A Data-Driven Routing and Scheduling Approach for Activity-Based
Freight Transport Modelling
Ali Nadia,*, Neil Yorke-Smithb, J.W.C Van Linta, Lóránt Tavasszya, Maaike Sneldera,caDepartment of Transport and Planning, TU Delft, Delft, The Netherlands
a.nadinajafabadi@tudelft.nl, J.W.C.vanLint@tudelft.nl, L.A.Tavasszy@tudelft.nlbElectrical Engineering, Mathematics and Computer Science, TU Delft, Delft, The Netherlands
N.Yorke-Smith@tudelft.nlcTNO, Den Haag, The Netherlands
M.Snelder@tudelft.nl* Corresponding author

Extended abstract submitted for presentation at the 11th Triennial Symposium on
Transportation Analysis conference (TRISTAN XI)
June 19-25, 2022, Mauritius Island

Keywords: Activity-Based Freight Modelling, Baysian Optimization, Data-Driven Vehicle
Routing Problem

1

INTRODUCTION

Truck flow patterns can best be understood through the study of freight activities on a transportation
network (Tavasszy and De Jong, 2013). These activities are often observable after the execution of
tours resulting from a routing and scheduling optimization process, where the traditional Capacitated
Vehicle Routing Problem (CVRP) is used to minimize multiple objectives under spatial, temporal,
and vehicle constraints. Researchers have put forward in recent years that there should be
distinctions between freight and passenger transport modelling due to the complexity associatedwith logistics (Gonzalez-Calderon and Holguín-Veras, 2019). The most important distinction is to
involve the tour behaviour of carriers considering all spatial and temporal constraints (You et al.,2016). In current tour-based models, tours are constructed through incremental trip chaining in sucha way that the next destination in a tour is estimated based on the conditional probability of thecurrent stop. These types of models are based on choice modelling and provide statistical agencies
with descriptive statistics and insights into freight demand. However, discrete choice methods are
not subject to constraints and therefore cannot capture spatial-temporal characteristics of tours(Heinitz and Liedtke, 2010). Additionally, trip chaining decisions are made once at the tactical level
and hence incremental reconstruction of the tour at the operational level is not identical to the tour
planning process in reality.
To deal with this problem, micro-simulations have used a family of vehicle routing problems tomodel the pickup and delivery of carriers within a multi-agent microsimulation framework(Donnelly et al., 2010). Although normative models can perfectly capture space-time constraints,
their outcome could deviate from observed tours due to heterogeneity in the tour planning decisionsof planners. Hence, You et al. (2016) proposed an inverse optimization approach to calibrate a familyof VRP using the method of successive averages. They estimate the weights of a weighted sum ofmultiple objectives from a set of observed tours. Parameter estimation of these methods requires
fully observed truck movement patterns. However, tour data, if available, are often partiallyavailable to traffic agencies and policymakers due to privacy issues. To the best of our knowledge,
the development of a method to calibrate the VRP model based on shipment flows with partially
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2

observed tour data has not yet been explored and is therefore of interest . To address this gap in theliterature, we propose an efficient Bayesian optimization method to calibrate a VRP model based onpartially observed tour information.

2

Activity-Based Freight Tour Modelling Framework

In this paper, we propose a disaggregate simulation-based optimization framework to model tour
activities. In this framework, we begin with the available goods for pickup or delivery at each traffic
analysis zone for each carrier. This could come from a freight generation model or available
shipment flow data. Then, for all carriers, we simulate a parametrized capacitated vehicle routing
problem so that all the available goods in the network are transported at the end of the planninghorizon (e.g., one day). Afterwards, the planned tours are decomposed into trips and all trip
characteristics are derived. The parameters of the model are updated through a surrogate-based
optimization technique to minimize the difference between estimated and observed tour
characteristics, such as the total tour travel times, travel costs, departure times, and arrival times. To
solve this problem, we define a general approximation of the various type of VRPs with a weighted(β) sum of objectives Z in Equation 1:
minzβ xijm =min ∑Ll=1 βl zl =βT Z(1)xwhere 𝑥 is the binary route decision variable where its elements are 1 if a vehicle visits location jafter i in time interval m. Depending on the available data and the aim of the study, the modeller
can define various objectives for the calibration. In this study, we only use capacity constraints for
the VRP formulation. We adopted a compact form of a standard three-index formulation of the
pickup and delivery problem proposed by Furtado et al. (2017). We formulate our objectives asfollows:m
z1 = ∑m∈M ∑i∈V ∑j∈V t m(2)
ij x ijz2 = ∑m∈M ∑i∈V ∑j∈V cij xijm

(3)

Z1 and Z2 in Equations 2 and 3 are two cost functions that minimize the total tour travel time anddistance-related costs respectively, and Z2 and Z4 are the disutility of a firm to visit a location anddisutility of a specific commodity being transported between locations i and j. All typical VRP
constraints like capacity and conservation of flow and sub tour elimination constraints are used as
proposed in the study of Furtado et al. (2017). For the calibration of this general approximation of
CVRP, we solve the CVRP iteratively for each firm minimizing a loss function. This loss function
includes the deviation between the estimated and observed tour cost, time, start time, and end time
for all firms. This loss function is defined in Equation 4.
min ∑ 𝐽(𝜃) = 𝑚𝑖𝑛(4)
Since the CVRP is computationally expensive and we must solve it repeatedly, a regular
optimization algorithm cannot be easily used. Surrogate-based algorithms are a class of optimization
methods that can find the minimum of functions that are expensive to evaluate. Such an algorithm
works in the following steps:
1- Initialization: Generate n initial Θ={θ1,θ2,…,θn} parameters for the CVRP model of eachcarrier using Latin hypercube sampling. In our case, we started with three samples.
2- Evaluation: For each parameter setting, solve the CVRPΘ and evaluate the loss function.
3- Surrogate construction: Fit a surrogate surface f to the evaluated samples using a
Multivariate Gaussian process with mean μ and covariance Σ.
f(Θ)~N(μ,Σ)(5)
4- Search for minimum: Find the minimum of the surface interpolated for the sample ofparameters.

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3(6)θmin =argminf(θ)θ∈Θ

5- Next evaluation point: the next evaluation point θ* in parameter space is where the expected
improvement (EI) measure is maximum.
EI(θ* )=E[max(f(θmin )-f * (θ),0)](7)
where 𝑓(𝜃 ) is the average stochastic prediction at point θmin
6- Update the surrogate surface: With the new parameter θ*, we update the covariance matrix
and consequently the surrogate surface. The process iterates until the stopping criteria.

3

Results and findings from model calibration

In the Netherlands, the Central Bureau for Statistics (CBS) has digitally collected over 2.7 million
records of shipments across the country for the year 2015. After data pre-processing, a set of 3,629
tour activities of the 10 largest carriers are selected for this study. All tours together visit, on average,
86 zones on a planning day. The loading/ unloading and handling time at each visiting location is
proportionally distributed (based on weight and number of commodities) over visited locations andis randomly drawn from an exponential distribution. The parameters of this distribution are
estimated from a sample of data. Three parameters are estimated for each feature based on thedeparture time of the trips, i.e., morning, noon, and afternoon. The model run time was 238 minutes
for calibration and simulation of the tours. The surrogate optimizer stopped on the optimality gap
after 20 iterations and 87 function evaluations. Table 1 shows the estimated parameters of the VRP
model.

Table 1 –Estimated parameters of the model for different departure time intervals
Param
θ βc
θ βt
θ βUC
MAPE
R2

Morning (6:00-11:00)
estimates
Std
5.76
1.2e-30.098
1.4e-8-7.2
1.5e-68.7%
0.86

Noon (11:00-15:00)
estimatesstd
4.293
4.38e-5
0.08193.29e-4-7.66
1.3e-54.8%
0.91

Afternoon (15:00-20:00)
estimatesstd
6.631
2.56e-2
0.107
1.3e-2-5.89
1.7e-418.1%
0.83

The most salient findings go to the interpretation of cost (θ βc), time (θ βt), and capacity utilization ofvehicles (θ βUC). Comparing tour preferences of carriers in different time intervals shows that travel
time and cost are more important when carriers start a tour in the afternoon period. This means thatcarriers are likely to plan a shorter tour in distance with less total tour travel time. One possible
reason for this is that carriers should reach the customers before the closing hours. On the contrary,
the magnitude of the cost and time parameters for the noon period is relatively lower. This meansthat carriers are likely to make longer trips or plan tours with longer total tour travel times.
Interestingly, the value of the capacity utilization parameter is also lower for the tours starting in theafternoon meaning that it is more likely to have less-than-truckload trips in the afternoon. The model
estimates on average 42 minutes of (un)loading handling time using a bounded exponential
distribution (minimum bound of 20 minutes). Drivers’ break times are estimated together with thehandling time. Our dataset does not report on the time and location of drivers’ breaks but reports on
the total tour duration. Therefore, the model can only capture these extra times along with the service
time of each zone. The MAPE ranges between 8.7% and 18.1% with the maximum belonging to theafternoon mode and the correlation coefficient R2 is 0.86, 0.91 and 0.83 for the morning, noon andafternoon respectively. These measurements confirm the overall good performance of the model.
The tour distance and number of stop distributions are two important aggregate features that should
be captured well by tour models. We grouped tour distances into different clusters and compared the

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4estimated tour distance distribution with the observations in Figure 1. The results show that themodel can approximate this feature reasonably well. It is noticeable that the model generates local
tours (distance <50km) more frequently as compared to the observations. Similarly, we can see thatthe model captures the general pattern in the frequency of tours with different numbers of stops. In
general, it can be concluded that tours with a smaller number of stops are slightly overestimated.

Figure 1 – Estimated vs. observed tour distance and number of stops

4

DISCUSSION

In this concluding section, we discuss the ability and limitations of the proposed model. Estimatinga general tour model which can represent the collective tour activities of large carriers can become
an undetermined problem especially when a limited imperfect amount of disaggregated data isavailable. Researchers have been dealing with these problems in transportation science for decades.
The performance and accuracy of models in these cases depend largely on the amount of priorinformation used to help the model converge to the real behaviour of road users. Our proposed
method shows that additional, although imperfect, tour information like tour duration, cost, start
time, and end time can provide a robust and accurate estimation of a single tour model withmeaningful parameters that can reproduce the preferences of carriers in planning tours. Developing
such models with effective algorithms for robust estimation of model parameters is therefore
essential due to the fact that perfect data are not always available to the public traffic sectors. This
tool can also be used to understand the impact of freight activities on the traffic system. This isbecause the activities resulting from this model can be easily translated into a time-dependent truck
OD table which can be coupled with a traffic simulation model. This could provide interesting
insights into the interrelation between logistics and traffic. We also recommend a comparison study
to examine the accuracy of our model among other tour models.

Acknowledgments
We thank the TRISTAN XI reviewers. This work was supported by the Dutch Research Council(NWO), TKI Dinalog, Commit2Data, Port of Rotterdam, SmartPort, Portbase, TLN, Deltalinqs,
Rijkswaterstaat, and TNO under project ‘ToGRIP-Grip on Freight Trips’ with grant number
628.009.001, and also partially supported by TAILOR, a project funded by EU Horizon 2020
research and innovation program under grant number 952215. The authors thank CBS and
Rijkswaterstaat for providing shipment data and travel time matrices, respectively.

References
Donnelly, R., Wigan, M. & Thompson, R. 2010. A hybrid microsimulation model of urban freight
travel demand. Transportation Research Board.
Furtado, M. G. S., Munari, P. & Morabito, R. 2017. Pickup and delivery problem with time
windows: a new compact two-index formulation. Operations Research Letters, 45, 334-341.
Gonzalez-Calderon, C. A. & Holguín-Veras, J. 2019. Entropy-based freight tour synthesis and therole of traffic count sampling. Transportation Research Part E: Logistics andTransportation Review, 121, 63-83.
Heinitz, F. M. & Liedtke, G. T. 2010. Principles of Constraint–Consistent Activity‐Based Transport
Modeling. Computer‐Aided Civil and Infrastructure Engineering, 25, 101-115.
You, S. I., Chow, J. Y. & Ritchie, S. G. 2016. Inverse vehicle routing for activity-based urban freight
forecast modeling and city logistics. Transportmetrica A: Transport Science, 12, 650-673.
TAVASSZY, L. & DE JONG, G. 2013. Modelling freight transport, Elsevier.

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