Multi-vehicle synchronized arc routing problem to restore post-disaster network connectivity

Abstract

After a natural disaster roads can be damaged or blocked by debris, while bridges and viaducts may collapse.This commonly observed hazard causes some road sections to be closed and may even disconnect the road network. In the immediate disaster response phase work teams are dispatched to open a subset of roads to reconnect the network. Closed roads are traversable only after they are unblocked/cleared by one of the teams. The main objective of this research is to provide an efficient solution method to generate a synchronized work schedule for the road clearing teams. The solution should specify the synchronized routes of each clearing team so that: 1) connectivity of the network is regained, and 2) none of the closed roads are traversed unless their unblocking/clearing procedure is finished. In this study we develop an exact Mixed Integer Programming (MIP) formulation to solve this problem. Furthermore, we propose a matheuristic that is based on an MIP-relaxation and a local search algorithm. We prove that the optimality gap of the relaxation solution is bounded by K times the lower bound obtained from the relaxed model, where K is the number of teams. We show computationally that the matheuristic obtains optimal or near-optimal solutions.

An updated annotated bibliography on arc routing problems

“…The matheuristics involve a relaxed model, a Lagrangian relaxation and the resolution of single vehicle problems in order to obtain lower and upper bounds. The instances used align with those in [3], and very good results are reported.…”

“…Debris clearance in an arc routing context is also addressed in references [3,4,37,117,153,171,199], as detailed below.…”

“…Akbari and Salman focus on debris removal and on the need to identify a synchronized work schedule for road clearing teams when reconnecting the damaged network. Each team is assigned to a different vehicle, giving rise to the multiple ARCP (K‐ARCP).…”

Post-disaster assessment routing problem

“…Campbell et al [22] No D Houming et al [23] No D Ozkapici et al [24] No D Camacho-Vallejo [25] No D Tzeng et al [26] Yes D Yuan and Wang [27] Yes D Yan and Shih [28] Yes D Ozdamar [29] No D Nafaji et al [30] Yes S Debris Removal Sahin et al [31] No D Berktas et al [32] No D Akbari and Salman [33] No D Hua and Sheu [34] Yes S Celik et al [35] No D Table 3.2. Next, we will examine the pioneering studies that mainly focus on GRP and its variants.…”

Location-Routing Problem for Relief Distribution in the Early Post-Earthquake Stage from the Perspective of Fairness

“…To restore the connectivity of post-disaster networks, Akbari and Akbari (2017) studied a multi-vehicle synchronized arc routing problem. They developed an exact mixed integer programming formulation (MIP) for relief delivery, and proposed a heuristic based on an MIP-relaxation and a local search algorithm to solve this problem [27]. To delivery vital relief to affected areas, Vahdani et al (2018) developed an integer nonlinear multi-objective, multi-period, and multi-commodity model by considering emergency roadway repair.…”