Public transport services in support to the last mile freightdeliveries
Irecis Azcuy† , Ricardo Giesen ‡,∗ , and Niels Agatz∓
Department of Transport Engineering and Logistics, Pontificia Universidad Católica de Chile,† ilazcuy@uc.cl, ‡ giesen@ing.puc.cl∓ Rotterdam School of Management, Erasmus University, nagatz@rsm.nl∗ Corresponding author.
Extended abstract submitted for presentation at the 11th Triennial Symposium onTransportation Analysis conference (TRISTAN XI)
June 19-25, 2022, Mauritius IslandApril 13, 2022
Keywords: Sustainable urban freight transport, freight on public transport, strategic designmodel, Location-Routing problem.

1INTRODUCTION

Last-mile urban deliveries for e-commerce are growing (Statista, 2020) and becoming less efficientdue to the rise of short lead time requirements. Also, in congested cities is very hard to meetdelivery deadlines. To overcome these challenges, some companies such as Amazon are using
satellite facilities which are closer to final customers. However, adding these facilities may befrowned upon by neighbors (Citizen, 2021) and could increase delivery costs. In general, logistics
facilities are sprawl outside metropolitan areas (Dablanc et al., 2014). The logistics sprawl further
increases costs if the level of service is time-sensitive due to the low number of customers thatcan be served per route.
One solution is to go for a collaborative approach with public transport services, using a
two-tier delivery system where freight is first moved by segregated public transport services,and then by last-mile vehicles to customer locations. We envision that, in the first leg, public
transport vehicles can carry packages on a hitched cart that its then dropped at one transit stop,from where the packages are transfer to a last-mile delivery vehicle. In this manner, packages
do not interact with passengers and and the public transport vehicle is only marginally delayedwhen disconnecting the hitched cart.
The general objective of this paper is to analyze the value of using public transport services
in the first leg in systems with time-tight delivery deadlines. As a benchmark, we use the caseof delivering everything directly from a remote depot. We study two settings. The first case fora single line transit structure, and the second case for a fork transit services with known routes
and schedules.

2METHODOLOGY

We focus on finding the best transfer station locations to facilitate transfer between transit andlast-mile vehicles. We assume one depot, and all customers spread uniformly in a delivery area
to be served before a deadline T . The scheduled transit service operates with an average speed
st , and with enough space in the cart to ship all goods. Each transit stop can potentially be used
TRISTAN XI Symposium

Original abstract submittalIrecis Azcuy, Ricardo Giesen, and Niels Agatz

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as a transfer station. Last-mile vehicles can depart from the transfer station and also directlyfrom the depot with an average speed of sl and a limited capacity. Our main goal is to minimize
the expected travel distance of the last-mile vehicles across different customer instances.
First, we study a stylized system for a single depot, a transit line, and a single transfer station(Azcuy et al., 2021). We look at several special cases using analytical expressions to get insights
into the transfer location decisions when customers are continuously distributed on the transitline. Then, we analyzed customers located discretely over the region. This last case generalizes
the multi-depot, multi-trip vehicle routing problem with variables starting times of the last milevehicle routes. We use an Adaptive Large Neighborhood Search with local search to solve it.
Next, we study the case of delivery operations supported by scheduled fork-transit lines
for a single depot and multiples transfer stations. We model this planning problem as a facility
location problem considering aggregate and uncertain customer density over a delivery zone withtight delivery deadlines. In this case, we use the continuous approximation method to estimate
the routing cost as was proposed by Beardwood et al. (1959).

3RESULTS AND DISCUSSION

Below we present our base case results for the two settings considering a depot serving an areaof 10 km by 10 km and where delivery locations are: (i) discretely and uniformly distributed
over the region and there is one transit line to support deliveries (A single line setting); or (ii)continuously over the region and there is a scheduled fork transit line that branches 13 into threetransit lines running every 5 vehicles per hour at st = 20 each (A fork line setting).
For the line setting, the transit stops are located at one-third, two-third, and the end of theline from the depot. 50 customers are uniformly distributed across the delivery region. The
last-mile vehicles can serve 40 customers per trip. In the base case experiment, we ignore traveltimes, because we consider that the deadlines is not a boundary. For every experiment, wegenerate 10 demand location realizations.
In the fork line setting, there are 87 potential transfer stations to be operated at a fixed costof $ 22 per day. It takes 2 minutes to transfer orders from transit vehicle to last-mile vehicle.
The last-mile vehicle can serve 493 customer locations per trip at a speed of sl = 15 km/h. We
assume that it takes 5 minutes for each stop on the delivery route. The cost per unit distanceis $0.6 per kilometer and per last mile vehicle required is $31 per day. In all our experiments,
we generate 50 customer density realizations from a uniform distribution between 15 and 25
customers per km2 . We consider all customers to be served before 1, 2, 8 and 24 hours.
In both cases, the saving takes as benchmark the case without transfer stations.
Discussion Overall, both settings highlight that transit services can help reduce the total
system-wide distance in urban delivery operations and reduce negative externalities. This integrated scheme has a high potential for distance savings, especially with short delivery deadlines
in congested cities. Below we go into more detail on the results achieved in each setting.

3.1

A single line setting

Table 1 shows the main indicators of the base case. On average half of the customers are served
Table 1 – Baseline results of single line

minµmax% Customer via Transfer
2254.278.0

TRISTAN XI Symposium% Savings
1.2
4.9
7.1

Transfer Location
23L

Original abstract submittalIrecis Azcuy, Ricardo Giesen, and Niels Agatz

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via the transfer station. In terms of savings from using public transit, we see average distancesavings of 4.9% and up to 7.1%. We note that the transfer location coincides with the analyticalresults in which we simplified the routing.
Next, we perform a sensitivity analysis of different parameters. We vary the capacity of thelast-mile vehicles because it would be beneficial to use smaller, low- or zero-emission last-milevehicles at the transfer station. The results suggest that using the transfer station may not be
profitable, and the average savings drop from 4.9 to 2% as the capacity decreases.
We also vary depot location. As expected, when the depot is located farther away from thedelivery zone, the savings are as high as 36.2%.
In addition, we study the impact of the number of customers in the service area. The results
suggest that as the number of customers increases, savings decrease. One of the reasons is that as
the number of customers increases, the more the last mile vehicle travels throughout the region,similar to the case of direct shipments. Next, we look for different customer cluster around thetransit line. As expected, the savings are higher compared to the base case when customers areclose to the transit line.
Finally, we checked the impact of tight delivery deadlines. We observe that as deadlines
become tighter, savings increase when the last mile vehicle is slower than the transit vehicle(sl < st ) and decrease in the opposite case (sl > st ).

3.2

A fork line setting

Table 2 reports our key findings for the base case.
Table 2 – Base case results over 50 instances. Mean values next the deviation in parenthesis.

Total Transfer stations% Customer via Transfer
Cost per order% Cost Savings

1h5
44.1 (9.5)
10.7 (0.1)
1.5 (0.4)2h874.9 (4.5)
2.7 (0.1)
11 (1.3)

8h3
79.4 (1.4)
0.8 (0.1)
7.8 (2)24 h276 (0)0.6 (0.1)
6.6 (0.1)

Overall, we see that as deadlines become small, a lower percentage of customers are served
from a majority of transfer stations to the point that shipping via public transport is not as
profitable, so both indicators decrease. As expected, tight deadlines increase the average cost
per order, because fewer customers are consolidated per trip.In comparison to the case withouttransfer stations, we see that savings also increase until moving freight by public transport does
not provide benefits and then decrease.
Next, we perform a sensitivity analysis of the base case. We evaluate more sustainable lastmile vehicles at transfer stations such as electric vehicles, cargo bikes, and cargo motorcycles. We
assume the same congested network, but we set the cargo bikes to travel at 20 km/h, assuming
they operate in bike lanes. It costs approximately 0.02 $/km for electric vehicles and cargo bikes
and 0.0027 $/km for cargo motorbikes. The capacity per trip is 262, 91 and 8 customers forelectric vehicles, cargo bike and cargo motorbike, respectively.
The results indicate that small vehicles in transfer stations reduce the number of transferstations. This result is different from the single line setting. The reason is that in a fork line
setting, the last-mile vehicles in the transfer station are more profitable than those in the depot.
Furthermore, cost-effective vehicles allow traveling more distance from the transfer stations.
As expected, the percentage of customers decreases as the deadline decreases. Interestingly, itincreases sharply for cargo motorbikes when deadlines are very tight, because capacity no longer
constrains more than deadlines. In terms of savings, we see that small and cost-effective vehicles
available at the transfer station can provide further savings. The savings decrease with very
tight deadlines. Still, using dedicated transit lanes followed by bike lanes can provide savings up
TRISTAN XI Symposium

Original abstract submittalIrecis Azcuy, Ricardo Giesen, and Niels Agatz

4to nearly 42 %.
We study how sensitive the cost savings is to transit frequency, transit speed and transit
network branch point. Overall, we see that savings increase with better transit service performance, i.e. high operating frequency, higher transit speed or a branch point further away fromthe transit terminal. We summarize this results in Figure 1.
Diesel vehicle

electric vehicle

motorbikecargo bike

202530152020

1010500%%%

4015105 1015202530354045505560
Transit frequency in vehicles/h(a) Transit speed

50.50.60.70.80.9 1 1.11.21.31.41.5
Speed ratio α = sstl(b) Transit frequency

0L3

L
22L3L

Branching point(c) Transit branching point

Figure 1 – Impact on the cost savings, averaged over 50 random instances.
In a practical context, potential customers could cluster around the transit line. Furthermore,
the average customer density, the operating cost of each transfer station, and the cost of eachrequired last-mile vehicle could change. To test the impact of these situations, we perform further sensitivity analyses. The key insights about using a transit line to support urban delivery
operations are as follow.
■ The savings increase with customers clustered close to the transit line, similar to the singleline setting.
■ The savings decrease as customer density increase with time flexibility, but increase in tightdeadline situations until it is no longer possible to efficiently move many orders from thetransfer stations and so the trend is downward.
■ As the operating costs of transfer stations become expensive, fewer transfer stations areopened, lower percentage of customers are served via them and savings from using transferstations decrease.
■ The savings can be greater than the base case, if last mile vehicle costs are low, and evenoutweigh the higher costs as a result of very tight deadlines. Otherwise, the higher thevehicle cost, the lower the savings.

4REFERENCES

References
Azcuy, Irecis, Agatz, Niels, & Giesen, Ricardo. 2021. Designing integrated urban delivery systems using
public transport. Transportation Research Part E: Logistics and Transportation Review, 156, 102525.
Beardwood, Jillian, Halton, John H, & Hammersley, John Michael. 1959. The shortest path throughmany points. Pages 299–327 of: Mathematical Proceedings of the Cambridge Philosophical Society,vol. 55. Cambridge University Press.
Citizen, Islington. 2021. Residents complain of noise nuisance from ‘dark store’ warehouse on pedestrianised alley.
Dablanc, Laetitia, Ogilvie, Scott, & Goodchild, Anne. 2014. Logistics sprawl: differential warehousingdevelopment patterns in Los Angeles, California, and Seattle, Washington. Transportation Research
Record, 2410(1), 105–112.

TRISTAN XI Symposium

Original abstract submittal