  We consider a vehicle routing problem which seeks to minimize cost subject to
time window and synchronization constraints. In this problem, the fleet of
vehicles is categorized into regular and special vehicles. Some customers
require both vehicles' services, whose starting service times at the customer
are synchronized. Despite its important real-world application, this problem
has rarely been studied in the literature. To solve the problem, we propose a
Constraint Programming (CP) model and an Adaptive Large Neighborhood Search
(ALNS) in which the design of insertion operators is based on solving linear
programming (LP) models to check the insertion feasibility. A number of
acceleration techniques is also proposed to significantly reduce the
computational time. The computational experiments show that our new CP model
finds better solutions than an existing CP-based ANLS, when used on small
instances with 25 customers and with a much shorter running time. Our LP-based
ALNS dominates the cp-ALNS, in terms of solution quality, when it provides
solutions with better objective values, on average, for all instance classes.
This demonstrates the advantage of using linear programming instead of
constraint programming when dealing with a variant of vehicle routing problems
with relatively tight constraints, which is often considered to be more
favorable for CP-based methods.
