Multidepot Recycling Vehicle Routing Problem with Resource Sharing and Time Window Assignment

*is study aims to provide tactical and operational decisions in multidepot recycling logistics networks with consideration of resource sharing (RS) and time window assignment (TWA) strategies. *e RS strategy contributes to efficient resource allocation and utilization among recycling centers (RCs). *e TWA strategy involves assigning time windows to customers to enhance the operational efficiency of logistics networks. A biobjective mathematical model is established to minimize the total operating cost and number of vehicles for solving the multidepot recycling vehicle routing problem with RS and TWA (MRVRPRSTWA). A hybrid heuristic algorithm including 3D k-means clustering algorithm and nondominated sorting genetic algorithm(NSGA-) II (NSGA-II) is designed. *e 3D k-means clustering algorithm groups customers into clusters on the basis of their spatial and temporal distances to reduce the computational complexity in optimizing the multidepot logistics networks. In comparison with NSGA algorithm, the NSGA-II algorithm incorporates an elitist strategy, which can improve the computational speed and robustness. In this study, the performance of the NSGA-II algorithm is compared with the other two algorithms. Results show that the proposed algorithm is superior in solving MRVRPRSTWA. *e proposed model and algorithm are applied to an empirical case study in Chongqing City, China, to test their applicability in real logistics operations. Four different scenarios regarding whether the RS and TWA strategies are included or not are developed to test the efficacy of the proposed methods. *e results indicate that the RS and TWA strategies can optimize the recycling services and resource allocation and utilization and enhance the operational efficiency, thus promoting the sustainable development of the logistics industry.


Introduction
Sustainability is a constant topic in the logistics industry and research [1,2]. In reverse logistics, recycling waste products can save resources and facilitate sustainable development [3]. Recycling vehicle routing problem (RVRP), one part of reverse logistics, often appears in logistics operations. For example, empty beer bottles are recycled at convenience stores. An increasing number of enterprises have begun to consider recycling products to improve the utilization of resources due to economic, legal, and social concerns [4,5]. erefore, the growing demand for recycling services will stimulate the development of reverse logistics. e design, planning, and operation of sustainable reverse logistics systems pose a challenge to logistics organizations [6]. e low transportation resource utilization and irrational transport operations of logistics facilities still appear and need to be addressed [7,8]. Resource sharing (RS) strategies have been proposed to optimize resource utilization and reduce operating cost in multidepot logistics networks [9]. Customers are reassigned to appropriate logistics facilities through these strategies to avoid unreasonable routing via customer information sharing [10]. Transportation resources are shared within and between logistics facilities to improve transportation resource utilization. Specifically, vehicles can be used to serve customers of a single logistics facility or customers of multiple logistics facilities many times when the time windows of customers allow [11]. In this study, the RS strategy is developed in the multidepot RVRP with time window (MRVRPTW) to optimize the resource utilization.
In traditional vehicle routing problems with time window (VRPTW), the service time windows for customers are obtained by the logistics service providers after negotiation with customers or are determined by customers [12,13]. Logistics service providers often recycle cargoes from customers at the same time every day [14]. In real life, the time windows for most customers are viewed as soft time windows, that is, they can be violated by paying certain penalties [15,16]. Most logistics service providers try to recycle cargoes within the predetermined time windows in logistics operations to reduce the penalty cost [17]. However, the vehicles cannot provide recycling services for customers in the expected time windows due to long transportation distance and unreasonable service time windows for logistics facilities [18,19]. erefore, a set of candidate time windows are assigned to customers in this study, and recycling vehicle routes are designed on the basis of time window assignment (TWA) to optimize the operational efficiency and minimize the operating cost in multidepot RVRP with RS and TWA (MRVRPRSTWA).
In this study, the RS and TWA strategies are adopted to improve resource utilization, optimize resource allocation, and enhance the operational efficiency of multidepot recycling logistics networks. A bi-objective mathematical model is presented to obtain the minimum operating cost and the number of vehicles (TNV) in a multidepot logistics network with RS and TWA. A hybrid heuristic algorithm, including a 3D k-means clustering algorithm and nondominated sorting genetic algorithm-(NSGA-) II (NSGA-II), is devised to optimize the recycling routes. e 3D kmeans clustering algorithm groups customers on the basis of their spatial and temporal distances to reduce the computational complexity. NSGA-II is used to assign time windows to customers and find the optimal solutions in the MRVRPRSTWA strategy. A real-world case study is performed to verify the applicability of MRVRPRSTWA in logistics operations. e results confirm the capability of the RS and TWA strategies in optimizing multidepot logistics networks. e rest of this paper is organized as follows. In Section 2, relevant literature is reviewed. In Section 3, MRVRPRSTWA is described in detail. In Section 4, a multiobjective mathematical model is formulated to minimize the total operating cost and TNV. In Section 5, a hybrid heuristic algorithm is introduced to solve MRVRPRSTWA. In Section 6, a real-world case is presented to verify the applicability of the proposed method. In Section 7, the conclusions are drawn, and future research directions are proposed.

Literature Review
With the increasing attention on environmental protection, recycling and related problems have received great concern. e RVRP with time window (RVRPTW) as the main form of reverse logistics has been widely studied to reduce the operating cost in recent years [20]. e multidepot RVRPTW (MRVRPTW) is developed to coordinate the recycling services among logistics facilities [21], and the RS strategy can be considered to optimize the resource utilization in MRVRPTW (MRVRPRSTW) [22]. Candidate time windows are assigned to customers via the TWA strategy to improve operational efficiency compared with the traditional time window in MRVRPRSTW [23]. MRVRPRSTW with TWA (MRVRPRSTWA) investigates the RS and TWA strategies to optimize the resource allocation and operational efficiency in multidepot logistics networks.
Increasing interest in recycled products and materials has led to a growing concern in recycling logistics [24,25]. El korchi and Millet [26] investigated a framework, which used to generate and assess the reverse logistics channel structure, and proposed an environment-friendly structure with high economic benefits to optimize recycling services. Chan et al. [27] proposed a framework of reverse logistics on the basis of the value of reversed products, cost issue, and legislation perspective to optimize reverse logistics. Bai and Sarkis [28] introduced a flexible framework for reverse logistics and a performance measurement of third-party reverse logistics service provider model on the basis of a novel neighborhood rough set method to set the foundation for future research of reverse logistics. Roghanian and Pazhoheshfar [29] presented a probabilistic mixed liner programming model and genetic algorithm to minimize the total cost in reverse logistics. Shaik and Abdul-Kader [30] proposed a multi-criteria performance measurement model considering product lifecycle stages, strategies, capabilities, processes, perspectives, and measures to verify and enhance the enterprise's performance in reverse logistics. e RS strategy, as a major issue, has drawn increasing attention on the enhanced resource utilization and reduced operating cost [31][32][33]. An et al. [34] constructed a network DEA model to calculate the cost of logistics network before and after RS and show the performance of the RS strategy. Sun et al. [35] analyzed and evaluated the effect of the RS strategy on alleviating or solving the traffic and environmental problems in megacities from five perspectives of resource, environment, convenience, economy, and governance. Quintero-Araujo et al. [36] investigated different collaborative scenarios on the basis of the RS strategy to obtain a lower logistics cost. e RS strategy is developed to minimize TNV and the total operating cost for improving the efficiency and sustainability of logistics networks [37]. Molina et al. [38] established a mathematical model that aims at maximizing the number of served customers and minimizing the total cost in the case of RS. Wang et al. [39] studied the RS strategy in multiple service periods and multidepot to enhance resource efficiency and refine the resource configuration.
Clustering algorithms are always used to group customers before determining vehicle routes in MDVRPTW to simplify the complexity of calculation [40,41]. Min et al. [42] proposed the maximum-minimum distance clustering method to cluster customers in split-delivery VRP for the better performance of the algorithm. Ge et al. [43] added the service radius and load expansion factors to the clustering algorithm to avoid the vehicle overloading in MDVRPTW. Fan et al. [44] introduced a clustering algorithm based on the temporal-spatial distance to reduce the computational complexity and enhance the quality of initial solution in MDVRPTW. Liu et al. [45] investigated the clustering algorithm that groups customers in terms of the minimum distance and maximum demand to improve the efficiency of solving MDVRPTW.
Several algorithms are studied to improve the quality of solution in MRVRPTW [46][47][48]. Aras et al. [21] established two mixed-integer linear programming models and proposed a Tabu-search-based heuristic algorithm to solve MRVRPTW. Kim et al. [49] developed a two-stage solution procedure to minimize the total distance and cost in MRVRPTW. Liu and He [50] proposed a clustering-based multiple ant colony system algorithm to minimize the total cost for enhancing the route compactness in MRVRPTW. Ramos and Oliveira [51] developed a mathematical model to minimize the variable costs and attain equity, and designed a heuristic algorithm to address MRVRPTW. Liao [4] established the genetic mixed-integer nonlinear programming model to maximize total profit and designed a hybrid genetic algorithm to solve MRVRPTW. Govindan et al. [52] proposed a mathematical model and a fuzzy solution method to minimize the total cost in MRVRPTW.
TWA vehicle routing problem (TWAVRP) differs from the traditional VRPTW, where the service time windows are determined by customers. In TWAVRP, candidate time windows are assigned to customers to improve the operational efficiency of logistics networks [53,54]. Subramanyam et al. [55] introduced a scenario decomposition algorithm to solve TWAVRP for minimizing the expected routing cost of logistics facility. Neves-Moreira et al. [56] presented a twostage stochastic optimization problem of TWAVRP and addressed it by using a fix-and-optimize-based metaheuristic. Jalilvand et al. [57] developed a stochastic model and a progressive hedging algorithm to minimize the routing cost. e results show that the efficiency of the proposed method has good performance in addressing TWAVRP. A mathematics model is proposed to enhance the operational efficiency and reduce the total cost, and a hybrid heuristic algorithm is used for TWAVRP [58]. e aforementioned literature covers many aspects of MRVRPRSTWA but has the following limitations: (1) e RS strategy is rarely considered between and within logistics facilities. (2) e TWA strategy is insufficiently discussed in multidepot logistics network optimization. e contributions of this paper are as follows: (1) e RS strategy is incorporated in the MRVRPRSTWA to maximize resource utilization. (2) e TWA strategy is developed in the MRVRPRSTWA to improve the operational efficiency.
(3) A bi-objective integer programming model is proposed to minimize the total operating cost and TNV in multidepot logistics networks with shared resources. (4) A hybrid heuristic algorithm, including 3D k-means clustering and NSGA-II, is developed to solve MRVRPRSTWA.

Problem Statement
e RS and TWA strategies are proposed in MRVRPRSTWA to optimize the recycling service of the multidepot logistics network. e multidepot logistics network is composed of multiple RCs and customers. Longdistance and crisscross trips often exist in the initial nonoptimal logistics network ( Figure 1). e transportation resources are shared among logistics facilities, and customers with irrational time windows are reassigned new time windows to adjust optimized recycling routes through the TWA strategy. e comparison of the multidepot logistics network before and after optimization is shown in Figures 1 and 2.
In Figure 1, each RC operates independently in the nonoptimal logistics network. Several customers are served by the farther RC rather than the closer one. For example, customer 21 is closer to RC3, while it is served by RC1, resulting in long-distance and crisscross transportation. In addition, RCs can only provide on-time service for twothirds of customers, and the time windows for the remaining third of customers cannot be met. Relevant measures must be taken to enhance the operational efficiency and optimize the configuration of logistics networks. In Figure 2, centralized transportation is performed among RCs by a fleet of semitrailer trucks and is used to merge and transship goods between RCs, considering changes in customer demand assignment. Resources are shared among RCs, and customers are reassigned to the corresponding RC based on geographical locations and time windows. Irrational transportation phenomenon is reduced, and vehicles are shared among RCs. For example, due to the difference of service time between different routes, V2 is shared between RC1 and RC2, which first serve the customers of RC2 and then the customers of RC1, and thus the vehicle utilization rate is improved and the logistics operating cost is reduced. e violations of time windows are decreased when the TWA strategy is adopted. e RS and TWA strategies call for improving the utilization of transportation resources and operational efficiency and optimizing multidepot logistics networks.
is study assumes that the centralized transportation cost (TC) among logistics facilities is $22 per unit time, and the recycling cost from logistics facilities to customers is $20 per unit time. e penalty cost for earliness and delay service is $20 per unit time. e assignment cost (AC) from the initial time window to assigned time (AT) window is $5 per unit time. e maintenance cost (MC) of each semitrailer truck is $300, and that of each vehicle is $200. e AT, TNV, the number of semitrailer trucks (TNS), and the total cost are compared and listed in Table 1.
In Table 1, the total cost of reverse logistics network is decreased from $4640 to $4170. In addition, TNV is reduced from nine to five when sharing resources among logistics facilities. When the TWA strategy was applied, the penalty cost decreases by 63%. e RS and TWA strategies can improve the resource utilization and operational efficiency and optimize multidepot logistics networks.

Related Definitions and Variables.
In this section, the related notations and definitions on sets, parameters, and variables are shown in Table 2.

Mathematical Model.
A bi-objective optimization model for MRVRPRSTWA is formulated to minimize the total operating cost in equation (1) and minimize TNV in equation (2).
TC 1 contains three components in equation (3): m∈P n∈P s∈S (U s × D mn × W × y mns ) represents the centralized TCs by semitrailer trucks among logistics facilities. max m∈P n∈P (tq mn /Q s ) × (M s /B) is the MC of semitrailer trucks. m∈P FC m represents the fixed cost of logistics facilities.
TC 2 contains two components in equation (4): TC 3 contains five components in equation (5): represent the penalty cost caused by vehicles that provide earlier service than time windows of customers.     Journal of Advanced Transportation penalty cost caused by vehicles that provide delayed service than time windows of customers.       If vehicle v travels from logistics facility or customer i to j, then If vehicle v departs from logistics facility m to served customer i, ω ivm � 1; otherwise, ω ivm � 0, i ∈ C, v ∈ V, and m ∈ P y mns If semitrailer truck s transports between logistics facility m and n, y mnk � 1; otherwise, y mns � 0, m, n ∈ P, and s ∈ S τ imn If customer i's logistic facility changes from logistics facility m to n after optimization, τ imn � 1; otherwise, τ imn � 0, i ∈ C, and m, n ∈ P g ms If semitrailer truck s departs from logistics facility m, g ms � 1; otherwise, g ms � 0, s ∈ S, and m ∈ P 6 Journal of Advanced Transportation Subject to m∈P y mns � 1, ∀n ∈ P, s ∈ S, m ≠ n, m∈P y nms � 1, ∀n ∈ P, s ∈ S, m ≠ n, m∈P n∈P i∈C j∈C i∈C j∈C j∈C v∈V Journal of Advanced Transportation Constraint (6) ensures that each semitrailer truck originally departs from logistics facilities. Constraint (7) is the flow conservation on each logistics facility. Constraint (8) ensures that each semitrailer truck finally returns to logistics facilities. Constraint (9) is used to avoid subtours for semitrailer trucks. Constraint (10) calculates the transportation quantity among logistics facilities. Constraint (11) stipulates that each semitrailer truck has enough capacity to satisfy the transportation quantity of the assigned logistics facilities. Constraint (12) ensures that each vehicle departs from logistics facilities only. Constraint (13) ensures that each customer can be served once by one vehicle. Constraint (14) is the flow conservation on each customer. Constraint (15) ensures that each vehicle finally returns to logistics facilities. Constraint (16) is used to avoid subtours for vehicles. Constraint (17) represents that each vehicle has enough capacity to satisfy the total demand of assigned customers. Constraint (18) ensures that the total demand of customers served by a logistics facility should be beyond its capacity. Constraints (19) and (20) guarantee the continuous departure time of vehicles at logistics facilities. Constraints (21) and (22) guarantee the continuous arrival time of vehicles at customers. Constraints (23) and (24)
is algorithm, including the 3D k-means clustering and NSGA-II algorithms, is proposed to solve the MRVRPRSTWA. e 3D k-means clustering algorithm is often utilized to construct clusters according to the spatial and temporal distances of data [53]. e 3D k-means clustering algorithm can effectively reduce the computational complexity of multidepot logistics networks [37]. e NSGA-II can assign appropriate time windows to customers and obtain Pareto optimal solutions in MRVRPRSTWA. e elitist strategy in NSGA-II can effectively avoid the loss of the best individual and enhance the computational speed and robustness. e elitist strategy is composed of the genetic operations (i.e., selection, crossover, and mutation) and the fast nondominated sorting and crowding distance. e parameters utilized in the flow structure are defined as follows: i is the number of RCs and clustering centers, R is set as the present number of optimization runs, Rmax represents the maximum number of optimization runs, N is set as the present number of generations, and Nmax is set as the maximum number of generations. e flow structure of the hybrid heuristic algorithm is shown in Figure 3. e optimization procedure of MRVRPRSTWA is as follows: Step 1: 3D k-means clustering. Set the number of RCs as the number of clusters and the data from RCs as the initial data of each cluster. Calculate the spatial and temporal distances between cluster centers and customers. Assign each customer to the nearest cluster center.
Step 2: the NSGA-II algorithm is used to establish pickup vehicle routes. e initial parameters are set and the initial population is randomly generated.
Step 3: genetic operation, including selection, partialmapped crossover (PMC), and mutation is performed to generate offspring population. e parent and offspring population are combined.
Step 4: the new population is selected by performing nondominated sorting and calculating the crowding distance of each individual.
Step 5: determine whether the internal termination is satisfied. If the termination condition is unsatisfied, then select customers that accepted the TWA strategy and have time window violations, and assign the appropriate time windows to them; otherwise, return to Step 3.
Step 6: calculate the total cost and TNV with the adoption of the TWA strategy by NSGA-II and determine whether the termination condition is satisfied. If the termination condition is unsatisfied, then return to Step 1 to confirm whether the clustering results need to be adjusted; otherwise, terminate the algorithm procedure and find the optimal solution. e clustering algorithm is always utilized to construct clusters to each depot in multidepot VRP to reduce computational complexity [62,63]. e traditional k-means clustering algorithm groups customers on the basis of the spatial distances between customers and clustering centers [64,65]. e 3D k-means clustering algorithm, a variant of the traditional k-means clustering algorithm, constructs clusters according to the spatial and temporal distances among clustering centers and customers. In this study, the 3D k-means clustering algorithm is applied to optimize MRVRPRSTWA. e spatial and temporal distances based on geographic coordinates and time windows of customers and logistics facilities can be calculated by In equation (32), β 1 and β 2 represent the proportion of spatial and temporal distances, respectively. In equation (33), (x m , y m , z m ) expresses the geographic location and center point of time windows of logistics facility. (x p , y p , z p )  Journal of Advanced Transportation expresses the geographic location and center point of time windows of customer. e 3D k-means clustering algorithm procedure is shown in Algorithm 1. In Algorithm 1, the process of clustering can be divided into several components: First, the geographic locations and center point of the time windows of RCs and customers are used to construct the initial 3D data elements. Second, set i on the basis of the number of RCs as the number of clusters and the data from RCs as the initial clustering center of each cluster.
ird, traverse data elements and calculate the spatial and temporal distances from each element to every clustering center. Fourth, assign each element to the nearest clustering center, and elements assigned to the same clustering center are placed in one cluster. Fifth, update i clusters, and continue to execute this procedure till no existing customers need to be adjusted among clusters; then, i clusters, including RCs and their served customers, are reported.
e clustering results provide the initial population for multidepot vehicle routing optimization.

NSGA-II.
Heuristic algorithms have obvious performances in solving multidepot logistics networks [66]. e NSGA-II is an enhanced algorithm based on the NSGA to solve multiobjective evolutionary problems [67,68]. NSGA-II ranks different individuals via nondominated sorting algorithm and crowding distance comparison operators to force individuals to converge toward and diffuse along the Pareto front. e main procedures of NSGA-II are summarized below.

Selection.
e selection operation involves choosing certain individuals every time from the parent population with selection probability sp, and the best individual will be inserted into the offspring population. e selection operation will continue until the offspring population size reaches a predetermined size. e specific steps can be described as follows: First, individuals are chosen from the parent population with selection probability sp at random. en, the individual with the best fitness values is selected and added into the offspring population. e abovementioned procedures are repeated until the offspring population reaches a predetermined size.

PMC.
PMC is used as the operator of the crossover operation [69]. e specific procedure of PMC is shown in Figure 4, and the main steps of PMC are as follows: First, randomly select the beginning and ending positions of a gene sequence of a pair of chromosomes. Second, the two sets of genes selected on the two chromosomes are exchanged separately. ird, conduct conflict detection and establish a mapping relationship on the exchanged genes. Fourth, repeat this step until no duplicate genes are present on the same chromosome. e mapping relationship is illustrated in Figure 4. For example, a mapping relationship of 3-1and 5-6 genes is presented. Two genes 3 in offspring1 are selected in the second step, and the unselected gene is transformed into 1.
Two genes 5 in offspring 1 are selected in the third step, and the unselected gene is transformed into 6. Finally, two children with no conflict genes are generated.

Mutation.
Mutation operation aims to change the values of a gene at a certain locus of chromosome to generate a new chromosome [70]. Polynomial mutation is used in this work to prevent local convergence in the course of evolution. e main steps of polynomial mutation are shown in Figure 5.
In Figure 5, a chromosome is randomly selected from the parent generation in terms of the mutation probability pc.
en, three genes on the parental chromosome are randomly selected, and the exchange and regenerated operation are conducted on the three genes. If duplicate genes appear, then they should be removed and regenerated.

Nondominated Sorting and Crowding Distance
Assignment. Several definitions are provided to describe the procedures of nondominated sorting and crowding distance. , then we can say m is preferred to m''. e next generation is selected through the abovementioned method, which is nondominated sorting and crowding distance [71].

TWA Strategy.
e TWA strategy is designed in the NSGA-II algorithm to assign candidate time windows to customers with improved operational efficiency. e main procedures are presented as follows: Step 1: customers that accepted the TWA strategy with violation of time windows are selected.
Step 2: assume that the time window for customer A is [E A , L A ], and the actual service time of customer A is i hours earlier (or delayed) than E A . If E A -i (or L A + i) is between the candidate time window [E' A, L' A], then calculate the TWA cost, and compare it with the penalty cost.
Step 3: if the TWA cost is lower than the penalty cost, then [E' A, L' A] will assign to customer A; otherwise, keep the initial time window of customer A. erefore, the appropriate time windows are assigned to the corresponding customers. e process of NSGA-II is described in Algorithm 2.

Implementation and Analysis
6.1. Algorithm Comparison. In this section, benchmark instances are performed to test the quality of NSGA-II in MRVRPRSTWA for comparing its results with those received by multiobjective evolutionary algorithm (MOEA) [72] and multiobjective particle swarm optimization    Table 3. Table 3 presents the relevant characteristics of 20 benchmarks. e parameters for NSGA-II and MOEA are as follows: population size pop size � 150, selection probability sp � 0.6, crossover probability cp � 0.9, and mutation probability mp � 0.1. e parameters for MOPSO are as follows: maximum iteration number max_it � 200, inertia weight ω � 0.9, personal confidences pc � 2, and social learning confidences gc � 3. e results of the three algorithms, which contain total cost (cost), TNV (vehicle), and computation time (Ct), are compared in Table 4. Table 4 exhibits an adequate difference among the optimal results of those three algorithms on the basis of the values of t-test and p-value.
e NSGA-II algorithm is superior to MOEA and MOPSO in obtaining the optimal cost in MRVRPRSTWA. e costs of MOEA and MOPSO are higher than that of NSGA-II in 20 benchmark instances. For instance, the average cost of NSGA-II is $15479. However, the costs of MOEA and MOPSO are $20019 and $17520, respectively. e minimum number of vehicles calculated by NSGA-II is nine compared to TNV of MOEA and MOPSO. e NSGA-II outperforms MOEA and MOPSO in terms of the minimum computation time. e average computation time of NSGA-II is 237s, which is lower than the computation times of MOEA and MOPSO. erefore, the NSGA-II algorithm can achieve better performance in solving MRVRPRSTWA compared to MOEA and MOPSO.

Data Source.
A real reverse logistics network in Chongqing, China, is used to verify the applicability and feasibility of the proposed solution in MRVRPRSTWA. e logistics network has five RCs (i.e., RC1, RC2, RC3, RC4, and RC5) and 183 customers. e spatial distribution of logistics network is shown in Figure 6. e RCs and customers are marked as stars and rhombuses, respectively. Rhombuses in various colors represent customers served by different RCs. e initial vehicle routes are shown in Table 5.
In Table 5, customers are served by 21 vehicle routes among five RCs. Each RC is operated independently, which results in the waste of resources. For example, three customers (i.e., P180, P177, and P171) belonging to RC1 and two customers (i.e., P75 and P65) belonging to RC5 are served by a vehicle, respectively. e irrational vehicle routes should be decreased to enhance the operational efficiency of the multidepot logistics network.

Relevant Parameter Setting.
e objective of MRVRPRSTWA is to obtain the lowest operating cost and TNV in the multidepot reverse logistics network. e related parameters used in the optimization model and the hybrid heuristic algorithm initialization are shown in Table 6. e time window of RC1 is [6,18]. RC2 and RC3 have the same Nondominated Sorting Algorithm-II (NSGA-II) Input: pop size , nodes, R, Rmax, Nmax, sp, cp, and mp Output: Pareto front optimal solutions (1) Initialize parameters (2) # set the population size (pop size ), number of customers (nodes), number of generation (R), maximum number of generations (Rmax), maximum number of runs (Nmax), selection probability (sp), crossover probability (cp), and mutation probability (mp) (3) For N � 1:Nmax (4) For R � 1:Rmax (5) Generate the initial population with size pop size (6) Objective function evaluation (7) # compute the objective function to minimize the total operating cost and TNV (8) Divide pop size into nondominance front and calculate the crowding distance of each individual (9) For i � 1: R (10) Implement selection, PMC, and mutation operations to generate offspring population (11) Combine parent and offspring population, perform nondominated sorting and calculate the crowding distance of each individual (12) Build the new population on the basis of the parent and offspring populations following partial order (13) end (14) end (15) For n � 1: nodes (16) Select the customers that accept time window and have time window violation (17) Select the appropriate time window from candidate time windows to assign to customer (18) Calculate the TWA cost and compare it with the penalty cost (19) Assign the time window to the customer or keep the expected time window of customer (20) end (21) Find the Pareto front optimal solution (22) end ALGORITHM 2: NSGA-II algorithm operation. time window [8,20]. e time window of RC4 and RC5 is the same as [10,22]. e candidate time windows are constructed on the basis of the real situation of customers that accepted TWA. Hence, four candidate time windows are constructed: [8,10], [10,11], [12,15], and [16,18].

Optimization Results.
Customers are clustered on the basis of the 3D k-means clustering algorithm to reduce the computational complexity in the multidepot reverse logistics network. Customers are reassigned to the RC with the nearest spatial and temporal distances. e results of the 3D k-means clustering algorithm are shown in Table 7 and Figure 7. Table 7 illustrates that 183 customers are reassigned to the corresponding logistics facilities and grouped into five clusters. RC1 is allocated 28 customers, RC2 is allocated 28 customers, RC3 is allocated 42 customers, and RC4 and RC5 are allocated 42 and 43 customers, respectively. e spatial and temporal distances of the customers are shown in   Figure 7, wherein x represents the longitude of coordinate, y indicates the latitude of coordinate, and z denotes the mid value of the time window. e optimized vehicle routes with the RS and TWA strategies are shown in Table 8. Table 8 exhibits that seven vehicles are shared on different routes to serve customers in the multidepot reverse logistics network. For example, vehicle 1 is shared in three routes. One route (e.g., Vehicle sharing can improve the resource utilization and operational efficiency of logistics facilities and promote sustainable development among logistics networks. e comparison of results before and after optimization is shown in Table 9 and Figure 8.  In Table 9 and Figure 8, the total cost is reduced from $38025 to $21373 in the initial and optimized reverse logistics network on the basis of the RS and TWA strategies in the MRVRPRSTWA. In addition, the TC is decreased from $4675 to $1307. e sum of the penalty cost and AC after optimization is lower than that before optimization through the TWA strategy. e total number of vehicles is decreased to seven when the vehicles are shared among five RCs.
6.5. Analysis and Discussion. Four cases are considered to verify the applicability of the proposed method in MRVRPRSTWA. In Case 1, each logistics facility operates independently. In Case 2, the RS strategy is considered among logistics facilities. In Case 3, the TWA strategy is adopted among logistics facilities. In Case 4, the RS and TWA strategies are adopted among logistics facilities. e calculation results of the four scenarios are shown in Table 10 and Figure 9.
In Table 10 and Figure 9, the total cost, violated time, and TNV are significantly reduced in the optimized logistics network with the RS and TWA strategies. TNV in Case 2 is lower than that in Case 1, which shares vehicles among reverse logistics facilities. e violated time is significantly reduced when the TWA strategy is adopted among logistics facilities in Case 3 compared to that of Case 1. e total cost, violated time, and TNV of Case 4 have the minimum value of $21373, 87 min, and 7, respectively. e total cost, violated time, and TNV are compared in Figure 9. erefore, the proposed method in MRVRPRSTWA can effectively reallocate resources and improve the operational efficiency.

Implications.
e RS and TWA strategies are considered to optimize recycling service in the multidepot reverse logistics network. e implications obtained from this work are described as follows:        (1) e RS strategy contributes to the resource utilization of reverse logistics network and promotes the sustainable development of the intelligent logistics system. Vehicles often serve customers on one route in a working period, thereby resulting in low vehicle utilization. Vehicles serve customers on several routes in a working period based on satisfying customer service time window with the adoption of the RS strategy. is strategy shares the resources within and between logistics facilities to obtain the maximum resource utilization in MRVRPRSTWA. (2) e TWA strategy can enhance the operational efficiency of logistics networks. e candidate time windows of customers with high penalty costs on account of the violation of time windows are assigned to corresponding customers through the TWA strategy to achieve the maximum operational efficiency in MRVRPRSTWA. e TWA strategy is of great theoretical and practical significance to the sustainable development of reverse logistics networks.
(3) e RS and TWA strategies in reverse logistics network can reduce the negative impact of logistics enterprises on the environment, optimize resource allocation, maximize benefits, promote the development of green logistics, and provide related development decisions for logistics enterprises and government departments. e established mathematical model and the hybrid heuristic algorithm can also provide a reliable reference for the applicability and effectiveness of the RS and TWA strategies in addressing MRVRPRSTWA.

Conclusions
is work studies the RS and TWA strategies in multidepot recycling logistics networks. e RS strategy can effectively improve resource utilization and optimize resource configuration in logistics networks. A bi-objective optimization model is proposed for MRVRPRSTWA with the minimum operating cost and TNV. A hybrid heuristic algorithm, which includes 3D k-means clustering algorithm and NSGA-II algorithm, is also designed to address MRVRPRSTWA. e 3D k-means clustering algorithm is used to cluster customers in the first step of the hybrid heuristic algorithm for reducing the computational complexity of multidepot vehicle routing problem. Next, the NSGA-II algorithm is used to find the optimal vehicle routes and assign candidate time windows to customers.
A real-world case study in Chongqing City, China, is analyzed to verify the performance of the proposed mathematical model and the hybrid heuristic algorithm in MRVRPRSTWA.
e computational results demonstrate that the total operating cost and TNV can be decreased through the proposed method. e total operating cost is reduced from $38025 to $21373, and TNV is minimized from 21 to 7. e comparison of the performance of three algorithms shows that the NSGA-II has a better performance in solving MRVRPRSTWA than MOEA and MOPSO. Four different scenarios with and without RS and TWA strategies are presented to demonstrate the applicability of the proposed method. e results of four scenarios indicate that the operational efficiency of the logistics network can be improved via the RS and TWA strategies.
In this study, the RS and TWA strategies are encouraged to promote the sustainable development of multidepot logistics network. On the one hand, the RS strategy among logistics facilities can optimize the resource configuration and enhance the resource utilization. On the other hand, the TWA strategy can improve the operational efficiency of logistics network by assigning candidate time windows to customers. Although only the RS and TWA strategies can improve the operational efficiency of logistics network to a certain extent, the greatest benefits can be obtained by simultaneously adopting both, which is demonstrated in section 6.5. e RS and TWA strategies can be used as references when policy-makers make decisions for logistics development.
Many research questions can be studied in the future on the basis of this work. (1) Delivery activity can be considered on the basis of the MRVRPRSTWA to construct pickup and delivery logistics network. (2) e proposed algorithm can be combined with exact algorithms to enhance the accuracy and efficiency of computation. (3) Collaboration among logistics facilities and profit allocation mechanism can be investigated on the MRVRPRSTWA. (4) e environmental impact in the MRVRPRSTWA can be explored in the future.
Data Availability e vehicle routing data used to support the findings of this study are included within the article.

Conflicts of Interest
e authors declare no conflicts of interest.