arXiv subjects

John Gunnar Carlsson

Publications and source records attributed to John Gunnar Carlsson.

6 recordsLinked to original sources

arXiv2026

A unified solution framework for truck-and-drone routing problems

Coordinated truck-and-drone routing integrates the high capacity and range of ground vehicles with the flexible routing and speed of drones, enabling simultaneous service. Increasingly applied in last-mile delivery, this synchronization helps reduce completion time and operational costs. To improve its efficiency, various coordination modes between trucks and drones have been proposed. Each mode accommodates diverse operational constraints tailored to particular delivery requirements. In existing work, a slight change in the structural framework or operational characteristics could generate a totally different problem variant, which often requires the design of specialized algorithms. Consequently, under the requirement of maintaining structural validation and adapting to multiple operational features, this paper presents a unified three-phase solution framework based on the Lin-Kernighan-Helsgaun algorithm to solve a wide family of truck-and-drone routing problems. To validate its flexibility and effectiveness, we carry out numerical experiments on three problem variants: the Flying Sidekick Traveling Salesman Problem (FSTSP), the Traveling Salesman Problem with Multiple Drones (TSP-mD), and the Vehicle Routing Problem with Drones (VRP-D), benchmarking each against an effective algorithm. Computational results show that the framework can closely match optimal solutions on small-size instances and even improve the best-known solutions for several medium-size instances. Moreover, additional extensions are discussed to further highlight its versatility.

math.OC↗

arXiv2025

Individual and group fairness in geographical partitioning

Socioeconomic segregation often arises in school districting and other contexts, causing some groups to be over- or under-represented within a particular district. This phenomenon is closely linked with disparities in opportunities and outcomes. We formulate a new class of geographical partitioning problems in which the population is heterogeneous, and it is necessary to ensure fair representation for each group at each facility. We prove that the optimal solution is a novel generalization of the additively weighted Voronoi diagram, and we propose a simple and efficient algorithm to compute it, thus resolving an open question dating back to Dvoretzky et al. (1951). The efficacy and potential for practical insight of the approach are demonstrated in a realistic case study involving seven demographic groups and $78$ district offices.

econ.EM↗

arXiv2025

A lossless a priori splitting rule for split-delivery routing problems

Resource allocation problems in which demand is splittable are usually solved using different solution methods from their unsplittable equivalents. Although splittable problem instances can be the easier of the two (for example, they might simply correspond to a linear relaxation of a discrete problem), there exist many problems, including routing problems, for which the converse is true. That is, the technology for solving unsplittable problems is mature, but the splittable counterpart is not. For such problems, one strategy that has recently shown potential is the use of an a priori splitting rule in which each customer's demand is split into smaller pieces in advance, which enables one to simply solve the splittable problem as an instance of the unsplittable version. An important factor to consider is the number of pieces that result after this splitting. A large numbers of pieces will allow more splitting patterns to be realizable, but will result in a larger problem instance. In this paper, we introduce a splitting rule that minimizes the number of pieces, subject to the constraint that all demand splitting patterns remain feasible. Computational experiments on benchmark instances for the vehicle routing problem and a time-windows extension show that the solution quality of our proposed splitting rule can match the performance of existing approaches.

cs.DS↗

arXiv2019

Minimum size generating partitions and their application to demand fulfillment optimization problems

For $n$ and $k$ integers we introduce the notion of some partition of $n$ being able to generate another partition of $n$. We solve the problem of finding the minimum size partition for which the set of partitions this partition can generate contains all size-$k$ partitions of $n$. We describe how this result can be applied to solving a class of combinatorial optimization problems.

math.CO↗

arXiv2014

On the continuous Fermat-Weber problem for a convex polygon using Euclidean distance

We consider the continuous Fermat-Weber problem, where the customers are continuously (uniformly) distributed along the boundary of a convex polygon. We derive the closed-form expression for finding the average distance from a given point to the continuously distributed customers along the boundary. A Weiszfeld-type procedure is proposed for this model, which is shown to be linearly convergent. We also derive a closed-form formula to find the average distance for a given point to the entire convex polygon, assuming a uniform distribution. Since the function is smooth, convex, and explicitly given, the continuous version of the Fermat-Weber problem over a convex polygon can be solved easily by numerical algorithms.

cs.CG↗

arXiv2011

Dynamic Network Models

We analyze random networks that change over time. First we analyze a dynamic Erdos-Renyi model, whose edges change over time. We describe its stationary distribution, its convergence thereto, and the SI contact process on the network, which has relevance for connectivity and the spread of infections. Second, we analyze the effect of node turnover, when nodes enter and leave the network, which has relevance for network models incorporating births, deaths, aging, and other demographic factors.

math.PR↗