Abstract We propose a model for solving a parcel delivery problem with a fleet of trucks embedded with drones. When appropriate, drones are loaded with a parcel, launched directly from the truck, and sent to a client. Afterward, the drones autonomously return to the truck to be replenished and recharged. Inspired by the case of a large European logistics provider, the proposed modeling framework confronts realistic delivery problems involving time windows, limited drone autonomy, and the eligibility of clients to be served by drones. The considered global cost function includes fixed daily vehicle fares, driver wages, and the fuel and electricity consumption to power trucks and drones. To solve the problems at hand, we propose a mixed‐integer linear programming formulation and an adaptive large neighborhood search. Moreover, we introduce an efficient modeling framework to manage the numerous synchronization constraints induced by the simultaneous use of trucks and drones. We analyze the benefits of this new transportation concept for delivery problems involving up to 100 parcels. Results show that truck‐and‐drone solutions can reduce costs up to 34% compared to traditional truck‐only delivery. From a managerial perspective, we show that a certain percentage of client locations must be reachable by drone to make truck‐and‐drone solutions competitive (i.e., if the fixed costs of the drones are compensated for by the savings on truck routes) and compare the cost structures of truck‐and‐drone versus truck‐only solutions.

In this paper, we investigate a two-tier delivery network with robots operating on the second tier. We determine the optimal number of local robot hubs as well as the optimal number of robots to service all customers and compare the resulting operational cost to conventional truck-based deliveries. Based on the well-known p-median problem, we present mixed-integer programs that consider the limited range of robots due to battery size. Compared to conventional truck-based deliveries, robot-based deliveries can save about 70% of operational cost and even more, up to 90%, for a scenario with customer time windows.

Abstract The p‐median problem for networks is NP‐hard, but polynomial time algorithms exist for trees (n is the number of nodes): O(pn2) by Tamir, and O(n lgp + 2 n) by Benkoczi and Bhattacharya. Goldman gave an O(n) algorithm for the 1‐median problem on trees. Mirchandani and Oudjit proved localization properties for 2‐medians on trees; these were later used to obtain an O(nlg n) bound, and, in special cases, O(n) . We present a framework that unifies all efficient algorithms for the 2‐median problem on trees. Our framework isolates the nonlinear part of the computation so that future time‐bound improvements are easily incorporated. We also introduce a method for reducing the search space, improving all known runtimes in many instances. Finally, we give a new algorithm for the case where edge lengths are positive integers. The associated time bound is O(n + D) , where D is the sum of the logarithms of edge lengths. This is O(n) if edge lengths are bounded by a constant and O(n lglg n) if they are O(lg n) . The algorithm is flexible enough to extend to noninteger edge lengths, preserving the time bound in some circumstances.

Abstract An important issue in social network analysis refers to the development of algorithms for estimating parameters of a social network model, using data available from the network itself. This entails solving an optimization problem. In the paper, we propose a new method for parameter estimation in a specific social network model, namely, the so‐calledp‐star random graph model with three parameters. The method is based on the mean‐field approximation of the moments associated with the three subgraphs defining the model, namely: the mean numbers of edges, 2‐stars, and triangles. A modified gradient ascent method is applied to maximize the log‐likelihood function of thep‐star model, in which the components of the gradient are computed using approximate values of the moments. Compared to other existing iterative methods for parameter estimation, which are computationally very expensive when the number of vertices becomes large, such as gradient ascent applied to maximum log‐likelihood and maximum log‐pseudo‐likelihood estimation, the proposed approach has the advantage of a much cheaper cost per iteration, which is practically independent of the number of vertices.

Abstract We present here classes of integer programming problems that are solvable efficiently and with combinatorial flow algorithms. The problems are characterized by constraints that have either at most two variables per inequality that appear with opposite sign coefficients, or have in addition a third variable that appears only in one constraint. Such integer programs, referred to here as monotone IP2 or IP3, are shown to be solvable in polynomial time for polynomially bounded variables. This article demonstrates the vast applicability of IP2 and IP3 as models for integer programs in multiple scenarios. Since the problems are easily recognized, the knowledge of their structure enables one to determine easily that they are efficiently solvable. The variety of applications, that previously were not known to be solved as efficiently, underlies the importance of recognizing this structure and, if appropriate, formulating problems as monotone IP2 or IP3. Additionally, if there is flexibility in the modeling of an integer programming problem, the formulation choice as monotone IP2 or IP3 leads to efficient algorithms, whereas slightly different modeling choices would lead to NP‐hard problems.

Abstract A companion paper introduces models and algorithms for large‐scale zone‐based evacuation planning in which each evacuation zone is assigned a path to safety and a departure time. It also shows how to combine zone‐based evacuations with contraflows and impose additional path‐convergence and nonpreemptive constraints. This paper evaluates these algorithms on a real, large‐scale case study, both from a macroscopic standpoint and through microscopic simulations under a variety of assumptions. The results quantify, for the first time, the benefits and limitations of contraflows, convergent plans, and nonpreemption, providing unique perspectives on how to deploy these algorithms in practice. They also highlight the approaches best suited to capture each of these design features and the computational burden they impose. The paper also suggests new directions for future research in zone‐based evacuation planning and beyond in order to address the fundamental challenges by emergency services around the world.

Abstract We focus on the all‐pairs minimum cut (APMC) problem, a graph partitioning problem whose solution requires finding the minimum cut for every pair of nodes in a given graph. While it is solved for undirected graphs, a solution for APMC in directed graphs still requires an O(n2) brute force approach. We show that the empirical number of distinct minimum cuts in randomly generated strongly connected directed graphs is proportional to n rather than the theoretical value of n2, suggesting the possibility of an algorithm which finds all minimum cuts in less than O(n2) time. We also provide an example of the strict upper bound on the number of cuts in graphs with three nodes. We model the distributions with the Generalized extreme value (GEV) distribution and enable the possibility of using a GEV distribution to predict the probability of achieving a certain number of minimum cuts, given the number of nodes and edges. Finally, we contribute to the notion of symmetric cuts by showing that there can be O(n2) symmetric cuts in graphs when node replication is allowed.

Abstract Communication networks are subject to many challenges leading to single or multiple failures of its elements. Example failure scenarios include unintentional failures due to scheduled maintenance activities or massive failures caused by disaster‐induced events. Therefore, it is crucial to enhance the networks with redundancy and resilience mechanisms able to maintain the availability of network services after a failure. As these problems are often inherently hard to solve to optimality, the role of time‐efficient approximation schemes is essential. In this paper, we highlight the selected problems of communication networks resilience addressed in this issue of Networks.