• Journal of Korean Institute of Industrial Engineers
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• v.16 no.2
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• pp.71-79
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• 1990

In this paper, the Double Shortest Arborescence & Merging method is presented as an efficient heuristic algorithm for the Public Vehicle Routing Problem which is to find the minimum total cost routes of M or less vehicles to traverse the required arcs(demand streets) at least once and return to their starting depot on a directed network. Double Shortest Arborescence which consists of forward shortest aborescence and backward one informs M or less shortest routes to traverse all required arcs. The number of these routes is reduced to M or less by merging routes. The computational experiment based on randomly generated networks reports that this algorithm is efficient.

• Journal of the Korean Operations Research and Management Science Society
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• v.26 no.3
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• pp.79-94
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• 2001

This paper presents a new algorithm for the K shortest paths Problem which develops initial K shortest paths, and repeat to expose hidden shortest paths with dual approach and to replace the longest path in the present K paths. The initial solution comprises K shortest paths among shortest paths to traverse each arc in a Double Shortest Arborescence which is made from bidirectional Dijkstra algorithm. When a crossing node that have two or more inward arcs is found at least three time by turns in this K shortest paths, there may be some hidden paths which are shorter than present k-th path. To expose a hidden shortest path, one inward arc of this crossing node is chose by means of minimum detouring distance calculated with dual variables, and then the hidden shortest path is exposed with joining a detouring subpath from source to this inward arc and a spur of a feasible path from this crossing node to sink. If this exposed path is shorter than the k-th path, the exposed path replaces the k-th path. This algorithm requires worst case time complexity of O(Kn$^2$), and O(n$^2$) in the case k$\leq$3.