Introduction

The global urbanization trend has been remarkable. Since 2007, more than half of the world’s population reside in cities and this figure has risen to 57% currently1. This trend is expected to persist and the share of urban population is projected to reach nearly 70% by year 20502. This rapid urbanization leads to an increasing demand for efficient urban freight transport systems that support both business-to-business (B2B) and business-to-consumer (B2C) activities3. The growth of urban population, concentrated in densely populated areas, is driving demand for urban goods movement. Hence, there is an urgent need to find sustainable and innovative solutions for urban logistics.

Moreover, the rise of e-commerce and surge in parcel deliveries have further heightened the dependence on urban freight transport. E-commerce platforms rely heavily on timely and reliable urban logistics to meet consumer expectations for quick deliveries4, while businesses also depend on efficient freight networks to maintain their supply chains. In this complex landscape, effective urban freight management is essential to maintain cities’ livability and sustainability. It is crucial to tackle these challenges for the ongoing growth and development of urban areas.

Moving freight on transit is gaining interest as one practical and environmentally-friendly solution for addressing the aforementioned challenges. Freight on transit (FOT) is an logistics strategy that utilizes public transportation resources, such as public transit vehicles or infrastructure, to transport goods5. This approach takes advantage of the existing public transport network to facilitate efficient freight movement, while reducing the reliance on delivery vehicles.

In particular, during off-peak hours when the public transport system often operates with surplus capacity, parcels can be securely stored and transported in public transport vehicles. This innovative exploitation of underutilized space optimizes the efficiency of the transport system. The parcels can be put into dedicated trolleys that can facilitate safe and convenient transport by a carrier completing the deliveries. Trials in cities like Paris, Tokyo, Sapporo, Beijing, Shenzhen, Singapore, and Madrid demonstrate global interest in this strategy6,7,8,9,10,11.

In this paper, we analyze scenarios of urban goods movement using public transport. The objective is to deliver parcels from a warehouse to their destinations through an urban rail network within a day. Initially, delivery vehicles transport the parcels from the origin warehouse to hubs located at train stations. Subsequently, the parcels are transferred using the rail network to satellites, also situated at train stations. At the satellites, the parcels are unloaded onto smaller delivery vehicles operating from the satellites. Finally, these vehicles will be used to deliver the parcels to their final destinations. The corresponding three-echelon configuration is depicted in Fig. 1.

Fig. 1: Illustration of a three-echelon freight on transit system.
figure 1

Initially, delivery vehicles transport the parcels from the origin warehouse to hubs located at train stations. Subsequently, the parcels are transferred using the rail network to satellites, also situated at train stations. At the satellites, the parcels are unloaded onto smaller delivery vehicles operating from the satellites. Finally, these vehicles will be used to deliver the parcels to their final destinations.

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In this transit-based freight transport system, various strategic and tactical decisions have to be made. The locations of the warehouse and the parcel delivery destinations are known in advance. However, there is a need to select hub and satellite locations from among all train stations along the rail network. Moreover, tactical decisions involve the assignment of parcels to specific hubs and satellites to ensure efficient, sustainable, and cost-effective logistics management.

In this paper, we propose a framework for determining the optimal locations of hubs and satellites in order to minimize the distance traveled by delivery vehicles for parcel deliveries. This problem is challenging due to the combinatorial complexity associated with potential hubs and satellites, which directly affects the distance traveled by vehicles. To tackle these challenges, we developed a scalable, iterative heuristic algorithm capable of solving the problem. In addition, we apply the approach to the case of parcel deliveries in Singapore, monitoring key performance indicators to evaluate the system performance. Real-world data, including parcel delivery and rail network information from the city-state of Singapore, are used in the detailed case study to demonstrate the effectiveness of the approach.

Methods

We first provide a detailed description for the three-echelon transit-based freight transport system and define it with mathematical formula. An overview of this system is initially presented, then the assumptions, constraints and objectives of this problem, followed by the notations and the problem formulation. Subsequently, we propose a divide-and-conquer approach that decomposes the problem into two distinct minimization sub-tasks to make it manageable.

Overview of three-echelon transit-based freight transport system

The problem in this study focuses on the optimization of a three-echelon transit-based freight transport system which aims to deliver parcels from a warehouse to their destinations by utilizing the rail network, as shown in Fig. 1. In this system, train stations will be considered as intermediate storage and distribution points, which can act as hubs and satellites to store and distribute parcels. We consider the daily operations of the courier company where parcels will be consolidated at the warehouse at the beginning of the day and aims to achieve 100% same-day delivery. This system operates in the following manner: given a set of parcels to delivered from a warehouse, the carrier will deliver the parcels to their assigned hub first, which is the first echelon. Following, in the second echelon, the parcels are sent from the hubs to their assigned satellites on trains. Finally, in the third echelon, the carrier will deliver the parcels from the satellites to their final destinations.

Problem description and formulation

We first introduce the assumptions, constraints and objectives of this problem. This study focuses on the daily operations of the courier company, where the daily parcel demand is predetermined at the beginning of the day and does not vary throughout the day. The system requires all parcels to be delivered by the end of the day, which means no parcels will be stored overnight in the warehouse, hubs or satellites. For simplicity, we assume that all parcels have identical size and weight characteristics in this study. This assumption allows us to model vehicle capacity constraints introduced later based on parcel count rather than varying physical dimensions. Additionally, there is no capacity limitation for the hubs and satellites, meaning that each hub and satellite is assumed to have an infinite capacity for parcel assignment. In addition, each parcel can be delivered to one and only one hub in the first echelon and similarly, each parcel can be assigned to one and only one satellite.

The road vehicle travel distances in this study are based on road network distance, specifically the distance between the warehouse and the hubs (train stations) in the first echelon and the distance between the satellites (train stations) and parcel destinations in the third echelon. Two types of vehicles are assumed to be used in this study: large vehicles for delivering parcels in the first echelon and small vehicles in the third echelon.

This study also assumes that there are no additional transport costs incurred in the second echelon. This is because both the carrier and the rail operator are known to collaborate to utilize existing train infrastructure, as observed in recent freight-on-transit trials8,9,10. It is also assumed that the travel times between the train stations via the urban rail network in the second echelon are assumed to be constant throughout the day.

The constraints in this study are related to capacity constraints and time constraints. Each vehicle in the first and the third echelon has a fixed capacity, limiting the number of parcels it can carry. Moreover, each vehicle also has a maximum daily working time.

From the perspective of the carrier, the objective is to deliver the parcels from the warehouse to their destinations with minimal vehicle kilometers traveled (VKT). Conventionally, the carrier will deliver the parcels to their destinations from the warehouse directly. With the integration of the rail network, VKT is only incurred in the first and the third echelons. Therefore, one needs determine which train stations should be selected as hubs and satellites, such that the total VKT for delivering the parcels from the warehouse to their end destinations is minimized.

Subsequently, the problem is formulated as a mixed graph G = (V, E), where V is a set of nodes with a warehouse (node 0), a set of potential candidate hubs H (train stations), a set of potential candidate satellites (train stations) S and a set of parcel destinations P. The edge set of E can be divided into three subsets, each corresponding one of the three echelons. We first introduce the definition of the edge set for each echelon, following by its respective connectivity network and the objective of this problem. Some notations related to this model are summarized in Table 1.

Table 1 Three-echelon urban freight on transit system model notations
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We first define the edge set for each echelon. The first set E1 is defined as \({E}_{1}=\left\{(i,j)| i,j\in \left\{0\right\}\bigcup H\right\}\), connecting the warehouse and hubs. We assume that the parcels are consolidated at the warehouse first and then transported to the hubs by a homogeneous fleet of vehicles F1 with capacity Q1 in the first echelon. Each vehicle has a maximum route duration D1. Following, the second edge set is denoted as E2 where \({E}_{2}=\left\{(i,j)| i,j\in H\bigcup S\right\}\), connecting the hubs and satellites by the rail network. The maximum travel time between the hub(s) to the satellites on the rail network is denoted as Tmax. The third edge set is defined as E3: \({E}_{3}=\left\{(i,j)| i,j\in S\bigcup P\right\}\), which aims to deliver the parcels from the satellites to the parcels’ final destinations. We assume that there is a homogeneous fleet of vehicles with capacity Q2 located at each satellite to conduct parcel deliveries from the satellites. Each vehicle in the third echelon has a maximum route duration D2.

Further, we define the connectivity network for each echelon. Each edge in E1 is associated with a distance between i and j, denoted by c1(i, j) where (i, j) ∈ E1. Following, in the second echelon, we define an edge (i, j) ∈ E2 with c2(i, j) denoting the time taken to travel along the edge via rail network. Finally, similar to the first echelon, each edge (i, j) ∈ E3 is related with the distance between i and j, denoted as c3(i, j).

To determine which train stations should be selected in the first echelon, this problem includes two sub-problems, a parcel-hub assignment problem to assign the parcels to the hubs and a routing problem to delivering the parcels from the warehouse to their assigned hubs. As such, we define the following binary variables:

  • Let xh denote whether train station h ∈ H is selected as a hub, where xh = 1 if hub h ∈ H is selected and 0 otherwise.

  • Let zhp be a binary variable where zhp = 1 if parcel p ∈ P is assigned to hub h ∈ H, and zhp = 0 otherwise.

Then for each selected train station h where xh = 1, h ∈ H, there exists a unique assigned parcel set Ph such that Ph ⊂ P and ⋃h∈HPh = P. It is important to note that the destination for each parcel p ∈ Ph is changed to the location of the hub h. Following, we denote the vehicle kilometers traveled for delivering parcels Ph for each h ∈ H as Lh, which is subject to a capacitated vehicle routing problem.

Similarly, in the third echelon, to determine the selection for satellites, we also address two essential sub-problems: the parcel-satellite assignment problem and the routing problem to deliver the parcels from the satellites to their destinations are involved.

To formalize this, we define the following binary variables:

  • Let ys denote whether satellite s ∈ S is selected, where ys = 1 if satellite s ∈ S is selected and 0 otherwise.

  • Let wsp be a binary variable where wsp = 1 if parcel p ∈ P is assigned to satellite s ∈ S, and wsp = 0 otherwise.

Then for each selected train station s where ys = 1, s ∈ S, there exists a unique assigned parcel set Ps such that Ps ⊂ P and ⋃s∈SPs = P. The vehicle kilometers traveled Ls for delivering parcels Ps from satellite s ∈ S is determined by solving a capacitated vehicle routing problem.

Therefore, the objective can be written as: Minimize L = ∑h∈HLh + ∑s∈SLs.

Solution approach

This section presents the solution approach employed in this study. In addressing the optimization problem formulated in the previous section, this section begins with a comprehensive overview of its complexity and underlying challenges stemming from the joint optimization of hub/satellite selection, hub-satellite assignment, parcel-satellite assignment and vehicle routing problems, demonstrating its NP-hardness. To tackle this, we propose a divide-and-conquer approach that decomposes the problem into two distinct minimization sub-tasks to make it manageable.

We first give an overview of the solution approach to address the problem proposed previously. It is undeniable that the core of this system is the second echelon, which links the first echelon and the third echelon. More specifically, the decision on selecting trains stations as hubs in the first echelon is related to the decision on train stations as satellites in the second echelon, considering the network of train stations. The delivery fleet will depart from the warehouse and then transport the parcels to the hubs, which is subject to a capacitated vehicle routing problem. Similarly, in the third echelon, for each selected train station s where ys = 1, s ∈ S, there exists a unique assigned parcel set Ps such that Ps ⊂ P and ⋃s∈SPs = P. It is important to note that the allocation set is a disjoint set for any two different selected stations (satellites). Then the delivery fleet located at each satellite will depart from the satellite, complete delivery of parcels assigned to this satellite and return to this satellite.

Finding the exact optimal solution for this problem is computationally intensive due to the combinatorial nature of hub and satellite selection decisions as well as the intricacies of the capacitated vehicle routing problem. This multi-echelon problem combining facility location and vehicle routing is known to be NP-hard12. Therefore, a divide-and-conquer approach is introduced to solve the optimization problem by decomposing it into two distinct minimization sub-tasks.

The first sub-task involves the assignment of parcels to the satellites and the determination of the most efficient vehicle routes, accounting for both routing complexities and vehicle capacity constraints while the second sub-tasks focuses on identifying the optimal subsets of hubs from its candidate sets, aiming to minimize the total travel distance for the delivery vehicles. This systematic approach allows us to effectively address the challenges of the optimization problem, and the subsequent sections will detail the methodologies and algorithms developed for each sub-task, culminating in a cohesive framework aimed at minimizing delivery vehicle kilometers traveled.

In addition, in the third echelon, a delivery vehicle based at each satellite is responsible for delivering parcels assigned to that satellite to their respective destinations and returning to the satellite. However, due to capacity limitations, the distance for each route may be shorter if the parcels assigned to the same satellite are close together. Consequently, certain shorter routes can be combined and executed by the same vehicle. This scenario can be modeled as a bin-packing problem, which aims to determine the minimum number of bins required to pack items of different sizes into a finite number of bins, each with a predetermined capacity. To solve this problem, the Best Fit Decreasing algorithm is utilized to determine the minimum fleet size needed to complete all the tours13 (Algorithm 1).

Algorithm 1

Best fit decreasing algorithm for route-to-vehicle assignment

BEST-FIT-DECREASING(lmax, R)

for i = 1 to ∣R∣ do

 for j = 1 to 2, 3, … do

  If route Ri can be conducted by vehicle j satisfying capacity constraint (lmax)

then

   Calculate residual capacity after the route Ri has been conducted

  end if

 end for

 Assign route Ri into vehicle j where vehicle j has the smallest residual capacity after conducting route Ri

 If no such available vehicle conducts route Ri then

  add a new vehicle to conduct route Ri

 end if

end for

return number of vehicles required

In the first sub-task, two steps are involved: parcel-satellite assignment and vehicle routing optimization. In our approach to assign parcels to satellites, we propose a proximity-based strategy where each parcel is assigned to its nearest satellite, allowing for efficient allocation of parcels based on geographical proximity, thereby reducing vehicle kilometers traveled for parcel deliveries from the satellites to destinations. As introduced in Section “Base case”, the distance in this study is based on road network distance. To begin this assignment, the distances between parcels and train stations on the road network were calculated using open source routing machine (OSRM). This routing machine, based on data from OpenStreetMap, provides high-performance routing capabilities for finding the shortest paths in road networks14.

Before addressing the joint optimization with the determination of the optimal vehicle routes, it is important to define an initial candidate satellites including a predefined set of train stations from S. It is expected that as more satellites are involved in the system, the vehicle kilometers traveled will decrease due to the fact that the parcels assigned to the same satellite generally have closer destinations. However, there exists a trade-off that should be considered. While introducing more satellites is likely to reduce vehicle kilometers traveled, an excessive number of satellites may result in under utilization. The underutilized satellites not only incur unnecessary additional trips from the hub without generating sufficient volume but also lead to excess vehicle capacity operating at the satellites.

To optimize the system further, the follow-up step of parcel assignment is to remove the satellites with only a few number of parcels assigned to them. We will be guided by a centrality metric, which is used to measure the importance of the nodes in a network15,16. Freeman et al. reviewed and summarized measures on the centrality as three distinct conceptions: degree centrality, betweenness centrality and closeness centrality17. The first point of view in centrality is based on the count of the degree or number of adjacencies for the node, termed as degree centrality. In terms of the betweenness centrality, it measures the frequency of a node that connects the shortest path between other pair of nodes. While the third conception, closeness centrality, is defined on the degree to which the node is close to other nodes. The satellites with only a small number of parcels assigned to them will be removed. In addition, the number of satellites should ideally not exceed the vehicle fleet size in the base case. It should also not be too few in order to ensure adequate coverage. We denote N as the number of initial satellites and to this end, the initial candidate satellite set can be calculated. More detailed steps and algorithm are presented as follows, shown in Algorithm 2

Algorithm 2

Potential candidate satellite construction

1: Input: Initial set of all parcels to be delivered P, set of train stations R and road network distance matrix D = (di,j) where {i, j ∈ {0} ⋃ P ⋃ R}.

PARCEL-SATELLITES-ASSIGNMENT (P, R, D)

2: Initialize an empty set Si for initial candidate satellites

3: Initialize an empty dictionary assignment to store parcel-satellite assignments

4: S ← R

5: for parcel p in P do

6:   Find the nearest satellites s from S for the parcel p based on the distance matrix D1 = (dp,s) where p ∈ P and s ∈ S

7:   Assign the parcel p to satellite s

8:   Increment the assignment count for satellite s in assignment

9: end for

CALCULATE-DEGREE-CENTRALITY (S, N, assignments)

10: Calculate Degree Centrality for all satellites s in S based on the assignment count from assignments

11: Sort the satellites in S based on Degree Centrality in descending order

12: Select the top N train stations from S based on Degree Centrality to form the potential candidate satellite set and update \({S}_{i}\leftarrow \left\{S[j]| j=1,2,\cdots \,,N\right\}\)

13 return:Si, initial candidate satellite set

The following parts of this section aim to optimize vehicle routing for parcel deliveries from the assigned satellites to their destinations. As we described in Section “Base case”, there is a fleet operating at each satellite. Moreover, each vehicle in the fleet has a fixed capacity limiting the number of parcels it can carry and each vehicle also has a maximum route duration (working time). As such, this problem can be modeled as a capacitated vehicle routing problem (CVRP).

Given that parcel volume in the real-world often involves large instances, to address this complexity, we use Google OR-Tools to minimize the vehicle kilometers traveled (VKT) by solving the CVRP, as shown in Algorithm 3.

Algorithm 3

Google OR-tools Algorithm for Capacitated Vehicle Routing Problem

GOOGLE-OR-TOOLS(D, assignment, demand, vehc, lmax)

1: Set the following parameter values: vehc and lmax. ⊳ Input vehicle capacities of the fleet and the maximum travel distance for each route.

2: Create a distance matrix D(i, j) from distance matrix D where (i, j) ∈ satellite ∪ assignment ⊳ Each assignment includes the satellite and the delivery destinations of parcels assigned to this satellite.

3: Input the assignment (parcel delivery destinations) and corresponding demand for each satellite into Google OR-tools programming.

4: return minimum vehicle kilometers traveled, visiting sequence, and distance of each route.

Given an initial candidate satellite set Si obtained from the last section, there are \({2}^{| {S}_{i}| }-1\) possible combinations of satellites. The core of this optimization is to find the optimal combination that minimizes vehicle kilometers traveled (VKT). Moreover, the challenge of optimizing the routing for parcel deliveries from the satellites to their destinations adds to the computational complexity.

To alleviate computational complexity in solving the problem, we refine the combinations by specifying a fixed number m for selection. This approach can be formulated as a p-median problem, where the objective is to identify m satellites that minimize the sum of the distances from the parcels to the satellites. Following this selection, we can then calculate the minimized VKT for the third echelon within each predefined subset.

Algorithm 4

Optimizing satellite selectiion

OPTIMIZE-SATELLITE-SELECTION (P, Si, D, m)

P-MEDIAN-FACILITY-LOCATION(P, Si, D, m)

1: Initialization: Initialize an empty set of selected satellites generated from p-median facility location problem, F

2: Construct distance matrix DS = (dp,s) for all parcels p ∈ P and potential candidate satellites s ∈ S generated from Algorithm 2

3: Solve the P-Median Location Problem by using candidate satellite set Si, distance matrix D2 from D and m

4: return: F, the optimal solution to the p-median problem

 OPTIMIZE-SATELLITE-SELECTION (F, P, D)

5: Initialization: Initialize \({{\mathcal{A}}}\triangleq {\{{A}_{f}\}}_{f\in F}\) to store set of parcels assigned to each satellite f ∈ F where \(\left\{{A}_{i}\bigcap {A}_{j}=\varnothing | \forall i,j\in F,i\ne j\right\}\) and ⋃f∈FAf = P

6: Construct distance matrix DF = (dp,f) based on distance matrix D for all parcels p ∈ P and potential candidate satellites f ∈ F

7: for parcel p in P do

8:   Find the nearest satellites f from F for the parcel p based on the distance matrix D3 = (dp,f) from D where p ∈ P and f ∈ F.

9:   Assign the parcel p to satellite f and add the parcel p into Af

10: end for

11: Solve Capacitated Vehicle Routing problem for Af by Algorithm 3

To evaluate this strategy, we consider a combination that involves all the train stations as satellites and retain only those satellites with at least one parcel assigned as a benchmark. This is because VKT is expected to decrease as more satellites are involved in the system, due to the fact that parcels assigned to the same satellite generally have destinations that are close to one another. We refer to this scenario as the “maximum number of satellites" scenario. If the reduction in VKT achieved by this proposed method, compared to the maximum satellite scenario, meets an acceptable criteria, we can conclude that the proposed method is valid.

The second sub-task involves satellite-hub assignment and vehicle routing optimization. Regarding the hub selection for satellite-hub assignment, we consider two strategies. The first strategy considers the train station closest to the warehouse with the highest priority, ensuring that parcels can be quickly transported from the warehouse to the sole hub.

The second strategy involves multiple hubs, aiming for reduction in transfers between stations while considering proximity to the warehouse. Given the set of selected satellites, our goal is to connect hubs with satellites without any transfers between train lines.

This approach begins with sorting the hubs according to the distances between the warehouse and each hub h ∈ H. Starting from the nearest hub (train station), we attempt to match it with each selected satellite f ∈ F. If the satellite f can be connected with h directly satisfying travel time constraint, satellite f will be removed from the set. This process will stop until all the satellites f ∈ F are assigned with a hub.

The process concludes by replacing single-line stations with transfer stations among the set of selected hubs. This filter aims to reduce the additional visiting, ensuring that our network is efficient and robust. More details are shown in Algorithm 5.

Subsequently, the set of selected hubs and their corresponding satellites can be determined. In additions, with the parcel-satellite assignment derived in last section, parcel-hub assignment can be obtained accordingly, thereby subject to a capacitated vehicle routing problem. To solve this, we adapt the solver Google OR-Tools, similar to Algorithm 3.

Algorithm 5

Assignment for satellites and multiple hubs

1: Input: F, H, Dist, Trail

2: Output: Set of selected hubs G and satellite-hub assignment C

3: Sort H by distance to the warehouse

4: Initialize \(G\leftarrow {{\emptyset}}\)

5: for each h ∈ H do

6:  for each f ∈ F do

7:   If h and f can be connected without transfer and Trail(h, f) ≤ Tmax then

8:    Add h to G

9:    Record this assignment to C

10:     Remove f from F ⊳ Remove assigned satellite

11:  end if

12:  end for

13:  If F is empty set then ⊳ Check if all satellites are assigned

14:   break ⊳ Exit loop if all satellites are assigned

15:  end If

16: end for

17: Replace single-line stations with transfer stations from G where applicable and update G and Ag

18: return G, Ag

Results

We select Singapore, a city-state located in the south-east of Asia as a case study to demonstrate the methodology proposed in the previous sections. Singapore enjoys a highly accessible and affordable public transport system. Currently, the island of Singapore is served by an extensive rail network consisting of around 120 train stations, spanning six rail lines and covering a total distance of 200 km. This rail system accommodates a daily ridership exceeding three million trips. For our case study, we examine all 120 train stations within this network.

Data collection and description

This subsection briefly introduces the dataset used in the experimental study conducted in Singapore. It includes information on travel time between train stations extracted from the Singapore rail network and daily parcel delivery information obtained from an e-commerce carrier in Singapore.

To gather travel time between train stations, we adopted the Selenium WebDriver18, an open-source tool, to interact with the TransitLink website19 and retrieved the necessary data. The obtained travel times reflect the travel time between the origin and destination train stations via the rail network, excluding any waiting time. Data extraction occurred in September 2023, reflecting actual operational conditions. We set a maximum travel time of 1 h (Tmax) for the second echelon, from the hub to the satellites. This is based on the maximum travel time across the rail network.

The parcel delivery dataset used in this study comprises daily delivery requests to be fulfilled and was obtained from an e-commerce carrier in Singapore in January 2019. Each delivery request includes the geospatial coordinates (latitude and longitude) of both the origin warehouse and the parcel destination. On average, 5841 parcels were delivered from a warehouse on a weekday. This dataset provides spatial distribution patterns and delivery demands.

Base case

To assess the potential benefits of this three-echelon system that integrates public transport and freight transport, we will compare this with a base case scenario where only delivery vehicles are used to fulfill parcel deliveries. This scenario is subject to a capacitated vehicle routing problem. We assume a homogeneous fleet with each vehicle capable of delivering a maximum of 120 parcels. Additionally, we assume that each vehicle has a maximum working time of 10 hours per day. The working time includes two components: driving time on the road network and delivery time to the doorstep. We assume average vehicle speed of 30 km/h and delivery time to doorstep of 5 minutes per parcel. The parameter values used are summarized in Table 2. Given this, the vehicle kilometers traveled in the base case is 2979 km and the necessary vehicle fleet size is 60.

Table 2 Input parameter values for capacitated vehicle routing problem in the base case
Full size table

Results: vehicle kilometers traveled

We first present numerical results on vehicle kilometers traveled with and without rail network integration to determine the optimal selection of satellites. We first set the number of initial candidate satellites as N = 40 at the initialization of the solution algorithm. This setting aims to strike a balance between the managing the size of the satellite network and ensuring comprehensive parcel coverage. While this value represents almost a third of total train stations, it is sufficient to capture most parcel destinations and allow insights into system performance.

In addition, the parameter values for Algorithm 3 (see “Methods” section) are specified in Table 3.

Table 3 Input parameter values for capacitated vehicle routing problem in the first and third echelon
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The vehicle kilometers traveled in this system are incurred in the first and the third echelon. In the third echelon, VKT can be calculated using Algorithm 3 with the parameter values specified in Table 3, as described in the previous section. In the first echelon, two strategies were proposed as introduced in the Solution approach section: (1) a single hub by selecting the train station closest to the warehouse with the highest priority, and (2) multiple hubs that avoid train line transfers to the satellites along rail network, while also considering their proximity to the warehouse. Following the above steps, the total distance traveled by the vehicles can be calculated. In comparison to the base case that does not utilize rail network, the parameters in capacitated vehicle routing problem remain consistent, as presented in Table 3. The computational results for VKT compared to the base case are shown in Table 4.

Table 4 Vehicle Kilometers Traveled (VKT) and reduction (%) for different number of hubs and satellites
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The results demonstrate that integrating the rail network with freight transport provides substantial benefits in reducing delivery vehicle kilometers traveled across all scenarios. This reduction enables greater efficiency and sustainability in freight transport systems. What is particularly noteworthy is that the reduction becomes more significant as the number of satellites increases. This correlation is not coincidental; it is a consequence of the fundamental logistics dynamics in operation. With the introduction of more satellites into this network, the distribution of parcels among them becomes more refined and precise. As such, parcels are increasingly assigned to satellites that are in closer proximity to their intended destinations. Consequently, we observe a noticeable concentration of assigned parcels for each satellite. This phenomenon further enhances the overall reduction in vehicle kilometers traveled, further emphasizing the positive impact of integrating the rail network with the freight transport system.

Comparing the scenarios with a single hub versus multiple hubs, the multiple hubs strategy also demonstrates a reduction in VKT, although with slightly lower VKT savings compared to the single hub approach. Nevertheless, this highlights the potential of the proposed three-echelon system in reducing VKT as well as in promoting environmentally-friendly urban freight operations. Furthermore, involving different optimization strategies demonstrates the flexibility of the proposed model, which is adaptable to other urban environments.

Examining solution quality

Solution quality is a widely used metric to evaluate algorithms. It is calculated by using the percentage gap: 100(z − zb)/zb where z is the solution value obtained by the proposed method and zb denotes the best known solution value for the instance. Performing such an evaluation in this study is challenging as it is difficult to find optimal solutions due to the high computational complexity, as indicated in Section 4.1. In general, it is expected that involving more satellites will result in lower VKT in the third echelon. As such, the scenario with the maximum number of satellites required is selected to represent the optimal solution.

In the Singapore case, the maximum number of candidate satellites with at least one parcel assigned is 60. Under this setting with 60 satellites, the minimum VKT is 1622 km. Compared to the scenario with 30 satellites, the VKT is lower by 6.1%. Despite not knowing the optimal solution for computational comparison, we conclude that the proposed approach is both acceptable and capable of producing a reasonable solution.

Notes on vehicle fleet size

In addition to the discussion on the vehicle kilometers traveled, we should consider other relevant indicators of interest to the carrier, including delivery vehicle fleet size. The introduction of more satellites in the system may necessitate a larger fleet.

In the first echelon, it is assumed that a fleet of larger vehicles operates from the hub to transport parcels from the warehouse. For this case study, a larger vehicle capacity of 300 is assumed for the first echelon. The vehicles maintain an average speed of 30 km/h, resulting in the necessity of deploying 3 large vehicles. Taking the scenario of single hub as an example, the findings on fleet size can be found in Table 5.

Table 5 Computational results on delivery vehicle fleet size for single hub scenario
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The number of satellites will influence delivery vehicle fleet size in the following ways:

  • Additional handling: The parcels need to be loaded and unloaded at both hubs and satellites, often requiring dedicated vehicles at each point. Consequently, this leads to an increase in the fleet size.

  • Scheduling and coordination: Each vehicle operates within specified working time and capacity constraints. As more satellites are introduced, the number of parcels assigned to each satellite decreases. This reduction in assignments leads to a higher amount of residual capacity waste for certain satellites when the number of assigned parcels is low. This is due to the fixed capacity of the vehicles involved.

When considering both indicators of vehicle kilometers traveled and fleet size, it becomes apparent that the scenarios with only 5 or 10 satellites yield more benefits compared to other scenarios. In addition, there may be a possibility to use smaller delivery vehicles, such as cargo cycles, for each satellite. This smaller vehicle delivery mode can help keep vehicle costs low when the fleet size increases.

Impact of vehicle capacity on vehicle kilometers traveled

We explore additional scenarios keeping the same datasets and parameters in the algorithm, with only one difference: vehicle capacity in the third echelon. It is worthy noting that most of the VKT is incurred in the third echelon. Table 6 reveals the results with varying vehicle capacities from 30 to 120 parcels in the third echelon. The results show that all scenarios using vehicles of different capacities will realize VKT reduction. The results also show the possibility of using much smaller vehicles to carry out parcel deliveries from the satellites to parcel destinations, such as cargo cycles. These smaller vehicles can provide a sustainable alternative for last-mile deliveries, navigating urban environments easily, while minimizing environmental impact.

Table 6 Vehicle kilometers traveled (VKT) and reduction (%) for different vehicle capacities and number of satellites
Full size table

Discussion

In this paper, we investigate a novel and innovative freight on transit system wherein parcels are efficiently transported from a warehouse to their respective destinations, leveraging the urban rail network. The system comprises three distinct echelons. Initially, larger delivery vehicles transport parcels from the origin warehouse to hubs, strategically situated at train stations, establishing the first echelon. Subsequently, the parcels are transferred using the rail network to satellites, also positioned at train stations, representing the second echelon. Finally, within each satellite, the parcels are unloaded and assigned to smaller delivery vehicles to ensure successful delivery to their ultimate destinations.

A general method for optimal selection of hubs and satellites in order to minimize vehicle kilometers traveled is offered. An iterative heuristic algorithm was developed to derive solutions that reflect practical logistics operations. An analysis of key metrics for a parcel delivery carrier was conducted to evaluate system performance. Real-world data from Singapore, such as parcel deliveries and rail network details, were used to illustrate the approach. The computational findings demonstrate substantial reductions in delivery vehicle kilometers through the freight-on-transit concept.

A comprehensive method that integrates strategic and tactical planning decisions for transit-based freight transport encompassing matching, location selection, and routing has been presented. However, there are acknowledged limitations. Due to the lack of data on working hours and parcel delivery schedules, we did not consider time scheduling and all parcels are delivered by end-of-day basis. The rostering of delivery workers required to load and unload parcels was also not taken into account. Moreover, a mechanism for parcel assignment to satellites can be adapted to accommodate the dynamic nature of parcel movements. It is important to acknowledge that the distribution of parcel delivery destinations may vary on a daily basis.

Additionally, from an application perspective, stakeholder analysis also plays an important role in the successful implementation of this proposed system in practice. Engaging stakeholders is a next step for future work to ensure that the interests and needs of all parties involved are addressed. While this research lays the groundwork to demonstrate the potential of this innovative approach, these topics warrant further research and analysis to fully explore their feasibility in practice.