributes of each arc of the underlying transportation network are time-dependent, the proposed routing and scheduling problem pertains to the determination of the non-dominated time-dependent paths for servicing a given and fixed sequence of customers (intermediate stops) within specified time windows. Due to the heavy computational burden for solving this bicriterion problem, an alternative algorithm is proposed that determines the k-shortest time-dependent paths. Moreover an algorithm is provided for solving the bicriterion problem. The proximity of the solutions of the k-shortest time-dependent path problem with the non-dominated solutions is assessed on a set of problems developed by the authors.

show abstract

Section: Previous Related Work On the K-shortest Path Problemmentioning

confidence: 99%

Solving the bicriterion routing and scheduling problem for hazardous materials distribution

Androutsopoulos

Zografos

2010

Transportation Research Part C: Emerging Technologies

View full text Add to dashboard Cite

show abstract

“…However, if we need several paths, then the map-table method is more efficient, because it only needs O(L ϩ log ͉V͉) time for each query whereas the simpler method would require O(͉A͉) time for each query. As mentioned, it is possible to use existing algorithms for the first K shortest paths to find the Kth shortest paths [4,6,7,9,14]. These algorithms require, however, that the first K Ϫ 1 paths be found before finding the Kth shortest path.…”

Section: Remark 1: If Only Onementioning

confidence: 99%

“…A time window is a common form of time constraint considered in the TCSPP literature, which requires that a node can be visited only in a specified time interval [5,13]. In our recent papers [2,3,4], we introduce a new time constraint called a time-schedule constraint, which assumes that a node has a list of prespecified departure times and requires that departure from the node takes place only at one of the departure times. For example, suppose that (10,20,60,80,120) is a list of departure times at a node.…”

Section: Introductionmentioning

confidence: 99%

“…We have developed algorithms to find the shortest path from the source node to the destination node in a timeschedule network [2,3,4]. In this paper, we extend the problem to finding the Kth shortest path.…”

Section: Introductionmentioning

confidence: 99%

“…It can be argued that the Kth shortest path can be found by using existing algorithms for the first K shortest paths [4,6,7,9,14]. However, the computation time of the approach could be prohibitively long and wasteful for a large K because the Kth path can be found only after enumerating the first K Ϫ 1 paths.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Finding the Kth shortest path in a time‐schedule network

Chen

Tang

2004

Naval Research Logistics

View full text Add to dashboard Cite

Abstract:We consider the problem of finding the Kth shortest path for a time-schedule network, where each node in the network has a list of prespecified departure times, and departure from the node can take place only at one of these departure times. We develop a polynomial time algorithm independent of K for finding the Kth shortest path. The proposed algorithm constructs a map structure at each node in the network, using which we can directly find the Kth shortest path without having to enumerate the first K Ϫ 1 paths. Since the same map structure is used for different K values, it is not necessary to reconstruct the table for additional paths. Consequently, the algorithm is suitable for directly finding multiple shortest paths in the same network. Furthermore, the algorithm is modified slightly for enumerating the first K shortest paths and is shown to have the lowest possible time complexity under a condition that holds for most practical networks.

show abstract

Finding K shortest looping paths with waiting time in a time–window network

Yang

Chen

2006

Applied Mathematical Modelling

View full text Add to dashboard Cite

The first K minimum cost paths in a time-schedule network

Cited by 8 publications

References 6 publications

Solving the bicriterion routing and scheduling problem for hazardous materials distribution

Solving the bicriterion routing and scheduling problem for hazardous materials distribution

Finding the Kth shortest path in a time‐schedule network

Finding K shortest looping paths with waiting time in a time–window network

Contact Info

Product

Resources

About