On the exact solution of vehicle routing problems with backhauls

Abstract

In this paper, we are interested in the exact solution of the vehicle routing problem with backhauls (VRPB), a classical vehicle routing variant with two types of customers: linehaul (delivery) and backhaul (pickup) ones. We propose two branch-cut-and-price (BCP) algorithms for the VRPB. The first of them follows the traditional approach with one pricing subproblem, whereas the second one exploits the linehaul/backhaul customer partitioning and defines two pricing subproblems. The methods incorporate elements of state-of-the-art BCP algorithms, such as rounded capacity cuts, limited-memory rank-1 cuts, strong branching, route enumeration, arc elimination using reduced costs and dual stabilization. Computational experiments show that the proposed algorithms are capable of obtaining optimal solutions for all existing benchmark instances with up to 200 customers, many of them for the first time. It is observed that the approach involving two pricing subproblems is more efficient computationally than the traditional one. Moreover, new instances are also proposed for which we provide tight bounds. Also, we provide results for benchmark instances of the heterogeneous fixed fleet VRPB and the VRPB with time windows.

Multi-Depot Pickup and Delivery Problem with Resource Sharing

“…e MDVRPPDTW is an extension of MDVRPPD, which considers the characteristics of customer service time windows [46,47]. Many scholars have studied MDVRPPD and MDVRPPDTW considering diverse aspects and proposed different mathematical models and algorithms [30,48]. In terms of models, many of the proposed mathematical models reflect the characteristics of their problem studied by different constraints, including capacity, time windows, and priority constraints [29,49].…”

Estimating optimal objective values for the TSP, VRP, and other combinatorial problems using randomization

“…Since we observe good performance from our model, we extend this experiment to all 10,000 instances with known optimal solutions introduced by Queiroga et al. (2021). Additionally, we note from Table 4 that considering more savings can, in general, result in worse VRP heuristic solutions on average.…”

“…To understand the relationship between the mean and standard deviation of feasible heuristic solution values and $$D$$, we consider instances from the VRP study by Queiroga et al. (2021). We use 162 instances from the set with names starting with XML_100_111.…”

“…Details of instance formulation can be found in Queiroga et al. (2021). The key point here is that although instances in this dataset share some similarities, they differ greatly in depot and customer distribution, demand, and average route size.…”

Heuristics for Vehicle Routing Problem: A Survey and Recent Advances

“…11, we list in Table 1 some representative ones, together with their detailed configurations with respect to different algorithm components. It should be noted that we are far from being able to review all the SOTA methods, such as the works on exact methods [18,19,254,22,148,230,160] and those for routing problems with other attributes [84], but by "representative" we suppose the included methods are enough to shed light on the success of SOTA methods, which we summarize as follows:…”