Branch and Price for the Time-Dependent Vehicle Routing Problem with Time Windows

Abstract

This paper presents a branch-and-price algorithm for the time-dependent vehicle routing problem with time windows (TDVRPTW). We capture road congestion by considering time-dependent travel times, i.e., depending on the departure time to a customer, a different travel time is incurred. We consider the variant of the TDVRPTW where the objective is to minimize total route duration and denote this variant the duration minimizing TDVRPTW (DM-TDVRPTW). Because of time dependency, vehicles' dispatch times at the depot are crucial as road congestion might be avoided. Because of its complexity, all known solution methods to the DM-TDVRPTW are based on (meta-)heuristics. The decomposition of an arc-based formulation leads to a set-partitioning problem as the master problem, and a time-dependent shortest path problem with resource constraints as the pricing problem. The master problem is solved by means of column generation, and a tailored labeling algorithm is used to solve the pricing problem. We introduce new dominance criteria that allow more label dominance. For our numerical results, we modified Solomon's data sets by adding time dependency. Our algorithm is able to solve about 63% of the instances with 25 customers, 38% of the instances with 50 customers, and 15% of the instances with 100 customers.

A hybrid metaheuristic for the time-dependent vehicle routing problem with hard time windows

“…An exact algorithm for the TDVRPTW was presented by Dabia, Ropke, Van Woensel, and De Kok (2013) using a modified set of the well-known instances of Solomon (1987) for the VRPTW. Speed patterns in links between nodes were allocated randomly and the solution approach was based on a pricing algorithm utilising a column generation and a labelling algorithm.…”

A Survey of Recent Research on Optimization Models and Algorithms for Operations Management from the Process View

“…Except software package service as programming solver, MP-based approaches observed in the field of three targeted fields are as follows: Branch-and-Bound [34], Branch-and-Cut [146], Branch-and-Price [219], Branch-and-Cut-and-Price [142], Dynamic Programming [220], Lagrangian Relaxation [221], Column Generation [222], Set Partitioning [223], Constraint Programming [224], Goal Programming [225], Set Covering [226], and so forth. As shown in Table 1, it can be observed that the most frequently used mathematical programming-based method in the field of scheduling is B&B (Branch-and-Bound), while B&P (Branch-and-Price) is the most popular branching method in the field of VRP.…”

Dynamic Vehicle Scheduling for Working Service Network with Dual Demands

“…It was formulated as an integer programming model to minimize makespan of the whole discharging course and solved by a two stages tabu search algorithm. Dabia et al [4] presented a branch and price algorithm for time-dependent vehicle routing problem with time windows. Han et al [5] considered a vehicle routing problem with uncertain travel times in which a penalty is incurred for each vehicle that exceeds a given time limit and given robust scenario approach for the vehicle routing problem.…”