The Dynamic Traveling Repair Problem: Examination of an Asymptotically Optimal Algorithm (original) (raw)

On-line algorithms for the dynamic traveling repair problem

2004

Abstract We consider the dynamic traveling repair problem in which requests with deadlines arrive through time on points in a metric space. Servers move from point to point at constant speed. The goal is to plan the motion of servers so that the maximum number of requests are met by their deadline. We consider a restricted version of the problem in which there is a single server and the length of time between the arrival of a request and its deadline is constant.

The risk-averse traveling repairman problem with profits

Soft Computing, 2018

In this paper, we study a stochastic variant of the traveling repairman problem with profits in which travel times are random. The introduction of the arrival time in the objective function instead of the travel time, which is common in most vehicle routing problems, poses compelling challenges, emphasized by the incorporation of the stochasticity in travel times and by the presence of profits. A risk-averse perspective is considered in the model, which is then formulated as a nonlinear integer model and heuristically solved by means of a beam search heuristic. Experimental results have been performed on instances adapted from the available deterministic datasets, to show the effectiveness of the solution approach.

Stability of dynamic traveling repairman problem under Polling-Sequencing policies

2013 European Control Conference (ECC), 2013

We establish a necessary and sufficient condition for stability in the dynamic traveling repairman problem (DTRP) [3] under the class of polling-sequencing (P-S) policies satisfying unlimited-polling and economy of scale. The P-S class includes some of the policies proven to be optimal for the expectation of system time under light and heavy loads in the DTRP literature. The number of tasks inside each polling partition is shown to be a Markov chain. Policies such as first come first serve, traveling salesman policy, nearest neighbor and Daganzo's algorithm are shown to have economy of scale.

The multi-depot k-traveling repairman problem

Optimization Letters, 2022

In this paper, we study the multi-depot k-traveling repairman problem. This problem extends the traditional traveling repairman problem to the multi-depot case. Its objective, similar to the single depot variant, is the minimization of the sum of the arrival times to customers. We propose two distinct formulations to model the problem, obtained on layered graphs. In order to find feasible solutions for the largest instances, we propose a hybrid genetic algorithm where initial solutions are built using a splitting heuristic and a local search is embedded into the genetic algorithm. The efficiency of the mathematical formulations and of the solution approach are investigated through computational experiments. The proposed models are scalable enough to solve instances up to 240 customers.

The dynamic traveling repairman problem

1989

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The orienteering problem with stochastic travel and service times

Annals of Operations Research, 2011

In this paper, we introduce a variant of the orienteering problem in which travel and service times are stochastic. If a delivery commitment is made to a customer and is completed by the end of the day, a reward is received, but if a commitment is made and not completed, a penalty is incurred. This problem reflects the challenges of a company who, on a given day, may have more customers than it can serve. In this paper, we discuss special cases 2 of the problem that we can solve exactly and heuristics for general problem instances. We present computational results for a variety of parameter settings and discuss characteristics of the solution structure.

A repairable queueing model with two-phase service, start-up times and retrial customers

Computers & Operations Research, 2010

A repairable queueing model with a two-phase service in succession, provided by a single server, is investigated. Customers arrive in a single ordinary queue and after the completion of the first phase service, either proceed to the second phase or join a retrial box from where they retry, after a random amount of time and independently of the other customers in orbit, to find a position for service in the second phase. Moreover, the server is subject to breakdowns and repairs in both phases, while a start-up time is needed in order to start serving a retrial customer. When the server, upon a service or a repair completion finds no customers waiting to be served, he departs for a single vacation of an arbitrarily distributed length. The arrival process is assumed to be Poisson and all service and repair times are arbitrarily distributed. For such a system the stability conditions and steady state analysis are investigated. Numerical results are finally obtained and used to investigate system performance.

Heuristics for the traveling repairman problem with profits

Computers & Operations Research, 2013

In the traveling repairman problem with profits, a repairman (also known as the server) visits a subset of nodes in order to collect time-dependent profits. The objective consists of maximizing the total collected revenue. We restrict our study to the case of a single server with nodes located in the Euclidean plane. We investigate properties of this problem, and we derive a mathematical model assuming that the number of visited nodes is known in advance. We describe a tabu search algorithm with multiple neighborhoods, and we test its performance by running it on instances based on TSPLIB. We conclude that the tabu search algorithm finds good-quality solutions fast, even for large instances.

The k-traveling repairman problem

Proceedings of the …, 2003

We consider the k-traveling repairman problem, a generalization of the metric traveling repairman problem, also known as the minimum latency problem, to multiple repairmen. We give an 8.497α-approximation algorithm for this generalization, where α denotes the best achievable approximation factor for the problem of finding the least cost rooted tree spanning i vertices (i-MST) problem. This can be compared with the best known approximation algorithm for the case k = 1, which is 3.59α. We are aware of no previous work on the approximability of the present problem.