Polynomial-Time Approximation Scheme for the Capacitated Vehicle Routing Problem with Time Windows
The capacitated vehicle routing problem with time windows (CVRPTW) is a well-known NP-hard combinatorial optimization problem. We present a further development of the approach first proposed by M. Haimovich and A. H. G. Rinnooy Kan and propose an algorithm that, for an arbitrary ε > 0, finds a (1...
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| Vydáno v: | Proceedings of the Steklov Institute of Mathematics Ročník 307; číslo Suppl 1; s. 51 - 63 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article Konferenční příspěvek |
| Jazyk: | angličtina |
| Vydáno: |
Moscow
Pleiades Publishing
01.12.2019
Springer Nature B.V |
| Témata: | |
| ISSN: | 0081-5438, 1531-8605 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | The capacitated vehicle routing problem with time windows (CVRPTW) is a well-known NP-hard combinatorial optimization problem. We present a further development of the approach first proposed by M. Haimovich and A. H. G. Rinnooy Kan and propose an algorithm that, for an arbitrary
ε
> 0, finds a (1 +
ε
)-approximate solution for the Euclidean CVRPTW in
, where
q
is an upper bound for the capacities of the vehicles,
p
is the number of time windows, and TIME(TSP,
ρ
,
n
) is the complexity of finding a
ρ
-approximation solution of an auxiliary instance of the Euclidean TSP. Thus, the algorithm is a polynomial-time approximation scheme for the CVRPTW with
p
3
q
4
=
O
(log
n
) and an efficient polynomial-time approximation scheme for arbitrary fixed values of
p
and
q
. |
|---|---|
| Bibliografie: | ObjectType-Article-1 ObjectType-Feature-2 SourceType-Conference Papers & Proceedings-1 content type line 22 |
| ISSN: | 0081-5438 1531-8605 |
| DOI: | 10.1134/S0081543819070058 |