A dynamic programming heuristic for vehicle routing with time-dependent travel times and required breaks

Abstract

For the intensively studied vehicle routing problem (VRP), two real-life restrictions have received only minor attention in the VRP-literature: traffic congestion and driving hours regulations. Traffic congestion causes late arrivals at customers and long travel times resulting in large transport costs. To account for traffic congestion, time-dependent travel times should be considered when constructing vehicle routes. Next, driving hours regulations, which restrict the available driving and working times for truck drivers, must be respected. Since violations are severely fined, also driving hours regulations should be considered when constructing vehicle routes, even more in combination with congestion problems. The objective of this paper is to develop a solution method for the VRP with time windows (VRPTW), time-dependent travel times, and driving hours regulations. The major difficulty of this VRPTW extension is to optimize each vehicle's departure times to minimize the duty time of each driver. Having compact duty times leads to cost savings. However, obtaining compact duty times is much harder when time-dependent travel times and driving hours regulations are considered. We propose a restricted dynamic programming (DP) heuristic for constructing the vehicle routes, and an efficient heuristic for optimizing the vehicle's departure times for each (partial) vehicle route, such that the complete solution algorithm runs in Computational experiments demonstrate the trade-off between travel distance minimization and duty time minimization, and illustrate the cost savings of extending the depot opening hours such that traveling before the morning peak and after the evening peak becomes possible.

Optimizing practical orienteering problems with stochastic time-dependent travel times: towards congestion free routes

“…The choice to apply this commercial solver to the MILP of the TD-OP was motivated by the fact that commercial solvers like CPLEX and Gurobi are known to be very effective in tackling this kind of problems. We refer to the exact solution methods of [6,46,67] for variants of the OP and CPLEX is also used for vehicle routing problems in a time-dependent context by Kok et al [79]. The restriction of 48 hours (!)…”

“…They achieved improvements of up to 47% reduction in perished goods. Kok et al [79] presented a heuristic based on dynamic programming for TD-VRP while considering driving hour regulations. Kuo [81] studied a variant of TD-VRP aiming to minimize the total fuel consumption.…”

A metaheuristic for the time-dependent vehicle routing problem considering driving hours regulations – An application in city logistics

“…After this first formulation, a number of variants that introduce additional constraints have been proposed in the literature. Variants account for conditions that are present in logistics operations such as the following: i) time windows, where customers expect delivery within a specific period of time (VRPTW) (Solomon, 1987); ii) time-dependent travel time, where the time spent travelling between locations varies according to the departure time due to congestion (TDVRP) (Figliozzi, 2012); iii) driving hours regulations that limit the amount of hours that can be driven in a day and during a continuous period (VRP-EC) (Kok, Hans, Schutten, & Zijm, 2010).…”

Hybrid simulation and optimization approach for green intermodal transportation problem with travel time uncertainty

“…Therefore, the reliability of transportation plans is progressively considered as a key performance indicator for logistics service providers and freight forwarders. A direct consequence of this changed operating environment is increasing awareness for the new developments in OR literature, such as modeling travel time uncertainties (see e.g., Noland and Small 1995;Gendreau et al 1996;Kok et al 2010).…”