EU/ME 08, Troyes, 23th October – 24th October 2008
Adaptive Large Neighbourhood Search
for the Vehicle Routing Problem with
Drivers’ Working Hours
Asvin Goel
MIT-Zaragoza International Logistics Program
Zaragoza Logistics Center
[email protected]
Drivers’ working hours
 New EC regulation 561/2006 entered into force in April 2007
 Shippers and carriers can be made liable for infringements
committed by the drivers
 Carriers must organise the work of drivers in such a way
that drivers are able to comply with the respective
regulations
Provisions of EC regulation 561/2006
1. After a driving period (i.e. the accumulated driving time
between subsequent breaks and rest periods) of 4½ hours
a driver shall take an uninterrupted break of not less than
45 minutes, unless she/he takes a rest period.
2. The daily driving time (i.e. the accumulated driving time
between the end of one daily or weekly rest period and
the beginning of the following daily or weekly rest period)
shall not exceed 9 hours. A regular daily rest period is any
period of rest of at least 11 hours.
Provisions of EC regulation 561/2006
(continued)
3. Within each period of 24 hours after the end of the
previous daily rest period a driver shall have taken a new
daily rest period.
4. The weekly driving time (i.e. the accumulated driving time
during a week) shall not exceed 56 hours.
5. A weekly rest period shall start no later than 144 hours
after the end of the previous weekly rest period.
Examples

A time constrained example with alternative schedules:
Further provisions of EC regulation 561/2006
(not considered in the remainder)
6. The daily driving time may be extended to at most 10
hours not more than twice during the week.
7. The daily rest period may be reduced to 9 hours not more
than 3 times during the week.
8. The break may be replaced by a break of at least 15
minutes followed by a break of at least 30 minutes.
9. The daily rest period may be taken in two periods, the first
of which must be an uninterrupted period of at least 3
hours and the second an uninterrupted period of at least 9
hours.
Extended daily driving times and reduced daily
rest periods
 In case of delays extended daily driving times and reduced
daily rest periods can be used to repair otherwise infeasible
schedules:
Splitting up regular breaks

EC regulation 561/2006 explicitly states the following
reason for replacing the old regulation:
It has proved possible under the rules of Regulation (EEC)
No 3820/85 to schedule daily driving periods and breaks to
enable a driver to drive for too long without a full break,
leading to reduced road safety and a deterioration in the
driver’s working conditions.

For t ! 0 the goal of the new regulation is not
achieved!!!
Naïve method for scheduling with drivers
working hours
Drive as long as possible
Stop if destination is reached
Add daily rest period if required
Add break
Naïve method for scheduling with drivers
working hours (continued)
 Let n be the first node in tour
 Repeat while n is not last node in tour
• Determine labels for successor node of n using the naïve
method
• If there is enough slack between arrival and begin of
time window add break or rest period
• Set n à successor node of n
Limitations of naïve method
found by naïve
method
Not found by
naïve method
Multi-label method for scheduling with drivers
working hours
Drive as long as possible
Add label if destination is reached
Add daily rest period if required
Generate new label with additional rest period
Add break
Recursively call method to expand new label
Multi-label method for scheduling with drivers
working hours (continued)
 Let n be the first node in tour
 Repeat while n is not last node in tour
• Determine all labels for successor node of n using the
multi-label method
• Copy each label calculated by the multi-label method and
add optional break and rest period
• Delete all “dominated” labels
• Set n à successor node of n
Naïve vs. Multi-label method
found by naïve
method
found by multilabel method
Include provisions not considered thus far

So far provision 3 has not been considered:
Within each period of 24 hours after the end of the previous daily rest
period a driver shall have taken a new daily rest period.

Increase duration of rest periods in order to make sure
that all daily rest periods are completed within the 24 hour
limit (not always possible!!!)
Large Neighbourhood Search
 Initialisation:
• Find an initial solution s
• choose a stopping condition
 Repeat the following until the stopping condition is met:
• Choose a number k
• Until k customers are removed from their tour repeat:
– Randomly choose a customer n to be removed
– Remove customer n from its tour if naïve or multi-label method
for scheduling drivers’ working hours finds a feasible solution
• Apply an insertion method to re-insert all removed customers
• If all customers are re-inserted and the modified solution s’ has
lower costs than the current solution s set s := s’
Concluding Remarks
 Drivers’ working hours have significant impact on total travel
times
 Carriers can be made liable for infringements committed by
the drivers
 Labelling methods can be used to generate tours complying
with the new regulations
 Computational experiments have shown that LNS based on
multi-label approach significantly outperforms LNS based on
naïve method for scheduling drivers’ working hours
 Current and future research will study how to remove
customers more effectively, in particular for PDP-DWH
Thank you!
Merci!
Asvin Goel
MIT-Zaragoza International Logistics Program
Zaragoza Logistics Center
[email protected]