The heterogeneous multicrew scheduling and routing problem in road restoration

Highlights

• The heterogeneous multicrew scheduling and routing problem in road restoration is introduced.

• Three mathematical formulations and valid inequalities are developed.

• Valid inequalities are based on the dominance of the paths between nodes in the damaged network.

• The approach is validated through real-world instances based on floods and landslides in Rio de Janeiro, Brazil.

Abstract

This paper introduces the heterogeneous multicrew scheduling and routing problem (MCSRP) in road restoration. The MCSRP consists of identifying the schedule and route of heterogeneous crews that must perform the restoration of damaged nodes used in the paths to connect a source node to demand nodes in a network affected by extreme events. The objective is to minimize the accessibility time defined as the time that the demand nodes remain unconnected from the source node. The main contributions of the paper include three novel mathematical formulations that differ in the way of modeling the scheduling decisions and the synchronization of the crews, and the development of valid inequalities based on some particular properties of the problem. Additionally, we prove that the MCSRP is NP-hard. Extensive numerical experiments with randomly generated instances and a case study based on floods and landslides disasters in Rio de Janeiro, Brazil, are performed to assess the efficiency and applicability of our approach. In particular, we show that the valid inequalities significantly improve the solvability of the mathematical models. In terms of managerial implications, our results suggest that the incorporation of multiple crews helps to reduce the worst-case accessibility times across the demand nodes, thus providing more equitable solutions.

Introduction

Hurricanes, floods, landslides and earthquakes are examples of natural hazards that affect millions of people every year (EM-DAT, 2019). Specifically, these types of extreme events cause disruptions in the transportation infrastructure composed of roads, bridges, tunnels, etc., impeding access to affected areas. For instance, the 2010 Haiti earthquake generated more than 30 million cubic yards of debris (Booth, 2010) from damaged infrastructure, which includes the airport, seaport and roads within the country, constraining the access of the victims to relief aid (Van Wassenhove et al., 2010). Other examples of extreme events that have significantly affected road networks, thus compromising the accessibility to affected areas, are hurricanes in the southeastern region of the United States (Rawls and Turnquist, 2010), earthquakes in China (Hu et al., 2019), and floods and landslides in Rio de Janeiro State in Brazil (Moreno et al., 2018). Inaccessible affected areas result in a lack of commodities and delays in evacuation, rescue and medical assistance activities, thus causing victim suffering and loss of life. In an attempt to provide an effective emergency response in disaster aftermath, it is essential to restate the accessibility of the affected areas, which is popularly known in humanitarian logistics as road restoration.

In general, in road restoration problems, the affected areas and the damaged components of the transportation infrastructure are represented by demand and damaged nodes, respectively. A demand node is called accessible when there exists a path connecting it with a central supply depot using only undamaged and/or repaired nodes. Consequently, to restate the accessibility of the demand nodes, a critical subset of damaged nodes must be repaired. In this context, the multicrew scheduling and routing problem (MCSRP) primarily focuses on the restoration of the critical subset of damaged nodes that are essential to emergency response operations. Multiple crews, associated with various agencies, such as civil defense, armed forces, and firefighters, are available to perform the repair operations. The crews must be assigned to repair the damaged nodes. Additionally, for each crew, the sequence in which the damaged nodes must be repaired and the route used to reach them and return to the depot must be determined.

The crews consist of workforce teams equipped with heavy machinery, dozers, excavators, light vehicles, etc., and they may not have the same equipment. For example, one crew may have dozers and excavators to remove heavy debris from a blocked road, while another may have only workers using shovels. Some crews may not have enough resources (machinery, workforce, etc.) to repair some damaged nodes. For instance, during the removal of downed trees and debris after a flood, there are potential hazards of electrocution from contact with downed power lines or tree limbs in contact with power lines (OSHA, 2019). Only crews with the appropriate knowledge and protective equipment against electrical hazards should remove such debris. Furthermore, a crew with heavy machinery may take more time to reach the damaged nodes than a crew with only light vehicles, although the former may perform a faster restoration with the help of heavy machinery. Consequently, the crews differ in the time required to repair the damaged nodes, in the travel time between nodes, and in the set of damaged nodes that they can repair. However, the consideration of multiple heterogeneous crews in the problem has been neglected in the literature because of the complexity involved in such consideration. In fact, the single crew scheduling and routing problem (SCSRP) is challenging due to the scheduling and routing decisions that must be integrated (Maya-Duque, Dolinskaya, Sörensen, 2016, Moreno, Munari, Alem, 2019). In the multicrew version of the problem, an additional complexity factor is the synchronization of the crews at the damaged nodes (Akbari, Salman, 2017, Akbari, Salman, 2017) because these nodes cannot be traversed unless they are completely repaired, and a crew may have to wait at some damaged nodes, while another crew performs the restoration of such nodes. In fact, the MCSRP is NP-hard, as we prove in Appendix A.

The contributions of this paper to the literature are summarized as follows: (1) we define for the first time the multicrew scheduling and routing problem (MCSRP) for road restoration; (2) we develop three mixed integer programming (MIP) models that differ in the way of modeling the scheduling decisions and the synchronization of the crews; (3) we study some particular properties of the problem and derive valid inequalities based on these properties; (4) we carry out computational experiments based on a real-world case and randomly generated instances to compare the performance of the proposed formulations and the effectiveness of the valid inequalities. Regarding practical contributions, we use our models in a thorough, real-world case study of road restoration after the 2011 megadisaster of the Serrana Region in Rio de Janeiro, Brazil. Our approach consisting of models and valid inequalities enables us to derive prescriptive recommendations to the political bodies in charge of the post-disaster operations. For example, we find that the use of more crews significantly reduces the time required to recover the accessibility of the network at the same time that provides more equitable accessibility times. Additionally, the proposed approach provides good-quality solutions in reasonable computational times and can be a first step to further develop faster solution approaches and user-friendly decisions-support tools that can help decision-makers in the aftermath of disasters.

The remainder of the paper is organized as follows. Section 2 reviews the relevant background literature. Section 3 describes the heterogeneous multicrew scheduling and routing problem. Section 4 presents the MIP models, while Section 5 defines some properties and valid inequalities for the problem. Section 6 describes the instances and discusses the computational results. We close with concluding remarks in Section 7.