Vehicle scheduling on a tree with release and handling times

Yoshiyuki Karuno, Hiroshi Nagamochi and Toshihide Ibaraki

Annals of Operations Research, 1997, vol. 69, issue 0, 193-207

Abstract: In this paper, we consider a single-vehicle scheduling problem on a tree-shaped road net-work. Let T =(V,E) be a tree, where V is a set of n vertices and E is a set of edges. A task is located at each vertex v, which is also denoted as v. Each task v has release time r(v) and handling time h(v). The travel times c(u, v) and c(v, u) are associated with each edge (u, v) of E. The vehicle starts from an initial vertex v_0 of V, visits all tasks v in V for their processing, and returns to v_0 . The objective is to find a routing schedule of the vehicle that minimizes the completion time, denoted as C (i.e., the time to return to v_0 after processing all tasks). We call this problem TREE-VSP(C). We first prove that TREE-VSP(C) is NP-hard. However, we then show that TREE-VSP(C) with a depth-first routing constraint can be exactly solved in O(n log n) time. Moreover, we show that, if this exact algorithm is used as an approximate algorithm for the original TREE-VSP(C), its worst-case performance ratio is at most two. Copyright Kluwer Academic Publishers 1997

Date: 1997
References: Add references at CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
http://hdl.handle.net/10.1023/A:1018928911513 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:annopr:v:69:y:1997:i:0:p:193-207:10.1023/a:1018928911513

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10479

DOI: 10.1023/A:1018928911513

Access Statistics for this article

Annals of Operations Research is currently edited by Endre Boros

More articles in Annals of Operations Research from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().