Emergency material scheduling optimization model and algorithms: A review

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Review Article

Emergency material scheduling optimization model and algorithms: A review Hui Hu a,*, Jing He a, Xiongfei He a, Wanli Yang a, Jing Nie a, Bin Ran b a b

School of Automobile, Chang'an University, Xi'an 710064, China School of Civil and Environmental Engineering, University of Wisconsin at Madison, Madison, WI 53706, USA

highlights
The optimization of emergency material scheduling (EMS) is summarized.
The EMS optimization models are categorized and the common objectives are introduced.
The existing algorithms are categorized and the common heuristic algorithms are summarized.
The development trends of EMS optimization model and algorithms are proposed.

article info

abstract

Article history:

In the emergency management of disruptions, efficient emergency material scheduling

Received 11 March 2019

(EMS) is a key factor to save people's lives and reduce loss. Based on the literature of EMS

Received in revised form

and related areas in recent years, the research was summarized from two aspects of EMS

16 July 2019

optimization model and algorithms. It is concluded that the EMS optimization models

Accepted 28 July 2019

mainly aim at the shortest time, shortest distance, minimum cost, maximum satisfaction

Available online xxx

and fairness, etc. The constraints usually include the quantity of supply depots, relief supply and vehicles, the types of commodities, the road network conditions, the budgets

Keywords:

and the demand forecast of emergency materials. Multi-objective model is more complex

Emergency material scheduling

and it usually considers more than one objective. To find the optimized solution, the multi-

(EMS)

objective model with complex constraints needs more efficient algorithms. The existing

Optimization model

algorithms, including mathematic algorithm and heuristic algorithm, have been catego-

Heuristic algorithm

rized. For NP-hard (non-deterministic polynomial hard) problems, heuristic algorithms

Disruption

should be designed, which mainly include genetic algorithm (GA), ant colony optimization (ACO), particle swarm optimization (PSO), etc. Based on the characteristics of the optimization model and various algorithms, appropriate algorithm or tools should be chosen and designed to obtain the optimized solution of EMS model. Finally, the development trends of EMS optimization model and algorithm in the future are proposed. © 2019 Periodical Offices of Chang'an University. Publishing services by Elsevier B.V. on behalf of Owner. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/).

* Corresponding author. Tel.: þ 86 29 8233 4426. E-mail address: [email protected] (H. Hu). Peer review under responsibility of Periodical Offices of Chang'an University. https://doi.org/10.1016/j.jtte.2019.07.001 2095-7564/© 2019 Periodical Offices of Chang'an University. Publishing services by Elsevier B.V. on behalf of Owner. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Please cite this article as: Hu, H et al., Emergency material scheduling optimization model and algorithms: A review, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.07.001

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1.

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Introduction

In recent years, earthquakes, floods and other disruptions have occurred frequently, causing huge casualties and property losses. According to the global analysis annual report by NASA and the USA National Oceanic and Atmospheric Administration, the direct losses caused by weather and climate-related disasters in the United States in 2018 reached 91 billion US dollars. The China National Ministry of Emergency Management and the National Disaster Reduction Commission announced that in 2018, various natural disasters in China have affected 130 million people, killed 589 people and caused a direct economic loss of 264.46 billion RMB. Taking earthquake as an example, in 2018, a total of 3068 people were killed in the world and more than 16,000 people injured in earthquakes of magnitude 6.0 or above. After a disruption occurs, it is urgent to distribute emergency materials timely, accurately and effectively to the disaster areas to minimize the casualties and property loss. Since most disruptions are hard to predict, and the factors of emergency material scheduling (EMS) are very complex, emergency rescue tends to be very urgent. Therefore, it is of great theoretical and practical significance to use the method of operational research (OR) and computer simulation to formulate the EMS plan as soon as possible. From a chronological point of view, the process of emergency management can be divided into four phases, including mitigation, preparedness, response and recovery. The mitigation and preparedness phases are before the disaster, which aim at lowering the probabilities of a disaster or minimizing its effects and losses. The response and recovery phases are post-disaster phases. The response phase seeks to minimize the disaster's effects by helping people as quickly as possible and preventing any further loss, while the recovery phase supports the community in its effort to return to a normal state (Anaya-Arenas et al., 2014). Emergency logistics is increasingly drawing the attention of researchers. However, most current researches discuss about facility location. The emergency material scheduling (EMS) after a disaster is the focus of this study. It aims at making optimal schemes to

Fig. 1 e The emergency management domain.

deliver emergency materials from the supply depots to disaster depots after a disaster occurs. The emergency management domain is shown in Fig. 1. EMS is a special kind of vehicle routing problem (VRP), which studies how to deliver relief supplies from the supply depots to the demand depots (disaster areas) to meet the needs of the victims and complete the reconstruction of the disaster area after the occurrence of a disaster. According to the number of supply depots, EMS is usually divided into oneto-many and many-to-many situations, which are shown in Fig. 2(a) and (b). It should firstly focus on timeline. Only when the emergency materials are delivered to the disaster depots in time and accurately, can the loss be minimized. Therefore, the shortest delivery time is basically the primary factor to be considered in the EMS optimization model. If there are multiple disaster depots, EMS should also give priority to the needs of the most seriously affected areas, and take other factors into consideration, that is, fairness of the scheduling. For complex relief supply collaboration of multiple organizations, supply-demand imbalance of EMS is the objective to discuss. Therefore, the shortest delivery time, the maximum fairness, and the highest satisfaction are usually objectives of the EMS optimization model. The EMS problem can consider one or more modes of transportation, including road, air,

Fig. 2 e Classification of EMS. (a) One to many EMS network. (b) Many to many EMS network.

Please cite this article as: Hu, H et al., Emergency material scheduling optimization model and algorithms: A review, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.07.001

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railway and multimodal transport. From this point of view, it is more complex than the traditional VRP. In addition, the disruptions usually cause serious damage to traffic facilities. For example, after an earthquake occurs, roads are usually damaged, making vehicle carrying materials impassable and making emergency rescue hard to implement. Therefore, EMS should also fully consider dynamic vehicle routing problems (DVRP) such as road damage maintenance and secondary disasters, and constantly revise the initial scheduling scheme. In fact, some researches considered both relief distribution and victims transportation in the optimization model, which finds the optimal solution to deliver relief products and transport victims between disaster areas and health centers or supply depots. This leads to a much more complex network problem, even a multi-commodity problem presented with a multi-period planning horizon. In EMS, we ignore victim transportation, and only concentrate on the logistics management of emergency materials. In the practical rescue process, there exist many deficiencies. In the Wenchuan earthquake, due to the lack of detailed classification, varied types of emergency supplies lead to unreasonable distribution of emergency material supplies and chaotic distribution (Lai, 2011). In addition, the inaccurate demand forecast of emergency materials lead to excessive delivery of relief, which results in waste to a certain extent (Liu and Wang, 2008). All these problems in the Wenchuan earthquake are caused by the lack of largescale earthquake response experience. However, in the subsequent Yushu earthquake, not fully considering the high altitude of Yushu leads to insufficient medical emergency supplies, which seriously affects the rescue efficiency (Zhuo et al., 2010). In view of this, research on EMS has important theoretical and practical significance. We collect and sort out relevant papers published in this field in the past ten years, focusing on reviewing the EMS from the following two aspects-optimization model construction and algorithm design, in order to understand the latest research progress in this field, find out the problems, and propose the future research trend.

2.

EMS optimization model

2.1.

Single optimization objective

2.1.1.

Minimum time

Minimum time should be the primary objective of EMS, which is significant for improving the rapid response ability and the effect of emergency rescue. Hu et al. (2016b) layered the road network and analyzed the vehicles in each layer. Based on this, a two-level EMS model of multi-commodity, multi-vehicle type was proposed, whose objective was the minimum time. The optimized scheme was obtained by genetic algorithm (GA) and hierarchical solution method. Yan and Guo (2016) studied the EMS for multi-rescue point under real-time/time-varying complex road conditions, and the dynamic path adjustment was realized by an improved GA to find the shortest path. Zhang et al. (2015) set up a two-level EMS model with the objective of minimizing the completion time. Wex et al. (2014)

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developed an EMS model for effectively allocating and arranging rescue units, which minimized the total amount of accident completion time weighted by severity. Hamedi et al. (2012) studied the scheduling model of humanitarian emergency supplies such as water and food, aiming at the shortest delivering time, and adopted GA to solve the problem. Ahmadi et al. (2015) proposed a multi-warehouse location-route model considering network failures, multiple vehicle use and standard rescue time, which significantly reduced scheduling time at the expense of more local warehouses and vehicles. Lu et al. (2016) presented a rolling horizon-based framework for real-time relief distribution in the aftermath of disasters. The objective was to minimize the total time to deliver relief supplies to satisfy the demand, considering uncertain data and the risk-averse attitude of the decision-makers. Ding (2011) established an EMS optimization model to seek the shortest delivery time based on the urgency, road conditions and shortage of relief supplies in disaster depots. Hu et al. (2016a) put forward the concept of “virtual vehicle”, combined different materials in an orderly manner, and constructed an optimization model with the objective of minimizing time. Besides the minimum time, the shortest distance should also be considered.

2.1.2.

Shortest distance

Emergency response should be initiated immediately after the occurrence of a disaster, and relief supplies should be delivered to the disaster areas in time. Therefore, the shortest distance to deliver emergency materials to the disaster areas is especially important for EMS. Ma and Wang (2014) established an EMS model for single distribution center (DC) and multiple disaster depots, and put forward the requirements of two-way distribution, which greatly improved the efficiency of EMS. Taking the shortest distance for vehicles and emergency supplies as the objective, Liu (2010) built an EMS model to deliver the emergency materials and direct the victims to flee the disaster area in time, so as to reduce loss of life and property. Vidal et al. (2013) established three EMS models with time windows, which were multi-cycle, multidistribution center and disaster point that can only be guaranteed by specific vehicles. To obtain the shortest distance, they comprehensively considered possible situations in the material distribution process. Batmetan et al. (2017) investigated the shortest path in the logistics of the eruption of the Lokon volcano and tried to apply the formula by introducing a speed indicator, distance, bend, density and secure point to calculate the shortest path to be selected by using multi-objective optimization algorithm for cloud computing task scheduling based on improved ant colony algorithm (MO-ACO). Ferrer et al. (2018) built a compromise programming model for multi-criteria optimization in humanitarian last mile distribution. Chiou and Lai (2010) proposed an integrated multi-objective model to determine the optimal rescue path and traffic-controlled arcs for EMS under uncertainty environments. Yuan and Wang (2007) built an EMS model targeting minimum total travel time and path complexity respectively. Taking into account the real-time effect of disaster extension, the travel speed on each arc was modeled as a continuous decrease

Please cite this article as: Hu, H et al., Emergency material scheduling optimization model and algorithms: A review, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.07.001

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function with respect to time. Cheung (1998) proposed a routing policy in EMS that formed a dynamic shortest path in a network with independent, positive and discrete random arc costs.

2.1.3.

Fairness/satisfaction

Unlike the business distribution where profit directly decides whether visiting a customer or not, in EMS, not only all disaster depots should be covered, but an equity of the amount of relief received by people should also be guaranteed. Therefore, for EMS, it is an important indicator to improve the overall demand satisfaction of the disaster areas and guarantee the fairness simultaneously. Demand satisfaction has become an important objective which can be fulfilled by either minimizing unmet demand or maximizing demand coverage. Chang et al. (2014) proposed a greedy-search-based, multiobjective, genetic algorithm capable of automatically generating a variety of feasible emergency logistics schedules for decision-makers. It dynamically adjusted the distribution schedules from various supply depots according to the requirements of the demand depots to maximize satisfaction with resources, time to delivery, and transportation costs. Das (2018) identified seven factors that affected the demand for disaster relief, and based on this, a warehouse location model with the goal of maximum satisfaction was constructed. Two different versions of the proposed model were tested by using the GLPK solver via python programming language and verifying the feasibility of the model. In view of the equity and fairness of EMS, Lin et al. (2011) analyzed relief distribution problem, proposed three different objectives and sought equity by minimizing the great gap of the unsatisfied demand. Huang et al. (2012) presented three different ways to measure equity. The first approach computed a deviation measure like the one used by Lin. The second measured the standard deviation of the demand satisfaction using a non-linear formula. The third approach used a piecewise-linear function to penalize inequity. Vitoriano et al. (2011) applied an optimized multicriteria goal programming model that covered certain aspects of distribution. The model incorporated issues of time of response, cost and equity of the distribution for decision support under relief distribution plan. Wang and Wang (2013) constructed a multi-level EMS optimization model for marine disasters by using the cooperative scheduling method to maximize the reliability of material supply. Chen and Wang (2010) took the satisfaction of the whole disaster areas as the objective of the EMS and built a model for multi-commodity, multi-supply depot, multidisaster depot, multi-mode of transportation, so as to maximize the rescue efficiency of EMS. Sheu (2014) and Sheu and Pan (2015) proposed a relief supply collaboration approach to address the issue of post-disaster relief supplydemand imbalance in EMS. First, a clustering mechanism to identify potential relief suppliers was presented. Then a stochastic dynamic programming model to minimize the impact of relief supply-demand imbalance was established. The decision-maker could choose from existing relief suppliers and decide the amount and the type of relief to be delivered to the disaster areas. Mishra et al. (2018) applied

two basic round-robin based greedy search algorithms and proposed an optimized algorithm for fair distribution of relief. The fairness was measured by considering minimization of the absolute standard deviation between demand and supply at the disaster depots and also by considering the number of disaster depots receiving the relief.

2.2.

Multiple optimization objectives

Besides the above-mentioned single objective like the shortest distance, the minimum time and the highest fairness, some literature takes more factors into account, such as the minimum cost, the least vehicle used and the lowest route complexity, or combines them to form a multi-objective model. Hu et al. (2017) introduced the possibility goal oriented (GO) method to determine the connectivity reliability of the delivery network. Based on the connectivity reliability of the network, a penalty parameter was introduced, and then a multi-objective model aiming at minimum time and delivery cost was established. In view of the characteristics of emergency material storage and scheduling, Xu et al. (2018) established a multi-objective optimization model concerning the constraints of relief supply and transshipment equilibrium. The objectives include minimizing the sum of construction cost, maintenance cost and transportation cost of the reserve, and minimizing the overall risk and the difficulty of disaster disposal. A discrete binary particle swarm optimization (PSO) with inertia weight was designed to solve the model. Song et al. (2017) established a multistage EMS optimization model for multi-supply depot and multi-demand depot, whose objectives included minimum total cost and maximum satisfaction of disaster areas. Zhang et al. (2017) constructed an EMS optimization model with the objectives of minimum rescue cost and minimum loss caused by untimely rescue when disaster occurred at multiple areas. Li et al. (2016) analyzed the characteristics of EMS in terms of optimization objectives and factors affecting EMS, and established an EMS model with the objectives of minimizing rescue time and improving material demand satisfaction. Alem et al. (2016) developed a new two-stage stochastic network flow model, and took more factors into account, such as budget, fleet size of multiple types of vehicles, procurement, and varying lead times over a dynamic multi-period horizon. Burkart et al. (2016) proposed a multi-objective location-routing model with the objectives of minimum unserved demand as well as cost for opening DCs and for routing relief supplies. Zhan et al. (2014) proposed a multi-objective EMS model based on information updates of disaster scenario to maintain the efficiency and equity through timely and appropriate decisions regarding issues such as vehicle routing and relief allocation. Gan et al. (2016) designed objectives to minimize the completion time of scheduling and the total unsatisfied time of all reliefs, and proposed a multi-agent genetic algorithm (MAGA) to solve the problem. Sheu (2010) proposed a multi-objective EMS model for dynamic demand based on fuzzy clustering of disaster-stricken demand. Owusu-Kwateng et al. (2017) evaluated the performance of relief logistics in a disaster in Ghana with an emphasis on the coordination of emergency

Please cite this article as: Hu, H et al., Emergency material scheduling optimization model and algorithms: A review, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.07.001

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relief operation and effectiveness of inventory management. Rahafrooz and Alinaghian (2016) proposed a novel multiobjective robust possibilistic programming model, which simultaneously considered maximizing the distributive justice in EMS, minimizing the risk of relief distribution, and minimizing the total logistics costs. Zhang et al. (2013) proposed a multi-objective, multi-period EMS model, which minimized the unmet demand, total delivery time and unbalanced supply among demand areas. Bozorgi-Amiri et al. (2013) developed a multi-objective robust stochastic programming approach for the EMS under uncertainty, where not only demands but also supplies and the cost of procurement and transportation were considered as the uncertain parameters. Ransikarbum and Mason (2014) presented a multi-objective, integrated network EMS optimization model for making strategic decisions in the supply distribution and network restoration phases of humanitarian logistics operations. Yang et al. (2017) developed a two-layer emergency logistics system with a single supply depot and multiple demand sites for wildfire suppression and disaster relief. Based on the forecasted propagation behavior of fire, as well as the severity of fire sites, a multi-objective VRP model was developed to minimize both the travel time and cost of the resource delivery vehicles. After the optimization model is established, multiple objectives can usually be transformed into single objective to be convenient for finding the solutions. Wang et al. (2018) proposed a multi-objective nonlinear integer programming model with the objectives of minimum total transportation time and cost. Decision-makers could dynamically give weights to both of the objectives, so the flexibility of the model was improved. Nikoo et al. (2018) constructed a multiobjective optimization model based on network vulnerability, and took the length of path, travel time and number of paths as the performance indicators of network vulnerability. The multi-objective function was transformed into a single objective function by weighted sum and lexicographic methods, and the model was solved using a branch-and-cut method. Wang et al. (2018) proposed a twodimensional and multi-objective EMS optimization model to achieve the shortest time and the lowest cost. The rescue point decomposition method was used to reduce the dimension of the model, and the ideal point algorithm was designed to solve the model. Zhang et al. (2019) considered the primary and secondary disasters, and proposed a threestage stochastic programming model to minimize the transportation time, transportation costs and the amount of unsatisfied demand. The multi-objective function was processed with the help of fuzzy auxiliary variables of membership, and the method was proved to be better than the conventional ones when we took the Wenchuan earthquake as a sample. Ma et al. (2019) proposed a multiobjective supplementary location optimization model for earthquake emergency shelters. By using the elliptical attenuation model of seismic intensity, the uncertainty of population distribution time dynamics and the uncertainty of spatial non-uniform distribution of evacuees under different earthquake damage scenarios were combined into the position allocation problem, and the feasibility of the

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model was verified by the improved PSO algorithm. Cui et al. (2019) took supply chain interruption and path risk into consideration, and established a post-disaster material transportation model under uncertain conditions in order to minimize transportation time and cost. The genetic algorithm (GA) was used to solve the problem, and the optimization scheme of emergency material vehicle scheduling and material transportation after disaster was obtained. Hu et al. (2015) established an EMS model with crossing points, the goal of which was to spend the least time and the lowest cost, and the feasibility of the model was verified by the GA.

2.3.

Summary

All the above references and corresponding EMS models are listed in Table 1 for readers' convenience. In view of the optimization objective of EMS, most literature considers minimum time, minimum cost, shortest distance or lowest risk. A few scholars consider the EMS from the perspective of demand satisfaction and fairness, but they ignore the material loss and the urgency of demand. Most of the existing literature adopts multi-objective EMS models. Generally, linear weighting method is used to transform EMS from multi-objective scenarios into single-objective ones, but the priority of objective coefficient is determined by the preference of decision makers. As a result, it is difficult to determine the objective weight scientifically. In some literature, the demand, material satisfaction, risk and fairness are fuzzified. Due to the lack of standardized data collection and processing, the results are mostly unsatisfactory and not operable. Moreover, few papers extend into the field of supply chain management, nor do they explore how the government and enterprises can jointly achieve optimization objectives in the process of emergency logistics operation.

3.

Optimization algorithm

3.1.

Mathematic algorithm

When a problem can be solved, the mathematic algorithm usually provides the optimal solution, which means its calculation accuracy is better than heuristic algorithm. Commonly used mathematic algorithms include the Dijkstra algorithm, branch and bound method, cutting plane method, dynamic programming method, etc. For the situations of multiple rescue depots to multiple disaster depots and single rescue depot to single disaster depot, Zhao (2012) established two EMS models featuring the earliest start time and the least number of rescue points. Fuzzy optimization was used to transform the optimization objectives, and polynomial-level model accurate algorithm was adopted to solve the problems. These models and algorithms have been successfully integrated into the China National Emergency Material Scheduling System, and have been applied and validated in the 2010 Yushu earthquake in Qinghai Province. Li and Zhang (2012) weighted the rescue rate of each disaster area according to the urgency degree of disaster areas and tried to maximize the rescue rate and

Please cite this article as: Hu, H et al., Emergency material scheduling optimization model and algorithms: A review, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.07.001

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Literature

Model objective

Period

Constraint Commodity type

EMS network

Transport mode

Uncertain

One to many One to many Many to many Many to many Many to many One to one Many to many Many to many Many to many One to many One to many One to many Many to many Many to many e Many to many e Many to many e One to many Many to many Many to many e e Many to many Many to many Many to many Many to many One to many Many to many Many to many Many to many e

Multiple Single Single e e Multiple Single Single e Single Single e e Multiple Multiple Multiple Single Single Single Single Multiple Single e Multiple Multiple Single Multiple Multiple e Multiple Multiple e Multiple

e Yes Yes Yes Yes Yes Yes Yes Yes e e e e e Yes Yes Yes Yes Yes Yes e e Yes Yes e e e Yes Yes Yes e Yes Yes

Many to many Many to many Many to many Many to many One to many Many to many Many to many Many to many Many to many Many to many

e Single e Multiple Single Single Multiple e e Single

Yes e Yes Yes Yes Yes e Yes Yes e

Hu et al. (2016b) Yan and Guo (2016) Zhang et al. (2015) Guo et al. (2016) Wex et al. (2014) Hamedi et al. (2012) Ahmadi et al. (2015) Lu et al. (2016) Ding (2011) Hu et al. (2016a) Ma and Wang (2014) Liu (2010)

Minimum time Minimum time Minimum time Minimum time Minimum time Minimum time Minimum time Minimum time Minimum time Minimum time Shortest path Shortest path

Single Single Single Single Single Single Multiple Single Single Single Single Single

Vidal et al. (2013) Batmetan et al. (2017) Ferrer et al. (2018) Chiou and Lai (2010) Yuan and Wang (2007) Cheung (1998) Wang and Wang (2013) Chen and Wang (2010) Mishra et al. (2018) Sheu (2014) Chang et al. (2014) Song et al. (2017) Zhang et al. (2017) Li et al. (2016) Alem et al. (2016) Burkart et al. (2016) Zhan et al. (2014) Gan et al. (2016) Sheu (2010) Owusu-Kwateng et al. (2017)

Shortest path Shortest path Shortest path Shortest path Shortest path Shortest path Maximum satisfaction Maximum satisfaction Maximum fairness Maximum satisfaction Maximum satisfaction Minimum cost and maximum satisfaction Minimum cost and the least untimely rescue cost Minimum time and maximum satisfaction Minimum budget and time Minimum cost and shortest path Shortest path and maximum satisfaction Minimum time and maximum satisfaction Maximum value determined by the urgency of relief needs and satisfaction Highest coordination degree of rescue activity and highest mobilization rate of relief resources Maximum fairness and lowest risk Minimum time and maximum satisfaction Minimum demand, supply, procurement and transportation cost Maximum fairness and highest recovery degree of disaster Maximum satisfaction Minimum time and minimum cost Minimum time, minimum cost and minimum unsatisfied demand Acceptable evacuation distances and minimum budgets Minimum time and transportation cost Minimum time and minimum cost

Multiple Single Single Single Single Single Multiple Single Single Single Single Single Single Single Multiple Single Single Single Single Single

Multiple e e e e Multiple e Multiple e Multiple e e e e e e e e e Multiple Multiple Multiple e e e e Multiple e e e e e e

Single Multiple Single Single Single Single Single Single Single Single

e Single e e e e e e e e

Rahafrooz and Alinaghian (2016) Zhang et al. (2013) Bozorgi-Amiri et al. (2013) Ransikarbum and Mason (2014) Das (2018) Wang et al. (2018) Zhang et al. (2019) Ma et al. (2019) Cui et al. (2019) Hu et al. (2015)

J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx

Please cite this article as: Hu, H et al., Emergency material scheduling optimization model and algorithms: A review, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.07.001

Table 1 e Comparison of EMS models.

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minimize the cost of EMS. A multi-objective programming model for multiple supply depots, multiple demand points and multiple commodities was established. Then the multiobjective programming model was transformed into a twostage single-objective programming model, and the accurate algorithm was designed. The optimal solution was obtained by using the LINGO software. Qin et al. (2010) used the improved dynamic clustering algorithm to solve the vehicle assignment problem and also dynamic programming to solve the VRP. It can effectively solve the EMS problem in 13 demand locations. Wu et al. (2019) proposed a new method of mixed steepest descent, and the accuracy of the algorithm was verified by simulating the air logistics transportation and EMS problem in large earthquake disasters.

3.2.

Heuristic algorithm

Simulated annealing algorithm (SAA), artificial neural networks (ANN) and tabu search (TS) come into use in the 1980s. In recent years, evolutionary algorithm (EA), ant colony optimization (ACO) and quantum algorithm (QA) appeared one after another. Heuristic algorithms usually construct initial solutions, perform random operations to get new solutions, and then filter them according to the evaluation conditions, so that they iterate continuously until the termination conditions are reached. EMS is a kind of NP-hard (non-deterministic polynomial hard) problem. It's more complicated and intrinsically harder than the problem that can be solved by algorithms in polynomial time. When a decision version of a combinatorial optimization problem is proved to belong to the class of NP-complete problems, then the optimization version is NP-hard. The commonly used heuristic algorithms include GA, ACO, PSO and so on.

3.2.1.

Genetic algorithm

Inspired by the theory of biological evolution, GA simulates the problem to be solved as a process of biological evolution, generates the next generation solution through replication, crossover, mutation and other operations, gradually eliminates the solution with low fitness function value and increases the solution with high fitness function value. In this way, it is possible to evolve into individuals with high fitness function after many generations (Siam et al., 2018). Zhao (2012) designed an improved GA to solve a multiobjective EMS model for multi-supply depot and multidisaster depot under large-scale natural disasters. The algorithm adopted symbol coding and introduced special crossover operator and mutation operator which fused the characteristics of the problem to ensure the legitimacy of the solution. The simulation results showed that the algorithm could solve the optimized solution with fewer iterations. Zhang et al. (2017) combined GA and sequential linear programming (SLP) to solve the optimization model of multi-level EMS with continuous consumption. The numerical results showed that the GA global optimization combined with SLP local optimization strategy could effectively find a better solution than a single optimization algorithm. Chen and Ma (2017) designed a dynamic acceleration adaptive GA to solve the multi-warehouse EMS

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model under the optimal variable road network, which solved the dual effects of the variable road network structure and multi-warehouse with the scheduling algorithm. Wang et al. (2017) established an EMS optimization model for insufficient material supply and increase of demand depots, and designed improved GA with new elite retention strategy to accelerate the generation of optimal strategy. The simulation results showed that the improved algorithm had better problem-solving capability and adaptability than the standard genetic algorithm (SGA). Ma (2017) put forward two scheduling modes, i.e., vertical scheduling and vertical-horizontal coordinated scheduling, and built two models respectively. An improved GA was designed by combining the algorithm with the characteristics of the models. The algorithm was used to find the optimized EMS scheme of power system in the Ya'an earthquake. Bian (2017) constructed an EMS model with objectives of the maximum probability of arrival in time, maximum time satisfaction and material satisfaction according to the specific situation of the disaster area. Then, the GA based on the relative importance of the target was used to solve the model. Chen (2006) improved the SGA from coding method, fitness function, genetic operator and designed improved GA for solving an EMS model. The influence of penalty coefficient and algorithm control parameters on the experimental results were also analyzed. Chen and Ma (2017) constructed an EMS model of vertical distribution and coordinated vertical and horizontal transshipment distribution respectively, aiming at the shortest time and minimum cost, and designed GA to solve the models. The results showed that the coordinated distribution mode was superior to the traditional distribution mode. Ma (2011) established a two-stage EMS model for multi-commodity, multi-supply depot and multidisaster depot. The first stage aimed at the shortest emergency time, and the second stage aimed at the minimum emergency cost, emphasizing the least emergency time and the most economical way to deliver the emergency materials to the disaster area. GA for solving the two models was designed and symbolic coding and natural ordinal coding were used in the coding process. Hamedi et al. (2012) addressed a sub-problem of the general humanitarian supply-chain problem, where the routing and scheduling of humanitarian supply transportation was formulated as a mathematical model. A GA-based heuristic algorithm was proposed to solve the problem in reasonable computational time. The results showed that the proposed approach could provide prompt delivery while reduce the risk of undesirable delay caused by uncertainty, and the algorithm could also provide high quality solution within short computational time to fulfill the on-line operation requirement. Chen et al. (2019) proposed an innovative GA for emergency decision under resource constraints. According to the prospect theory (PT), the best-worst method (BWM) was used to distribute the weight of all emergency locations. On this basis, an improved GA based on prospect theory was proposed to solve the problem of emergency resource allocation among multiple emergency locations under resource constraints. GA has the following drawbacks, such as local optimum, premature solution and low convergence speed, which can be

Please cite this article as: Hu, H et al., Emergency material scheduling optimization model and algorithms: A review, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.07.001

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caused by the algorithm design and characteristics of the objective functions. So more and more improved GA are proposed to have efficient solution searching capability, including improving coding strategy, fitness function and operators.

3.2.2.

Ant colony optimization

ACO is a probabilistic algorithm used to find the optimal path. This algorithm has the features of positive information feedback, distributed computing and heuristic search, and is essentially a heuristic global optimization algorithm in evolutionary algorithm. Cao (2017) established a multi-objective EMS model and designed variable neighborhood ACO to find the solution, which considered the panic of victims, and obtained a better optimized scheme. Fu and Luo (2014) combined ACO with EMS to create an efficient emergency rescue system, whose functions included material management, city information management, vehicle management, emergency call and rescue. The multi-objective optimization problem was difficult to solve because of multi-objective constraints. In order to solve this problem, an improved multi-colony ACO was designed to find the solution under the condition of multi-vehicle types. Finally, the Pareto solution space of the problem optimized by data envelopment analysis (DEA) was obtained, and the best scheme of time balance was provided. Wang (2009) studied the EMS with multiple commodities, uneven and continuous consumption of emergency materials, and built an EMS model with the objectives of earliest emergency time and least supply depots. Then, ACO algorithm was designed to solve the model. In view of the insufficient supply, Wang et al. (2016) constructed a multi-objective EMS model for multi-reserve depot and multi-supply depot, and designed a hybrid intelligent algorithm based on non-dominated sorting genetic algorithm II (NSGA-II) and ACO to solve the problem. In the solution, two-dimensional binary chromosome coding and corresponding crossover and mutation operations were designed, and an improved coding strategy was proposed to solve the potential conflict of the EMS between multiple supply depots. Tang et al. (2008) used max-min ACO to solve the post-disaster EMS problem so that the relief supplies would be delivered to the disaster areas more efficiently. Hao and Li (2015) proposed a hybrid genetic ACO to find the solution of EMS model, where GA was used to search the initial solution quickly and globally, and then it was transformed into the initial pheromone distribution of the ACO. The positive feedback mechanism and parallelism of ACO were used to solve the optimal solution efficiently. Yi and Kumar (2007) presented a meta-heuristic of ACO for solving the EMS model. The EMS problem was divided into two stages, i.e., the vehicle routing, and the multicommodity delivery. The first stage built stochastic vehicle routes under the guidance of pheromone trails, and in the second stage, a network flow-based solver was designed to assign different types of vehicle flows and commodities. Zhang et al. (2017) established an EMS model based on emergency relief characteristics to seek the shortest delivery time as the ultimate objective, which considered both the road conditions and material shortage of demand depots.

The improved fish-swarm ant colony optimization (FSACO) was designed to find the solution. Zhang and Xiong (2018) proposed a hybrid algorithm based on artificial immunity and ant colony optimization algorithm. In this hybrid algorithm, the Pareto optimization model is used to calculate the congestion degree, and the population in the ant colony optimization algorithm is sorted undominated. Based on the fast global convergence and randomness of the improved immune algorithm, combined with the distributed search ability and positive feedback ability of ACO algorithm, a better solution set is generated quickly. ACO has many advantages, such as excellent global searching capability and robustness, distributed computing and easy combination with other algorithms. Its defects mainly include the following three points. Firstly, compared with other algorithms, its searching time is longer to construct the solution. Second, at the initial stage, the function of pheromones is not obvious because pheromones on each road are basically the same. After a period of time, the pheromone advantage on the path will become obvious, and eventually converge to the better path, which will lead to long time in the early stage. Finally, during the execution of ACO, it is easy to appear stagnation.

3.2.3.

Particle swarm optimization

PSO came from the foraging behavior of birds. Researchers found that birds often changed directions, scattered and gathered suddenly during flight, and their behaviors were unpredictable. However, their overall consistency and optimal distance between individuals were maintained. Through the research on the behaviors of similar biological groups, it was found that there existed a social information sharing mechanism in biological groups, which provided an advantage for the evolution of groups, which was also the basis of PSO. PSO is a stochastic population-based optimization method proposed by Kennedy (2011). Because PSO is simple and efficient, it has been successfully applied to many application fields such as artificial neural network training, function optimization, fuzzy control, and pattern classification (Bonyadi and Michalewicz, 2017; Kennedy, 2011). Tian et al. (2012) adopted the hybrid coding of discretecontinuous vector and weighted fitness function mechanism, combined with the continuous updating strategy of position and speed, and designed PSO for this kind of EMS optimization model with combination of discrete and continuous variables. Lin and Xu (2008) established an EMS model with multi-objective of the shortest time and the lowest cost, and transformed the multi-objective problem into a single-objective one by using the ideal point method. Then, the discrete PSO algorithm was designed to solve the problem. Wang and Wu (2011) designed PSO to solve the EMS model aiming at the earliest emergency start time and the lowest total transportation cost, which effectively solved the optimization problem caused by the increase of the number of variables and dimensions of the model. By setting learning factor and inertia weight as linear trend and increasing local disturbance, Yu (2014) established an improved PSO to solve the multi-objective model aiming at the least transportation cost and the shortest delay time. Gan et al. (2013) designed

Please cite this article as: Hu, H et al., Emergency material scheduling optimization model and algorithms: A review, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.07.001

J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx

an exponential utility function of time as an indicator of operational efficiency and built an EMS model. Then, PSO and multi-swarm cooperative particle swarm optimization (MCPSO) were designed. Wu and Wang (2012) proposed a chaos PSO with Gauss function to overcome the defects of long computing time and easily falling into local optimization. The improved algorithm enhanced the search ability of PSO by using the distribution curve of Gauss function and ergodicity of chaos, and was designed to solve an EMS problem with time constraints. The simulation results of example indicated that the algorithm had faster searching speed and stronger optimization ability than GA and standard PSO. Bozorgi-Amiri et al. (2013) applied mixedinteger nonlinear programming to minimize the expected total costs. The model simultaneously determined the location of relief distribution centers and the allocation of affected area to relief distribution centers. Furthermore, an efficient solution approach based on PSO was developed to solve the proposed model. Andreeva-Mori et al. (2013) proposed a robust particle model reflecting various properties of the helicopter and evacuation mission. They set the parameters according to numerical simulations, and the real data during the Great East Japan Earthquake and Tsunami in 2011 was used as cases. Meng (2015) constructed an EMS model for uncertain demand and road damage conditions. Combining with the case of disruptions, a hybrid genetic-particle swarm optimization (GPSO) algorithm was designed. Compared with the standard PSO, the hybrid algorithm was proved to be feasible and effective, which provided the feasibility for decision makers to solve the EMS under incomplete demand and road information. The research and practice in recent years show that PSO has the advantages of fast convergence speed, high solution quality and excellent robustness in multi-dimensional space function optimization and dynamic target optimization. It is especially suitable for engineering applications. The PSO converges quickly in the early stage of searching, but it tends to get into local optimum in the later stage. This is the main disadvantage of PSO algorithm. In view of this problem, some improved PSO algorithms have emerged in recent years, such as hybrid genetic-particle swarm optimization (GPSO) algorithm (Marinakis and Marinaki, 2010), particle swarm optimization with tabu search algorithm (PSO-TSA) (Gao et al., 2014), evolutionary game with particle swarm optimization (EGPSO) (Liu, 2008), fuzzy particle swarm optimization (FPSO) algorithm (Khan and Engelbrecht, 2014), etc.

3.2.4.

Others

Li et al. (2016) used the improved maximum flow algorithm to solve the multi-objective model aiming at minimum rescue time and maximum satisfaction of relief demand, and obtained effective optimized result. Song et al. (2019) proposed an improved differential evolution algorithm based on dual mutation strategy. The concept of Pareto non-dominant hierarchy and congestion distance was introduced into the improved algorithm to solve the constrained double-objective model. The improved differential evolution algorithm with double mutation strategy could get more Pareto frontier solutions. At the

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same time, the universality of solution distribution were significantly improved. Chen and Wang (2010) used the Lagrange decomposition method to solve the EMS for multi-commodity, multi-supply depot, multi-disaster depot, and multi-mode of transportation, with the objective of maximum satisfaction of disaster depots. He et al. (2016) used tabu search heuristic algorithm to solve the EMS problem based on forbidden time window. Tang et al. (2008) used the improved nearest search method to solve the multi-objective model with the minimum total time and the most balanced time of each vehicle, and obtained an effective EMS scheme. Chen et al. (2013) established a multi-commodity EMS model with the objective of minimizing total time and total cost. Then the model was transformed into an equivalent variational inequality problem, and the modified projection algorithm was used to solve the model. The numerical solution and simulation results of the Wenchuan earthquake showed that the reliability and emergency capability of emergency facilities and road network had important impacts on EMS decisionmaking. Alem et al. (2016) presented semi-deviation and conditional value-at-risk to improve demand fulfillment policy and designed a two-phase heuristic to solve the problem within a reasonable amount of computing time. Numerical tests based on the floods and landslides in Rio de Janeiro state, Brazil, showed that the model could help plan and organize relief logistics in most scenarios. Hu et al. (2019) constructed a scenario-based approach for emergency material scheduling (SEMS) with the goal of minimum time and maximum fairness, using vehicle to everything (V2X) communications, and designed the SEMS algorithm based on the artificial fish-swarm algorithm to obtain an optimized solution. Lei et al. (2016) defined EMS as a mixed integer programming model and proposed a new search heuristic algorithm. By solving a series of linear programming relaxation problems, the heuristic algorithm finds a feasible solution, and can terminate quickly. Besides algorithms, some tools can also be used to find the optimal or feasible solutions, such as Lingo, Cplex, and so on. Gao and Tang (2014) established an EMS model with the objective of minimum time, and used Lingo to find the optimal vehicle routes of the Ya'an earthquake. Cao (2017) took the city of Mianzhu, which was affected seriously in the Wenchuan earthquake in 2008, as the object, and used Lingo to find the optimal solution, which could provide reliable decision-making reference for military logistics in disasters. For small-scale EMS problems, Lingo can give optimized solutions in limited period. For large problems, however, it does not work. Cplex is stronger than Lingo in practical computation, which can also solve large-scale complex problems with many restrictions and provide the upper and lower bound of the optimized solutions.

3.3.

Summary

Through the analysis and summary of the above references, we compare the algorithms as Table 2. As shown in Table 2, the current research on EMS has the following problems.

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J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx

Table 2 e Comparison of optimization algorithms for EMS. Literature Gao et al. (2014) Cao (2017) Zhao (2012) Li and Zhang (2012) Qin et al. (2010) Zhao (2012) Zhao (2012) Chen and Ma (2017) Wang et al. (2017) Ma (2017) Bian (2017) Chen (2006) Chen and Ma (2017) Ma (2011) Hamedi et al. (2012) Cao (2017) Fu and Luo (2014) Dan et al. (2012) Wang (2009) Wang (2016) Shi et al. (2010) Qin et al. (2010) Batmetan et al. (2017) Yi and Kumar (2007) Zhang et al. (2017) Tian et al. (2012) Lin and Xu (2008) Wang and Wu (2011) Yu (2014) Xu et al. (2018) Gan et al. (2013) Wu and Wang (2012) Bozorgi-Amiri et al. (2013) Andreeva-Mori et al. (2013) Li et al. (2016) Song et al. (2019) Chen and Wang (2010) Tang et al. (2008) Cao (2017) Meng (2015) Chen et al. (2013) Alem et al. (2016) Chen et al. (2019) Wu et al. (2019) Hu et al. (2015) Zhang and Xiong (2018) Lei et al. (2016)

Number of objectives

Algorithm

Solution type

1 1 2 2 2 2 1 1 1 2 2 1 2 2 1 2 1 2 2 2 1 2 1 1 2 2 2 2 2 2 1 1 1 1 2 2 1 2 2 2 2 2 1 1 2 3 1

Accurate algorithm Accurate algorithm Accurate algorithm Accurate algorithm Improved dynamic clustering algorithm GA SLP and GA Dynamic accelerated adaptive GA Partheno-GA Improved GA Improved GA GA GA Improved GA Improved GA Variable neighborhood search ant colony optimization (VNS-ACO) ACO ACO ACO NSGA-II and ACO Improved ACO Improved ACO MO-ACO ACO Improved ACO PSO Discrete PSO PSO Improved PSO Discrete binary PSO Improved PSO Chaos PSO PSO Improved PSO Improved maximum flow algorithm Improved differential evolution algorithm Lagrange decomposition Nearest search algorithm Genetic-particle swarm optimization Genetic-particle swarm optimization Modified projection algorithm Two-stage heuristic algorithm Improved GA Mixed steepest descent algorithm Artificial fish-swarm algorithm Artificial immune and ACO Heuristic algorithm

Optimal Optimal Optimal Optimal Optimal Feasible Feasible Feasible Feasible Feasible Feasible Feasible Feasible Feasible Feasible Feasible Feasible Feasible Feasible Feasible Feasible Feasible Feasible Feasible Feasible Feasible Feasible Feasible Feasible Feasible Feasible Feasible Feasible Feasible Feasible Pareto Feasible Feasible Pareto Feasible Feasible Feasible Feasible Optimal Feasible Pareto Feasible

(1) EMS can be a multi-objective and multi-constrain problem, involving complex factors and situations. For the complex multi-objective EMS models, they are usually NP-hard problems. It is difficult to obtain the optimal or optimized solutions within a specified time using existing optimization algorithms. Most of the algorithms have low fault tolerance rate, and the optimization results cannot meet the distribution requirements every time, so they are easy to fall into local optimization. (2) Most literature mainly uses GA, PSO, ACO and other common heuristic algorithms to solve the EMS model. Few literature has studied the new algorithm and its hybrid algorithm, and the efficiency of the new algorithm is not validated sufficiently.

(3) At present, while most of the test data are generated randomly by computer, only a small part of them are real data. Moreover, there are still too few cases of successful application of heuristic algorithm in rescue operations, and most of the results cannot fully meet the needs of decision makers.

4.

Conclusions

This study focuses on the optimization of EMS, and summarizes the optimization model and algorithm progress of EMS in recent years. Through the analysis of the model research, the main factors affecting EMS are identified, and the

Please cite this article as: Hu, H et al., Emergency material scheduling optimization model and algorithms: A review, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.07.001

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optimization objectives and constraints considered in EMS are sorted out. In the review of algorithm design, the application characteristics of various optimization algorithms are compared and analyzed, and several emerging heuristic and hybrid algorithms are summarized. Moreover, some tools to find the optimized solution are mentioned. At present, the research on EMS has improved the rescue accuracy and efficiency to a certain extent, but the contradiction between the complexity of the model and the searching speed of optimized solution has not been well solved. There are some possible research directions for EMS in the future. (1) For modeling of EMS, more factors should be considered, such as psychological perception of victims, characteristics of the disaster, dynamic data of road network and so on. Railway and air transportation should also be included to deliver emergency materials. (2) Exploring more accurate and efficient algorithms has always been an important task in EMS research. In recent years, lots of emerging optimization algorithms, such as biogeographic optimization algorithm, cuckoo search, paddy field algorithm, bionic algorithm, fireworks algorithm, etc., have proved the effectiveness and efficiency of solving capability. In the future, these new algorithms can be combined with existing algorithms and improved to solve the EMS model under different conditions. (3) Combine the model and algorithm with actual disasters based on big data techniques. Key information affecting EMS is obtained through big data and data mining techniques, and parameters such as demand, material satisfaction, risk and fairness can be identified more accurately. Cloud computing also makes it possible to run complex heuristic algorithms. This will be a prominent trend in EMS research in the future. Besides optimization for EMS, in the whole field of EMS, it is urgent to study the layout of emergency materials reserve depots before the occurrence of disasters and the design of real-time disaster relief platform. It is also necessary to further analyze the inventory problem after the disaster, use the OR model to solve the inventory optimization problem in the EMS under the natural disasters, and enhance the emergency reserve capacity to quickly and effectively respond to the unexpected disruptions.

Conflict of interest The authors do not have any conflict of interest with other entities or researchers.

Acknowledgments This research was supported by the China Fundamental Research Funds for the Central Universities under Grant

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300102228402 and 3100102229103, China Xi'an Social Science Planning Fund under Grant 19Z73, Shaanxi Natural Science Foundation of China under Grant 2019JLP-07 and the China Innovation and Entrepreneurship Training Program for College Students under Grant 20191071245.

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Please cite this article as: Hu, H et al., Emergency material scheduling optimization model and algorithms: A review, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.07.001

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Hui Hu received her B.S. degree in railway transportation planning from Beijing Jiaotong University (BJTU), Beijing, China, in 2000, and her PhD degree in system engineering from the System Engineering Institute of Beijing Jiaotong University in 2008. She is currently an associate professor in the School of Automobile, Chang'an Univeristy. Her current research interests include supply chain disruptions, emergency material scheduling in disasters and logistics system planning.

Please cite this article as: Hu, H et al., Emergency material scheduling optimization model and algorithms: A review, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.07.001