The traveling salesman problem with delivery and backhauls

Shoshana Anily*, Gur Mosheiov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

51 Scopus citations


The problem that we consider here deals with a single vehicle of a given capacity that needs to serve N customers: some of the customers require a delivery of stock from the warehouse, whereas others need to deliver stock from their location to the warehouse. The objective is to find a shortest feasible tour visiting all customers, emanating from and ending at the warehouse. We introduce an efficient (O(N2)) heuristic for this problem. The heuristic improves the worst-case bound known in the literature from 2.5 to 2. However, its average performance is shown in our numerical study to be slightly worse than that of a previously published (O(N3)) solution method.

Original languageEnglish
Pages (from-to)11-18
Number of pages8
JournalOperations Research Letters
Issue number1
StatePublished - Aug 1994


  • Computational complexity
  • Heuristic
  • Traveling salesman problem
  • Vehicle routing
  • Worst-case analysis


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