June 22, 2015
Ruizhi Huang S2627205
e-mail: R.Huang@student.rug.nl
Supervisor: Dr. S. Fazi
Co-assessor: Prof. dr. I.F.A. Vis
University of Groningen
Faculty of Economics and Business
Hybrid Dynamic Model for Inland
Empty Container Repositioning with
Multi-commodity Situation
Abstract
The transportation by containers receives a boom due to its scale and economic efficiency. Yet in the whole transportation activities around containers, inland empty container repositioning is still a problem. Because the transportation cost from empty container repositioning cannot be avoided and remains comparably high, the problem draws concerns from many scholars in this field. This paper focuses on inland empty container repositioning problem, studies how to reduce the transportation cost of empty containers and fulfil the service level at the meantime. Previous studies for this problem are limited to single-commodity situation, and few of them take time issues into consideration. Therefore, in this paper, we propose a dynamic transportation model based on previous researches, dealing with multi-commodity empty container repositioning problem. The proposed model will contribute not only to the theory but also to the practice, as in the model realistic time issues are taken into account.
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1. Introduction
Due to the needs for lower cost and higher efficiency, transportations by containers grow rapidly and most of them are done by sea (Zhang and Wirth, 2012). As the result of this rapid growth, the management of containers turns to be important. Dejax and Crainic (1987) pointed out that the management problems around containers include fleet sizes, ownership of containers and empty container repositioning etc.
Empty container repositioning refers to the allocation of empty containers before shipping or after unloading (Dang et al., 2012), which basically is a non value-added process beyond transportation but cannot be avoided (Braekers et al., 2011). For the sake of cost reduction in empty container repositioning and other improvements (e.g. empties balancing, urban congestion reduction), more and more studies turned to focus on this problem rather than loaded container transportation (e.g. Jula et al., 2003; Braekers et al., 2011). And empty container repositioning activities are divided into two categories based where they happen: marine empty container repositioning and inland empty container repositioning (Le, 2003).
Marine empty container repositioning refers to the usage of surplus vessel capacity for empty container repositioning between sea terminals (Dang et al., 2012). And the needs for this mainly come from the imbalance between imports and exports volume (e.g. the U.S. and China). As indicated by Lopez (2003), most of the studies focused on marine empty container repositioning and a certain level of successful improvement was already achieved. Inland empty container repositioning is the empty container allocation problem in hinterland and is mostly done by trucks. Compared to marine empty container repositioning problem, the inland problem draws far less attention according to Dejax and Crainic (1987). In their following paper, Crainic et al. (1993) provided dynamic and stochastic models for both single- and multi-commodity situations. Yet no optimization solution was provided in their study.
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repositioning. The authors proposed a two-stage stochastic model which was also used by many other literature later (e.g. Choong et al., 2002; Jula et al., 2006). Based on the work of Cheung and Chen (1998), Choong et al. (2002) used an intermodal operation for inland empty container repositioning, addressing the length of the planning horizon as a critical issue because there may be no feasible solution in a certain time period. In Choong et al. (2002), time windows of different parties were considered. However in both Cheung and Chen (1998) and Choong et al. (2002), empty containers were handled separately from loaded containers, which did not reduce the transportation costs very effectively.
Erera et al. (2005) was one of the only few studies which focused on handling empty containers jointly with loaded containers. In the intermodal model of Erera et al. (2005), empty and loaded containers may share the same barges and their load factor was considered.
Jula et al. (2003) and Boile et al. (2008) were the only literature which proposed specific approaches for inland empty container repositioning, which made them the benchmark in this area. In their studies, approaches named street-turn and depot-direct were proposed and considered to be applied in reality. However, neither of them took multi-commodity situation and empty container exchange into account, which is apparently different from practice i.e. different container sizes and the needs for container cleaning and maintenance.
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order to reduce its costs? And the research question can be separated into three sub questions: 1. What existing problems and models related to inland empty container repositioning have been studied in literature? 2. Is it possible to develop a hybrid model handling empty container repositioning based on literature and what elements are included in this model? 3. If so, how is the new model working compared to existing situation?
The paper will be organized as follows: In Section 2, description and analysis are given out to clarify the problem of inland empty container repositioning. In Section 3, the extant inland empty container repositioning problems and models in literature are reviewed. In Section 4, a mathematical model will be developed based on existing approaches dealing with inland empty container repositioning. In Section 5, the results driven from Section 4 will be analyzed. In this section, comparisons between model application and practice will be done. Section 6 will be conclusion.
2. Problem Description
As mentioned in Section 1, inland empty container repositioning draws more and more attention, not only because of its unavoidable high costs, but also because of related environmental problems such as traffic congestion and air pollution. A variety of aspects (e.g. inland empty container transportation routing, network design, inventory of empty containers) are being focused on regarding to this problem, and different solutions are given out as well in different studies. Yet the problem definitions in most of these studies are similar, and they can be concluded and described as follows.
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Jula et al. (2003) argued that the back-and-forth transportation not only is cost wasted, but also increases the traffic volume and leads to congestion. Both Jula et al. (2003) and Boile et al. (2008) used figures to explain the existing practice and gave out different solutions.
Figure 1. Street-turn model (Jula et al., 2003)
Figure 2. Depot-direct model (Boile et al., 2008)
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containers once are released from the consignees, they will be transported to the shippers instead of being taken back to the sea terminal. Additionally, when empty containers are loaded with cargos at the shippers, they will be transported to the sea terminal for e.g. exports. In this way, the transportation activities around consignees and shippers are merged together, and there is no need for empty containers to be carried back and forth between sea terminal and hinterland.
Boile et al. (2008) provided a different solution called depot-direct (shown in Figure 2. Case B). In this solution, instead of sea terminal, inland depots play a role as the hub in the transportation network of empty containers. As inland depots are far more closely to the consignees/shippers, empty container transportation can be done by covering shorter distance, which saves costs. Solutions of street-turn and depot-direct are the fundamental approaches dealing with inland empty container transportation, later studies e.g. Jula et al. (2006) concluded the discovery of these two studies. Yet, there are still obstacles and disadvantages to implement either of these two
approaches. Therefore this paper will try to propose a hybrid model based on these two to reduce the transportation costs of inland empty container repositioning while fulfilling the service level. The advantages and disadvantages of street-turn and depot-direct are discussed in next section. The hybrid model building will be discussed in Section 4.
3. Literature Review
This section mainly focuses on the existing inland empty container planning problems and models. In this section, only planning models which consider inland empty container repositioning are reviewed. The goal of this section is to summarize the discoveries of previous papers and provide the needs and fundamental framework for a new model building.
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strategic planning level, the long-term empty container transportation network design i.e. choosing location and size of depots, fleet resource acquiring, defining customers etc. is discussed (Crainic and Laporte, 1997; Lam et al., 2007). In tactical planning level, service contents and fleet resource allocation of empty container transportation are discussed (Crainic and Laporte, 1997; Shintani et al., 2007).
Inland empty container repositioning, also called regional container allocation, belongs to the operational level (Braekers et al., 2011). As mentioned in Section 2, inland empty container repositioning mainly focuses on the container allocation and vehicle routing problem between multiple nodes (depots, consignees, shippers). Several factors can be taken into account in this level including problem type (container allocation or transportation routing), commodity type (single- or multi-commodity), input type (deterministic or stochastic), model type (static or dynamic), taking other elements into account or not (e.g. container substitution and planning horizon). An overview of a list of literature is shown in Table 1.
The later section of this paper will focus on the problem of container transportation routing, providing a deterministic and dynamic mathematical model, taking planning horizon but not container substitution into account, while considering
multi-commodity situation.
Table 1. Overview of literature
Author(s) Problem Type Commodity Type Input Type Model Type Other Elements Dejax and Crainic (1987) Container Allocation
Multi-commodity Stochastic Static No
Crainic et al. (1993) Container Allocation Single- and Multi-commodity Stochastic Dynamic Container Substitution
7 Chen (1998) Allocation Choong (2002) Container Allocation
Multi-commodity Stochastic Dynamic
Planning Horizon Olivo et al. (2005) Transportation Routing
Multi-commodity Deterministic Static
Planning Horizon Di Francesco et al. (2007) Transportation Routing
Multi-commodity Deterministic Dynamic
Container Substitution and Planning Horizon Erera et al. (2005) Container Allocation
Multi-commodity Stochastic Dynamic
Planning Horizon Jula et al. (2003) Transportation Routing
Single-commodity Stochastic Dynamic
Planning Horizon Jula et al. (2006) Transportation Routing
Single-commodity Stochastic Dynamic
Planning Horizon Boile et al. (2008) Transportation Routing
Single-commodity Stochastic Dynamic
Planning Horizon
This paper
Transportation Routing
Multi-commodity Deterministic Dynamic
Planning Horizon
Empty container repositioning was first proposed by Dejax and Crainic (1987) as a part of container management. They also pointed out that empty container
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As a multi-stage model will be too complex, based on Crainic et al. (1993), Cheung and Chen (1998) formulated a two-stage stochastic model. In the first stage of the model, all the decisions are made. In the second stage, decisions are carried out and the corresponding performance related to random supply and demand is recorded. Choong et al. (2002) used an intermodal model as a case study, indicating that the planning horizon in inland empty container repositioning problem is an important issue, since there may be no feasible solution in a planning horizon of a certain length. The insignificance of Cheung and Chen (1998) and Choong et al. (2002) is that they did not relate the loaded container transportation with inland empty container repositioning. Because in a certain network, the loaded and empty container
transportation will influence each other, in most of the cases dealing with them jointly is the most effective way to reduce costs (Erera et al., 2005).
Olivo et al. (2005) proposed a two-commodity model for empty container problem. Container substitution was not taken into account while a multimodal network was proposed. In their model, the planning horizon with the length of a week was divided into hours. Olivo et al. (2005) indicated that small time segmentations are more applicable in reality.
Di Francesco et al. (2007) used a two-stage model as well for the empty container repositioning problem. The possibility of container substitution was allowed in their work. In the first stage of their model, problem was solved without the substitution allowance. In the second stage, solutions were ameliorated by allowing substitution, which suggests that container substitution may help to improve the solution of empty container repositioning.
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the general way of sharing same barges. No specific approaches were formulated for inland empty container repositioning.
Jula et al. (2003) proposed the street-turn approach to deliver empty containers from consignees to shippers. By using street-turn, container delivery can be done with shorter distance, which on the other hand reduces the traffic volume and the
possibility of congestion. A stochastic dynamic model was provided. The model then was applied to the Los Angeles and Long Beach ports by using simulation. More simulations of the model including street-turns and depot-direct were performed by Jula et al. (2006).
Similar to Jula et al. (2003) and Jula et al. (2006), Boile et al. (2008) provided a stochastic and dynamic model considering inland empty container repositioning. The difference between Boile et al. (2008) and Jula et al. (2003)/Jula et al. (2006) is that Boile et al. (2008) proposed the concept of depot-direct. Since the inland depots are much more closed to consignees/shippers, the transportation around inland depots tremendously reduces transportation costs.
However there are some gaps in Jula et al. (2003)/Jula et al. (2006) and Boile et al. (2008) that can be studied further. Firstly, Jula et al. (2003)/Jula et al. (2006) mainly focused on solving the congestion around LA/LB ports area, instead of cost reduction. Secondly, as pointed out by themselves, some managerial issues still need to be dealt with in order to achieve the approach of street-turn. Thirdly, the only approach of street-turn cannot deal with the situation that empty containers need maintenance or cleaning. Finally, in the study of Boile et al. (2008), multiple inland depots may not always be available and in some occasions the usage of inland depots is redundant.
To fill the gap of existing literature, this paper will try to develop a hybrid
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allow the container exchange while considering multi-commodity situation, of which the contributions to this area include:
1. The hybrid model improves the performance of single approach as either street-turn or depot-direct. Since the switch allowance between two approaches provide a better possibility to reduce costs and fulfil service level.
2. The adoption of multi-commodity situation fits more to the reality because multiple sizes of containers exist in a container transportation network.
3. The joint management of loaded and empty containers helps to reduce the transportation costs further in a container network. The hybrid model makes this possible.
Additionally, the planning horizon will be treated as a critical issue in this paper as the combination of street-turn and depot-direct makes the problem more complex.
Therefore the planning horizon is very important for finding the feasible and
optimized solutions. In the next section of methodology part, a few assumptions are made to simplify the problem, and a mathematical model will be built regarding to the hybrid model.
4. Modelling
In the hybrid model proposed in this paper, several critical issues are included. As mentioned in Imai et al. (2007) and Shintani et al. (2007), time issue is the key factor that makes the transportation model more dynamic and realistic. In this paper, time issues including time window and time penalty are considered.
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but penalties will be needed as a kind of cost based on the delay. In conclusion, by taking time window and time penalty into account, the hybrid model will be more dynamic and thus of practical meaning.
4.1 Assumption
According to the existing literature, a few assumptions are made to simplify the problem:
1. A two-commodity situation is considered, which means that in the model there are two different kinds of containers, A and B. A two-commodity situation is the most simple among multi-commodity scenario, thus it is used to make the problem less complex.
2. It is also assumed that the location of the nodes (sea terminal, inland depots, consignees and shippers), the time and quantity of the supply and demand of empty containers are known beforehand, which means that the information is deterministic before a planning horizon of a certain length.
3. One sea terminal and multiple inland depots are included in the network.
4. In the system of inland empty container repositioning, there are plenty of empty containers of both kinds and plenty of vehicles, which means that the system will not be short of containers or trucks.
5. The loaded/empty containers should be delivered to consignees/shippers on time, otherwise there will be penalties based on the delay in a certain extent.
6. Only one empty container each time is supplied/demanded at consignees/shippers, as the transportation object is container and only one container can be handled by one vehicle each time.
7. Transportation cost occurs linearly based on the distribution time. If the distribution time is longer, then the transportation cost is higher.
8. Only the beginning time window is considered at the consignees’ side, and only the ending time window is considered at the shippers’ side.
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For modelling the hybrid model, following notation of parameters and decisions variables are used:
H the planning horizon with a specific length
I the set of consignees with empty container supply in horizon H J the set of shippers with empty container demand in horizon H
D the set of inland depots in which container storage and exchange can be done in horizon H
mn ij
x the indicator that the empty container is moved from consignees iI to shippers jJ between time m and n directly or not
mn ij
y the indicator that the empty container is moved from consignees iI to shippers jJ between time m and n through inland depots or not
m id
y the indicator that the empty container is moved from consignees iI to depots dD at m or not
n dj
y the indicator that the empty container is moved from depots dD to shippers jJ at n or not
m i
u the indicator that consignees iI have empty container supply of type A or not
m i
v the indicator that consignees iI have empty container supply of type B or not
n i
u the indicator that shippers jJ have empty container demand of type A or not
n i
v the indicator that shippers jJ have empty container demand of type B or not
ij
t the time used for moving the empty container from consignees iI to shippers jJ
id
t the time used for moving the empty container from consignees iI to depots dD
dj
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jJ
mn ij
s the overtime used for moving the empty container from consignees iI to shippers jJ between time m and n
c the cost used for moving the empty container based on time p the penalty caused by overtime delivery
With the notation, the dynamic model regarding to the multi-commodity situation can be proposed as follows: Min: *( ijmnij ijmn*(id dj)) * ijmn m H n H i I j J m H n H i I j J d D m H n H i I j J c x t y t t p s
(1) s.t.: ijmn ijmn 1, ; n H j J n H j J x y i I m H
(2) 1, ; mn mn ij ij m H i I m H i I x y j J n H
(3) , ; ; ; mn m n ij id dj d D d D y y y i I m H j J n H
(4) 1, ; m m i i u v i I mH (5) 1, ; n n j j u v j J nH (6) max{ , }, ; ; ; mn m n m n ij i j i j x u u v v i I jJ mH nH (7) *( ) 0, ; ; ; mn mn m n mn ij ij ij id id dj dj ij d D d D m x t y y t y t s n i I j J m H n H
(8) , , , , , , , {0,1}, ; ; ; ; mn mn m n m m n n ij ij id dj i i j j x y y y u v u v i I jJ dD mH nH (9)The objective function in (1) is to minimize the total transportation costs in a certain planning horizon, and the transportation costs consist of three parts: the transportation cost between consignees and shippers, the transportation cost between
consignees/shippers and inland depots, the time penalties due to delivery delay. As mentioned above, all three kinds of transportation costs are bind with the
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Constraints (2) and (3) consider the transportation of consignees’ side and shippers’ side respectively. As only one empty container is supplied/demanded each time, one specific consignee can only provide one empty container, no matter it is transported to a shipper directly (street-turn) or to an inland depot (depot-direct). And one specific shipper can only receive one empty container, no matter it is delivered from a consignee directly or through an inland depot.
Constraints (4) consider the situation of empty containers that are transported through inland depots. For a specific container, it can only be transported through one inland depot. This constraint ensures that no redundant distance will be covered for one empty container.
Constraints (5) and (6) indicate the type of an empty container supply/demand. For an empty container supply/demand, it can only be one of type A or type B. In constraints (7), it is ensured that if the type of the empty container does not match between a consignee and a shipper, the street-turn method cannot be used. In this case, only depot-direct can be adopted.
Constraints (8) consider the time condition during empty container repositioning. Basically, a delivery cannot happen before the earliest time window at a consignee, and is not allowed to finish after the latest time window at a shipper. In this paper, by introducing the time penalty, constraints (8) is relaxed to allow the delivery delay in a certain degree. Yet this delay will be restricted through minimizing the transportation costs in objective function (1).
Constraints (9) are the binary constraints to ensure that either only one empty
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5. Results 5.1 Data Input
A vehicle routing problem (VRP) instance from Networking and Emerging
Optimization Database is used to simulate the inland empty container repositioning problem. This problem belongs to the multiple depot VRP situation with time
windows. In this instance, one sea terminal, four inland depots, ten consignees and ten shippers are involved. Different symbols are used to show their geographic locations on the map (Figure 3) :
Figure 3. Geographic Location
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55.408) respectively. The time windows of these consignees are {75, 359, 375, 121, 159, 356, 200, 170, 203, 257}, representing the earliest time when an empty container is available at these consignees.
Squares are used to represent the ten shippers in Figure 3, with a coordinate of (-29.73, 64.136), (-35.297, -24.896), (-22.833, -9.814), (-4.175, -1.569), (25.482, 6.287),
(16.229, 9.32), (29.84, 11.633), (-43.03, 20.453), (-26.404, 29.529), (-41.376, 50.824) respectively. The time windows of these shippers are {525, 477, 448, 433, 525, 482, 425, 472, 500, 604}, representing the latest time when an empty container is
requested at these shippers.
The inland depots are represented by triangles in Figure 3, their coordinates are (4.163, 13.559), (21.387, 17.105), (-36.118, 49.097), (-31.201, 0.235) respectively. The inland depots in this instance are used for container exchange when the type of container does not match between a consignee and a shipper.
The sea terminal is represented by cross in Figure 3, with a coordinate of (18.597, 96.716). The instance is chosen to simulate the reality, as in reality most of the sea terminals are far away from inland.
5.2 Simulated Scenarios
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Table.2 Type Composition of Empty Containers
Scenario.1 Scenario.2 Scenario.3 Scenario.4 Scenario.5
Type A 9 8 7 6 5
Type B 1 2 3 4 5
Scenarios such as {A:4, B:6} are not needed because they are the same as the existed scenarios ({A:4, B:6} is the same as {A:6, B:4}).
5.3 Result Analysis
The model is coded in Xpress-IVE 7.5, using Mosel language to solve the linear programming problem. The data in Section 5.1 and scenarios in Section 5.2 are used to draw the results. Simultaneously, the models of Street-turn and back-and-forth distribution are also coded in Xpress-IVE and the same data is used. The results from different models in different scenarios are analyzed (shown in Table 3)
Table 3. Transportation Costs in Three Models
Scenario 1 Scenario 2 Scenario 3 Scenario 4 Scenario 5
Hybrid Model 2079.23 2088.34 2100.74 2088.6 2088.6
Street-turn 2146.77 2198.42 2188.93 2101.81 2101.81
Back-and-forth 3724.51 3724.51 3724.51 3724.51 3724.51
Firstly, we can see with the types of empty containers that are more balanced in supply/demand, basically the time used in delivery the containers drops. This is because that with more balanced supply/demand, there are more feasible combination between consignees and shippers ,which makes the delivery faster.
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model reduces the repositioning time tremendously compared to back-and-forth distribution (as the latter one is the worst method), it also reduces the time
comparably from the street-turn model. If we remove the time being used in delivery the loaded containers from sea terminal to consignees/from shipper to sea terminal (as this part takes huge percentage in the total repositioning time), the hybrid model reduces the empties repositioning time by 10%-30% in different scenarios compared to street-turn. And in extreme cases as Scenario 1 to Scenario 3, with a situation that in a certain time period, the supplies/demands are unbalanced (major one type and minor the other), the hybrid model outplays the street-turn model.
At last, what has to be mentioned is that the cases used in this paper are the basic and simple ones. The results shown in Table 3 are under the circumstance that the penalty is taken as a half of the transportation cost based on time, and there are only two types of containers in the system. As in reality there are more containers with different types, it is more complex to plan the repositioning, which makes it more meaningful for the hybrid model.
Despite the transportation cost, service level is another issue we concern about. If transportation cost is reduced heavily, yet service level is poor, then the proposed model cannot considered as a good solution towards the problem. By looking at the time delay, we can tell whether the service level of the proposed model is good enough or not. The delay cost is shown in Table 4, on one hand we can see that in all the scenario of hybrid model, there is no delay occurring. While on the other hand, due the extreme unbalanced container type in Scenario 1 to Scenario 3, overtime delivery occurs in street-turn model.
Table 4. Delay Cost
Scenario 1 Scenario 2 Scenario 3 Scenario 4 Scenario 5
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Street-turn 71 71 20 0 0
6. Conclusion
In this paper, inland empty container repositioning is considered. By looking into the previous researches, the hybrid method based on street-turn method and depot-direct method is proposed. And the corresponding model is built as a solution to the inland empty container repositioning problem under multi-commodity situation. The contribution of this model includes:
1. The model combines street-turn model and depot-direct model, allowing container exchange, which makes this model still feasible under multi-commodity situation. 2. The model is dynamic because time issues are involved. Not only time windows but also time delay penalties are taken into account, which makes this model more realistic and meaningful to the reality.
Different scenarios are designed to examine performance of the proposed model on transportation cost and service level aspects. The results show that the proposed model surpasses the models in previous studies, therefore it is reasonable to believe that the hybrid dynamic model is feasible in reality.
Despite the contribution, the model proposed in this paper still has its limitation, which mainly comes from the assumption made in Section 4.1:
1. Unlimited vehicles in the system can only be an ideal condition. In reality, vehicle is a kind of limited resource, which means that in practice, the service level may not be fulfilled due to vehicle shortage.
2. Information in the system is all deterministic. By using stochastic information, the multi-commodity situation will become a NP-hard problem that is too complex to be solved.
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may order multiple container of different types.
In conclusion, the hybrid dynamic model for inland empty container repositioning proposed in this paper takes multi-commodity situation into account, which not only fills the gap in literature but also contributes to practise. However, due the
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