New optimality cuts for a single‐vehicle stochastic routing problem

C. Hjorring and J. Holt

Annals of Operations Research, 1999, vol. 86, issue 0, 569-584

Abstract: In the Vehicle Routing literature, investigations have concentrated on problems in whichthe customer demands are known precisely. We consider an application in which the demandsare unknown prior to the creation of vehicle routes, but follow some known probabilitydistribution. Because of the variability in customer demands, it is possible that the actualtotal customer demand may exceed the capacity of the vehicle assigned to service thosecustomers. In this case, we have a route failure , and there is an additional cost related to thecustomer at which the vehicle stocks out. We aim to find routes that minimise the sum of thedistance travelled plus any additional expected costs due to route failure. Because of thedifficulty of this problem, this investigation only considers a single‐vehicle problem. Tofind optimal routes, the integer L‐shaped method is used. We solve a relaxed IP in which thedistance travelled is modelled exactly, but the expected costs due to route failure are approximated.Constraints are dynamically added to prevent subtours and to further improve therelaxation. Additional constraints (optimality cuts) are added which progressively form atighter approximation of the costs due to route failure. Gendreau et al. [6] apply a similarmethodology to a closely related problem. They add optimality cuts, each of which imposesa useful bound on the route failure cost for only one solution. In addition to that cut, wegenerate “general” optimality cuts, each of which imposes a useful bound on the route failurecost for many solutions. Computational results attesting to the success of this approach arepresented. Copyright Kluwer Academic Publishers 1999

Date: 1999
References: Add references at CitEc
Citations: View citations in EconPapers (26)

Downloads: (external link)
http://hdl.handle.net/10.1023/A:1018995927636 (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:86:y:1999:i:0:p:569-584:10.1023/a:1018995927636

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

DOI: 10.1023/A:1018995927636

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 ().