2,238 research outputs found
Locating Depots for Capacitated Vehicle Routing
We study a location-routing problem in the context of capacitated vehicle
routing. The input is a set of demand locations in a metric space and a fleet
of k vehicles each of capacity Q. The objective is to locate k depots, one for
each vehicle, and compute routes for the vehicles so that all demands are
satisfied and the total cost is minimized. Our main result is a constant-factor
approximation algorithm for this problem. To achieve this result, we reduce to
the k-median-forest problem, which generalizes both k-median and minimum
spanning tree, and which might be of independent interest. We give a
(3+c)-approximation algorithm for k-median-forest, which leads to a
(12+c)-approximation algorithm for the above location-routing problem, for any
constant c>0. The algorithm for k-median-forest is just t-swap local search,
and we prove that it has locality gap 3+2/t; this generalizes the corresponding
result known for k-median. Finally we consider the "non-uniform"
k-median-forest problem which has different cost functions for the MST and
k-median parts. We show that the locality gap for this problem is unbounded
even under multi-swaps, which contrasts with the uniform case. Nevertheless, we
obtain a constant-factor approximation algorithm, using an LP based approach.Comment: 12 pages, 1 figur
Minimum Makespan Multi-vehicle Dial-a-Ride
Dial a ride problems consist of a metric space (denoting travel time between
vertices) and a set of m objects represented as source-destination pairs, where
each object requires to be moved from its source to destination vertex. We
consider the multi-vehicle Dial a ride problem, with each vehicle having
capacity k and its own depot-vertex, where the objective is to minimize the
maximum completion time (makespan) of the vehicles. We study the "preemptive"
version of the problem, where an object may be left at intermediate vertices
and transported by more than one vehicle, while being moved from source to
destination. Our main results are an O(log^3 n)-approximation algorithm for
preemptive multi-vehicle Dial a ride, and an improved O(log t)-approximation
for its special case when there is no capacity constraint. We also show that
the approximation ratios improve by a log-factor when the underlying metric is
induced by a fixed-minor-free graph.Comment: 22 pages, 1 figure. Preliminary version appeared in ESA 200
A Two-Stage Approach for Routing Multiple Unmanned Aerial Vehicles with Stochastic Fuel Consumption
The past decade has seen a substantial increase in the use of small unmanned
aerial vehicles (UAVs) in both civil and military applications. This article
addresses an important aspect of refueling in the context of routing multiple
small UAVs to complete a surveillance or data collection mission. Specifically,
this article formulates a multiple-UAV routing problem with the refueling
constraint of minimizing the overall fuel consumption for all of the vehicles
as a two-stage stochastic optimization problem with uncertainty associated with
the fuel consumption of each vehicle. The two-stage model allows for the
application of sample average approximation (SAA). Although the SAA solution
asymptotically converges to the optimal solution for the two-stage model, the
SAA run time can be prohibitive for medium- and large-scale test instances.
Hence, we develop a tabu-search-based heuristic that exploits the model
structure while considering the uncertainty in fuel consumption. Extensive
computational experiments corroborate the benefits of the two-stage model
compared to a deterministic model and the effectiveness of the heuristic for
obtaining high-quality solutions.Comment: 18 page
An approximate approach for the joint problem of level of repair analysis and spare parts stocking
For the spare parts stocking problem, generally METRIC type methods are used
in the context of capital goods. A decision is assumed on which components to discard and which to repair upon failure, and where to perform repairs. In the military world, this decision is taken explicitly using the level of repair analysis (LORA). Since the LORA does not consider the availability of the capital goods, solving the LORA and spare parts stocking problems sequentially may lead to suboptimal solutions. Therefore, we propose an iterative algorithm. We compare its performance with that of the sequential approach and a recently proposed, so-called integrated algorithm that finds optimal solutions for twoechelon, single-indenture problems. On a set of such problems, the iterative algorithm turns out to be close to optimal. On a set of multi-echelon, multi-indenture problems, the iterative approach achieves a cost reduction of 3%on average (35%at maximum) as compared to the sequential approach. Its costs are only 0.6 % more than those of the integrated algorithm on average (5 % at maximum). Considering that the integrated algorithm may take a long time without guaranteeing optimality, we believe that the iterative algorithm is a good approach. This result is further strengthened in a case study, which has convinced Thales Nederland to start using the principles behind our algorithm
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