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

A new constraint programming model and a linear programming-based  adaptive large neighborhood search for the vehicle routing problem with  synchronization constraints