The time-dependent two-echelon capacitated vehicle routing problem with
environmental considerations
Keeping large vehicles away from congested areas allows to reduce the environmental
externalities of freight distribution (e.g., energy usage and congestion), and to improve the
social consequences of such activities (e.g., traffic-related air pollution, accidents and noise).
Multi-echelon distribution strategies in which freight is delivered to customers via
intermediate depots rather than direct shipments from the origin can be used to alleviate
burden of large vehicles on traffic.
We addressed a time-dependent two echelon capacitated vehicle routing problem (2E-CVRP)
that consists of a depot, and a set of satellites and customers. In two-echelon distribution
systems, large trucks are used to transport freight over long-distances to satellites where
consolidation takes place; afterwards, the products are transferred to destination points using
small and environmentally-friendly vehicles. In our problem, time-dependent travel times are
considered to account for traffic congestion effects when traveling on the defined arcs in the
second-echelon. The objective of the basic 2E-CVRP is to determine two sets of first and
second echelon routes that minimize total routing and satellite handling cost. Routing cost
includes that of driver and fuel consumption, calculated for each arc in the network.
We developed a comprehensive MILP formulation for a time-dependent 2E-CVRP that
accounts for vehicle type, traveled distance, vehicle speed, load, emissions and multiple time
zones that may occur during the planning horizon. To the best of our knowledge, this was the
first attempt to develop a mathematical model for the time-dependent 2E-CVRP with an
explicit consideration of fuel consumption through the use of a comprehensive emission
function. A case study was provided to present an implementation of the proposed model on
the distribution operations of a supermarket chain operating in the Netherlands. We focused
on four KPIs: total distance, total time, total fuel consumption, and total cost. The proposed
model was minimized over each Key Performance Indicator.
Findings
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The resulting routes and the performances of the solutions with respect to the KPIs
change according to the variation of the model.
The traditional objectives of distance and time minimization did not ensure
minimization of fuel consumption or cost.
The comprehensive cost-minimizing objective, which breaks away from the traditional
objective functions used in the 2E-CVRP by a detailed estimation of fuel
consumption, could achieve average savings in total cost by 6.9%. In particular, the
cost-minimizing objective outperformed the traditional approaches based on only
distance or time while estimating distribution cost. The respective saving is 12%
compared to the distance-minimizing objective and 4% compared to the time
minimizing-objective. However, the cost minimizing objective did not guarantee the
best solution in terms of emissions.
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The use of fuel-minimizing objective could ensure the most environmentally-friendly
solution by reducing total fuel consumption on average 2.5% in return for a cost
increase of 10.8%.
The sensitivity analyses revealed that the performances of the variations of the model
on the selected KPIs changed according to the handling fee in the satellites and
demand of the customers.
For our case study, the most environmentally-friendly solution was obtained by the
use of a two-echelon distribution system, although a single-echelon distribution
system provides a solution with lower total cost.
The proposed model also give users the opportunity to exploit the trade-offs among
sustainability KPIs through using different objectives.
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