a b s t r a c tThis paper studies a setting in emergency logistics where emergency responders must also perform a set of known, non-emergency jobs in the network when there are no active emergencies going on. These jobs typically have a preventive function, and allow the responders to use their idle time much more productively than in the current standard. When an emergency occurs, the nearest responder must abandon whatever job he or she is doing and go to the emergency. This leads to the optimisation problem of timetabling jobs and moving responders over a discrete network such that the expected emergency response time remains minimal. Our model, the Median Routing Problem, addresses this complex problem by minimising the expected response time to the next emergency and allowing for re-solving after this. We describe a mixed-integer linear program and a number of increasingly refined heuristics for this problem. We created a large set of benchmark instances, both from real-life case study data and from a generator. On the real-life case study instances, the best performing heuristic finds on average a solution only 3.4% away from optimal in a few seconds. We propose an explanation for the success of this heuristic, with the most pivotal conclusion being the importance of solving the underlying p -Medians Problem.
Some of the authors of this publication are also working on these related projects: Enhanced geometric models for access networks. View project Predictive Synchromodality View project
In logistic delivery chains time windows are common. An arrival has to be in a certain time interval, at the expense of waiting time or penalties if the time limits are exceeded. This paper looks at the optimal placement of those time intervals in a specific case of a barge visiting two ports in sequence. For the second port a possible delay or penalty should be incorporated. Next, recognising these penalty structures in data is analysed. Do certain patterns in public travel data indicate that a certain dependency is existing.
We introduce the Traveling k-Median Problem (TkMP) as a natural extension of the k-Median Problem, where k agents (medians) can move through a graph of n nodes over a discrete time horizon of ω steps. The agents start and end at designated nodes, and in each step can hop to an adjacent node to improve coverage. At each time step, we evaluate the coverage cost as the total connection cost of each node to its closest median. Our goal is to minimize the sum of the coverage costs over the entire time horizon.In this paper, we initiate the study of this problem by focusing on the uniform case, i.e., when all edge costs are uniform and all agents share the same start and end locations. We show that this problem is NP-hard in general and can be solved optimally in time O(ω 2 n 2k ). We obtain a 5approximation algorithm if the number of agents is large (i.e., k ≥ n/2). The more challenging case emerges if the number of agents is small (i.e., k < n/2). Our main contribution is a novel rounding scheme that allows us to round an (approximate) solution to the 'continuous movement' relaxation of the problem to a discrete one (incurring a bounded loss). Using our scheme, we derive constant-factor approximation algorithms on path and cycle graphs. For general graphs, we use a different (more direct) approach and derive an O(min{ √ ω, n})-approximation algorithm if d(s, t) ≤ 2 √ ω, and an O(d(s, t) + √ ω)-approximation algorithm if d(s, t) > 2 √ ω, where d(s, t) is the distance between the start and end point.
Problem statements and solution methods in mathematical synchromodal transportation problems depend greatly on a set of model choices for which no rule of thumb exists. In this paper, a framework is introduced with which the model choices in synchromodal transportation problems can be classified, based on literature. This framework should help researchers and developers to find solution methodologies that are commonly used in their problem instance and to grasp characteristics of the models and cases in a compact way, enabling easy classification, comparison and insight in complexity. It is shown that this classification can help steer a modeller towards appropriate solution methods.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.