Mixed integer formulations for the multiple minimum latency problem

Cardona-Valdés, Yajaira; Alvarez, Ada M.

doi:10.1007/s12351-017-0299-4

Cited by 12 publications

(28 citation statements)

References 35 publications

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“…They also proposed a metaheuristic to solve the problem for larger instances, which reached to optimality in 386 out of 389 instances in a short time. Recently, Angel-Bello et al (2017) introduced five mathematical models for the multi-vehicle MLP. The first three models are obtained from the classical and flow-based formulations while the last two ones are generalizations of the time-dependent MLP formulation.…”

Section: Minimizing Total Latencymentioning

confidence: 99%

Minimizing latency in post-disaster road clearance operations

Ajam

Akbari

Salman

2019

European Journal of Operational Research

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After a natural disaster, roads and bridges can be damaged or blocked by debris, causing inaccessibility between critical locations such as hospitals, disaster response centers, shelters and disaster-struck areas.We study the post-disaster road clearing problem with the aim of providing a fast and effective method to determine the route of a work troop responsible for clearing blocked roads. The problem is to find a route for the troop that starts at the depot and visits all of the critical locations. The objective is to minimize the total latency of critical nodes, where the latency of a node is defined as the travel time from the depot to that node.A mathematical model for this problem has already been developed in the literature. However, for real-life instances with more than seven critical nodes, this exact formulation cannot solve the problem optimally in a 3-hour limit. To find a near-optimal solution in a short running time, we develop a heuristic that solves a mixed integer program on a transformed network and a lower bounding method to evaluate the optimality gaps. Alternatively, we develop a metaheuristic based on a combination of Greedy Randomized Adaptive Search Procedure (GRASP) and Variable Neighborhood Search (VNS). We test both the matheuristic and the metaheuristic on Istanbul data and show that optimal or near-optimal solutions are obtained within seconds.We also compare our algorithms with existing work in the literature. Finally, we conduct an analysis to observe the trade-off between total and maximum latency.

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Section: Minimizing Total Latencymentioning

confidence: 99%

Minimizing latency in post-disaster road clearance operations

Ajam

Akbari

Salman

2019

European Journal of Operational Research

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“…A number of mixed integer formulations have been proposed and exact methods such as cutting-plane algorithms and branch-cut-and-price algorithms (e.g., [1,18,19]) and various meta-heuristics (e.g., [20,21,28]) have been proposed. More recently, several mixed integer formulations for k-MLP have been proposed and experimented with on routing and scheduling instances with the number of nodes ranging up to 80 [3].…”

Section: Related Workmentioning

confidence: 99%

“…, P k starting from respective depots that serve all the requests and minimize the total latency, that is, the sum of latencies of requests, where the latency of a request is equal to the distance from the depot to the destination of the request on the path of the vehicle that serves it. 3 After appropriate scaling and rounding, we may assume c e are integers and c r i s j + c s j d j ≥ 1 for every root node r i and request R j . For ease of exposition, we assume the distances c e are given in a unit of time and interpret the latency of a request to be its completion time, following the job scheduling literature.…”

Section: Problem Formulationmentioning

confidence: 99%

“…Constraints (1) ensure that every non-root node is visited at some time, and constraints (2) ensure that each node cannot be visited before the distance from the root is covered. Constraints (3)-(5) are for the vehicles' routes: (3) ensures that the portion of a vehicle's route up to time t must visit every node visited by that vehicle by time t, (4) ensures that this route indeed has length at most t, and finally (5) seeks to encode that the route forms a path. (Note that constraints (5) are clearly valid, and one could also include the constraints a ∈δ out (r ) z i a,t ≤ 1 for all i, t.)…”

Section: Lp Frameworkmentioning

confidence: 99%

“…To see this, let L be the length of the part of a tour Z i, ℓ without the root r 0 and L ′ be the length up to the destination of a request covered by the tour. With probability 3 4 , the additional latency incurred for the request is t ℓ + L ′ . With probability 1 4 , the additional latency is at most t ℓ + 3(L − L ′ ) because the length of a traversal in the opposite direction is upper bounded by 3 times the length of the corresponding traversal in the correct direction (accounting the s i -d i portions 3 times).…”

Section: Single Depotmentioning

confidence: 99%

See 2 more Smart Citations

Minimizing Latency in Online Ride and Delivery Services

Das

Gollapudi

Kim

et al. 2018

Proceedings of the 2018 World Wide Web Conference on World Wide Web - WWW '18

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Motivated by the popularity of online ride and delivery services, we study natural variants of classical multi-vehicle minimum latency problems where the objective is to route a set of vehicles located at depots to serve requests located on a metric space so as to minimize the total latency. In this paper, we consider point-to-point requests that come with source-destination pairs and release-time constraints that restrict when each request can be served. The pointto-point requests and release-time constraints model taxi rides and deliveries. For all the variants considered, we show constant-factor approximation algorithms based on a linear programming framework. To the best of our knowledge, these are the first set of results for the aforementioned variants of the minimum latency problems. Furthermore, we provide an empirical study of heuristics based on our theoretical algorithms on a real data set of taxi rides. CCS CONCEPTS • Theory of computation → Routing and network design problems; Discrete optimization;

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Online routing and scheduling of search-and-rescue teams

2020

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We study how to allocate and route search-and-rescue (SAR) teams to areas with trapped victims in a coordinated manner after a disaster. We propose two online strategies for these time-critical decisions considering the uncertainty about the operation times required to rescue the victims and the condition of the roads that may delay the operations. First, we follow the theoretical competitive analysis approach that takes a worst-case perspective and prove lower bounds on the competitive ratio of the two variants of the defined online problem with makespan and weighted latency objectives. Then, we test the proposed online strategies and observe their good performance against the offline optimal solutions on randomly generated instances.

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Mixed integer formulations for the multiple minimum latency problem

Cited by 12 publications

References 35 publications

Minimizing latency in post-disaster road clearance operations

Minimizing latency in post-disaster road clearance operations

Minimizing Latency in Online Ride and Delivery Services

Online routing and scheduling of search-and-rescue teams

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