1 research outputs found
Approximation of the Double Travelling Salesman Problem with Multiple Stacks
The Double Travelling Salesman Problem with Multiple Stacks, DTSPMS, deals
with the collect and delivery of n commodities in two distinct cities, where
the pickup and the delivery tours are related by LIFO constraints. During the
pickup tour, commodities are loaded into a container of k rows, or stacks, with
capacity c. This paper focuses on computational aspects of the DTSPMS, which is
NP-hard.
We first review the complexity of two critical subproblems: deciding whether
a given pair of pickup and delivery tours is feasible and, given a loading
plan, finding an optimal pair of pickup and delivery tours, are both polynomial
under some conditions on k and c.
We then prove a (3k)/2 standard approximation for the MinMetrickDTSPMS, where
k is a universal constant, and other approximation results for various versions
of the problem.
We finally present a matching-based heuristic for the 2DTSPMS, which is a
special case with k=2 rows, when the distances are symmetric. This yields a
1/2-o(1), 3/4-o(1) and 3/2+o(1) standard approximation for respectively
Max2DTSPMS, its restriction Max2DTSPMS-(1,2) with distances 1 and 2, and
Min2DTSPMS-(1,2), and a 1/2-o(1) differential approximation for Min2DTSPMS and
Max2DTSPMS