Abstract: In this article, we define a new routing problem that arises in the last-mile delivery of parcels, in which customers can be served either directly at home by a capacitated truck, or possibly with a drone carried on the truck, or in a self-service mode using one of the available lockers. We investigate four different formulations, and for one of them, we propose a branch-and-cut approach. We also discuss some possible variants of the original problem. In the computational experiments, we analyze and compare the performance of the four formulations for the problem and its variants, and we provide some useful managerial insights.

Abstract: We consider nonatomic routing games with one source and one destination connected by multiple parallel edges. We examine the asymptotic behavior of the price of anarchy as the inflow increases. In accordance with some empirical observations, we prove that under suitable conditions on the costs the price of anarchy is asymptotic to one. We show with some counterexamples that this is not always the case, and that these counterexamples already occur in simple networks with only 2 parallel links.

Abstract: This paper investigates the dynamic stability of an adaptive learning procedure in a traffic game. Using the Routh-Hurwitz criterion we study the stability of the rest points of the corresponding mean field dynamics. In the special case with two routes and two players we provide a full description of the number and nature of these rest points as well as the global asymptotic behavior of the dynamics. Depending on the parameters of the model, we find that there are either one, two or three equilibria and we show that in all cases the mean field trajectories converge towards a rest point for almost all initial conditions.

Abstract: We study the Vehicle Routing Problem with Probabilistic Customers (VRP-PC), a two-stage optimization model, which is a fundamental building block within the broad family of stochastic routing problems. This problem is mainly motivated by logistics distribution networks in which customers receive frequent delivery services, and by the last mile problem faced by companies such as UPS and FedEx. In a first stage before customer service requests realize, a dispatcher determines a set of vehicle routes serving all potential customer locations. In a second stage occurring after observing all customer requests, vehicles execute planned routes skipping all locations of customers not requiring service. The objective is to minimize the expected vehicle travel cost assuming known customer realization probabilities. We propose a column generation framework to solve the VRP-PC to a given optimality tolerance. Specifically, we present two novel algorithms, one that under -approximates a solution's expected cost, and another that uses its exact expected cost. Each algorithm is equipped with a route pricing mechanism that iteratively improves the approximation precision of a route's reduced cost; this produces fast route insertions at the start of the algorithm and reaches termination conditions at the end of the execution. Compared to branch-and-cut algorithms for arc-based formulations, our framework can more readily incorporate sequence-dependent constraints, which are typically required in routing problems. We provide a priori and a posteriori performance guarantees for these algorithms, and demonstrate their effectiveness via a computational study on instances with realization probabilities ranging from 0.5 to 0.9.

Abstract: We develop a heuristic for the consistent vehicle routing problem with time windows (ConVRPTW), which is motivated by a real-world application at a food company's distribution center. Besides standard VRPTW restrictions, ConVRPTW assigns each customer just one driver to fulfill his or her orders during the whole multiperiod planning horizon. For each driver and period, a route is sought to serve all their customers with positive demand. For each customer, the number of periods between consecutive orders and the ordered quantities is highly irregular. This causes difficulties in the daily routing, negatively impacting the service level of the company. Similar problems have been studied as ConVRP, where the number of drivers is fixeda priori, and only the total travel time is minimized. Moreover, the clients present no time window constraints, but the visits should be scheduled with a small arrival time variation. In our model, the objective is to minimize the number of drivers. We impose hard time windows but do not consider time consistency in more detail. We compare solutions given by the heuristic with solutions of a mixed-integer linear programming model on a set of small artificial instances and solutions used by the food company on real-world instances. The results show the effectiveness of the heuristic. For the company, we obtain significant improvements in the routing plans, with a lower number of vehicles and a higher rate of orders delivered within the prescribed time window.

Abstract: This paper studies the impact of demand-prioritization on Space-Division Multiplexing Elastic Optical Networks (SDM-EON). For this purpose, we solve the static Routing, Modulation Level, Spatial Mode, and Spectrum Assignment (RMLSSA) problem using 34 different explainable demand-prioritization strategies. Although previous works have applied heuristics or meta-heuristics to perform demand-prioritization, they have not focused on identifying the best prioritization strategies, their inner operation, and the implications behind their good performance by thorough profiling and impact analysis. We focus on a comprehensive analysis identifying the best explainable strategies to sort network demands in SDM-EON, considering the physical-layer impairments found in optical communications. Also, we show that simply using the common shortest path routing might lead to higher resource requirements. Extensive simulation results show that up to 8.33% capacity savings can be achieved on average by balanced routing, up to a 16.69% capacity savings can be achieved using the best performing demand-prioritization strategy compared to the worst-performing ones, the most used demand-prioritization strategy in the literature (serving demands with higher bandwidth requirements first) is not the best-performing one but the one sorting based on the path lengths, and using double-criteria strategies to break ties is key for a good performance. These results are relevant showing that a good combination of routing and demand-prioritization heuristics impact significantly on network performance. Additionally, they increase the understanding about the inner workings of good heuristics, a valuable knowledge when network settings forbid using more computationally complex approaches.

Abstract: Vehicle Routing Problems (VRP) comprise many variants obtained by adding to the original problem constraints representing diverse system characteristics. Different variants are widely studied in the literature; however, the impact that these constraints have on the structure of the search space associated with the problem is unknown, and so is their influence on the performance of search algorithms used to solve it. This article explores how assignation constraints (such as a limited vehicle capacity) impact VRP by disturbing the network structure defined by the solution space and the local operators in use. This research focuses on Fitness Landscape Analysis for the multiple Traveling Salesman Problem (m-TSP) and Capacitated VRP (CVRP). We propose a new Fitness Landscape Analysis measure that provides valuable information to characterize the fitness landscape's structure under specific scenarios and obtain several relationships between the fitness landscape's structure and the algorithmic performance.

Abstract: Efficient algorithms for computing routing tables should take advantage of particular properties arising in large scale networks. Two of them are of special interest: low (logarithmic) diameter and high clustering coefficient. High clustering coefficient implies the existence of few large induced cycles. Considering this fact, we propose here a routing scheme that computes short routes in the class of k-chordal graphs, i.e., graphs with no induced cycles of length more than k. In the class of k-chordal graphs, our routing scheme achieves an additive stretch of at most k – 1, i.e., for all pairs of nodes, the length of the route never exceeds their distance plus k – 1. In order to compute the routing tables of any n-node graph with diameter D we propose a distributed algorithm which uses O(log n)-bit messages and takes O(D) time. The corresponding routing scheme achieves the stretch of k – 1 on k-chordal graphs. We then propose a routing scheme that achieves a better additive stretch of 1 in chordal graphs (notice that chordal graphs are 3-chordal graphs). In this case, distributed computation of routing tables takes O(min{Delta D, n}) time, where Delta is the maximum degree of the graph. Our routing schemes use addresses of size log n bits and local memory of size 2(d-1) log n bits per node of degree d. (c) 2012 Elsevier B.V. All rights reserved.