Decision SupportEmergency response in natural disaster management: Allocation and scheduling of rescue units
Introduction
Natural disasters, such as earthquakes, tsunamis, floods, hurricanes and volcanic eruptions, have caused tremendous harm in the past and continue to threaten infrastructure and millions of people each year. Of particular importance for the reduction of casualties and economic losses is the response phase in natural disaster management, during which a large number of geographically-dispersed incidents, such as fires and collapsed buildings, require immediate processing by rescue units in the presence of severe resource scarcities and time pressure. Thus, one of the most critical emergency response tasks (Comfort, Ko, & Zagorecki, 2004) is the efficient allocation and scheduling of rescue units. However, this challenge has been addressed in the literature only very rarely.
In this paper, we propose a decision support model for emergency operations centers that allocates available rescue units to emerging incidents and schedules the processing time of these incidents. The model is formulated as a binary quadratic optimization problem, where the objective minimizes the sum of completion times of incidents weighted by their severity. We refer to this problem as the Rescue Unit Assignment and Scheduling Problem (RUASP). Our decision problem is related to problems from both routing and scheduling. We show that our problem can be modeled as a (more complex) modification of both the Multiple Traveling Salesman Problem (mTSP) and the parallel-machine scheduling problem with unrelated machines, non-batch sequence-dependent setup times and a weighted sum of completion times as the objective function, classified as in the scheduling literature. Using this relationship, we prove that our problem is NP-hard.
However, the NP-hardness of the underlying problem opposes one of the imposed requirements that decisions – even in complex emergency situations – must be derived timely. Therefore, we propose, implement and computationally compare several heuristics for the allocation and scheduling of rescue units. More specifically, we use a Monte Carlo-based heuristic as well as joint applications of 8 construction heuristics and 5 improvement heuristics. In addition, we embed these combinations of construction and improvement heuristics into GRASP metaheuristics. Thus, our work contributes not only to the field of disaster management, but also to the optimization literature in general.
The remainder of this paper is structured as follows. Section 2 examines and presents relevant literature and reveals the research gap that our paper addresses. In Section 3, we suggest the RUASP problem and propose an appropriate optimization model. Because of the NP-hardness, Section 4 proposes several solution heuristics. Our computational experiments are presented in Section 5, which also discusses our results. We summarize our results in Section 6, and conclude with an outlook on future research directions.
Section snippets
Related work
In the literature on disaster management, challenges and activities are classified (Ajami and Fattahi, 2009, Altay and Green, 2006, IFRC, 2012) into the preparedness phase (period before the disaster), the response phase (period during and shortly after the disaster) and the recovery phase (period long time after the disaster). More specifically, the preparation phase addresses tasks related to planning, training, early warning (i.e. prediction) and the establishment of necessary emergency
Optimization model
This section introduces the problem of scheduling rescue units and assigning them to incidents optimally after the occurrence of a disaster. We refer to this problem as the Rescue Unit Assignment and Scheduling Problem (RUASP).
Heuristics for solving the rescue unit assignment and scheduling problem
Beyond proving NP-hardness of the RUASP (see online appendix), we used small up to moderately large instances with m, n ⩽ 40 to evaluate practical runtimes. Using a mixed integer non-linear programming optimizer, more precisely, the Simple Branch and Bound solver in GAMS, we found that even small instances cannot be solved optimally in a practically reasonable time. As confirmed in interviews with the German Federal Agency of Technical Relief (THW), decision support in practice must be provided
Computational experiments
In our computational experiments, we evaluate the suggested heuristics against two benchmarks: (1) we compare the solutions of the heuristics with a lower bound of the optimal solution. We need to draw on lower bounds as finding optimal solutions even for moderately small instances turned out to be computationally infeasible. A gap between a solution found with a heuristic and the lower bound is an upper bound of the gap between the heuristic solution and the optimal solution. Thus, the
Conclusion and outlook
In this paper, we address the Rescue Unit Scheduling and Assignment Problem (RUASP), which is a key issue in emergency response management. Our contributions are as follows. We derive a binary quadratic optimization model of the problem. Considering literature on scheduling and routing, we propose a Monte Carlo-based heuristic, eight construction heuristics, five improvement heuristics and GRASP metaheuristics. Then, we computationally evaluate and compare these heuristics. In addition to that,
Acknowledgements
We are grateful to the editor and the anonymous reviewers, who all provided many valuable comments which helped improve the paper.
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