Two-Stage Robust Optimization for the Orienteering Problem with Stochastic Weights

In this paper, the two-stage orienteering problem with stochastic weights is studied, where the first-stage problem is to plan a path under the uncertain environment and the second-stage problem is a recourse action to make sure that the length constraint is satisfied after the uncertainty is realized. First, we explain the recourse model proposed by Evers et al. (2014) and point out that this model is very complex. Then, we introduce a new recourse model which is much simpler with less variables and less constraints. Based on these two recourse models, we introduce two different two-stage robust models for the orienteering problem with stochastic weights. We theoretically prove that the two-stage robust models are equivalent to their corresponding static robust models under the box uncertainty set, which indicates that the two-stage robust models can be solved by using common mathematical programming solvers (e.g., IBM CPLEX optimizer). Furthermore, we prove that the two two-stage robust models are equivalent to each other even though they are based on different recourse models, which indicates that we can use a much simpler model instead of a complex model for practical use. A case study is presented by comparing the two-stage robust models with a one-stage robust model for the orienteering problem with stochastic weights. The numerical results of the comparative studies show the effectiveness and superiority of the proposed two-stage robust models for dealing with the two-stage orienteering problem with stochastic weights

The median routing problem for simultaneous planning of emergency response and non-emergency jobs

This 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

Dynamic Orienteering on a Network of Queues

Abstract We propose a stochastic orienteering problem on a network of queues with time windows at customers. While this problem is of wide applicability, we study it in the context of routing and scheduling a textbook salesperson who visits professors on campus to gain textbook adoptions. The salesperson must determine which professors to visit and how long to wait in queues at each professor. We model the problem as a Markov decision process (MDP) with the objective of maximizing expected sales. We investigate the existence of optimal control limits and examine conditions under which certain actions cannot be optimal. To solve the problem, we propose an approximate dynamic programming approach based on rollout algorithms. The method introduces a two-stage heuristic estimation that we refer to as compound rollout. In the first stage, the algorithm decides whether to stay at the current professor or go to another professor. If departing the current professor, it chooses the professor to whom to go in the second stage. We demonstrate the value of our modeling and solution approaches by comparing the dynamic policies to a-priori-route solutions with recourse actions

The enriched median routing problem and its usefulness in practice

Emergency response fleets often have to simultaneously perform two types of tasks: (1) urgent tasks requiring immediate action, and (2) non-urgent preventive maintenance tasks that can be scheduled upfront. In Huizing et al. (2020), Huizing et al. proposed the Median Routing Problem (MRP) to optimally schedule agents to a given set of non-urgent tasks, such that the response time for urgent tasks remains minimal. They proposed both an exact MILP-solution and a fast, scalable and accurate heuristic. However, when implementing the MRP-solution in a real-life pilot with a Dutch railway provider, we found that the model needed to be extended by including additional practical objectives and constraints. Therefore, in this paper, we extend the MRP to the so-called Enriched Median Routing Problem (E-MRP), making the model much better aligned with considerations from practice. Accordingly, we extend the MRP-based solutions to the E-MRP. This allows us to compare the performance of our proposed E-MRP solutions to performance obtained in the current operational practice of our partnering railway infrastructure company. We conclude that the E-MRP solution leads to a strong reduction in emergency response times compared to current practice by smartly scheduling the same volumes of non-urgent tasks

Orienteering Problem: A survey of recent variants, solution approaches and applications

National Research Foundation (NRF) Singapore under International Research Centres in Singapore Funding Initiativ

Optimisation approaches for an orienteering problem with applications to wildfire management

During uncontrollable wildfires, Incident Management Teams (ITMs) dispatch vehicles for tasks aimed at reducing the hazard to key assets. The deployment plan is complicated by the need for vehicle capabilities to match asset requirements within time-windows determined by the progression of the fire. Assignment of the response vehicles to undertake protection activities at different assets is known as the asset protection problem. The asset protection problem is one of the real-life applications of the Cooperative Orienteering Problem with Time Windows (COPTW). The COPTW is a class of problems with some important applications and yet has received relatively little attention. In the COPTW, a certain number of team members are required to collect the associated reward from each node simultaneously and cooperatively. This requirement to have one or more team members simultaneously available at a vertex to collect the reward, poses a challenging task. It means that while multiple paths need to be determined as in the team orienteering problem with time-windows (TOPTW), there is the additional requirement that certain paths must meet at some of the vertices. Exact methods are too slow for operational purposes and they are not able to handle large scale instances of the COPTW. This thesis addresses the problem of finding solutions to COPTW in times that make the approaches suitable for use in certain emergency response situations. Computation of exact solutions within a reasonable time is impossible due to the nature of the COPTW. Thus, the thesis introduces an efficient heuristic approach to achieve reliable solutions in short computation times. Thereafter, a new set of algorithms are developed to work together as components of an adaptive large neighbourhood search algorithm. The proposed solution approaches in this work are the first algorithms that can achieve promising solutions for realistic sizes of the COPTW in a time efficient manner. In addition to the COPTW, this thesis presents an algorithmic approach to solve the asset protection problem. The complexities involved in the asset protection problem are handled by a metaheuristic algorithm. The asset protection problem is often further complicated by a wind change that is expected but with uncertainty in its timing. For this situation a two-stage stochastic model is introduced for the optimal deployment of response vehicles. The model addresses uncertainty in the timing of changes in the problem conditions for the first time in the literature. It is shown that deployment plans, which improve on current practices, can be generated in operational times thus providing useful decision support in time-pressured environments. The performance of the proposed approaches are validated through extensive computational studies. The computational results show that the proposed methods are effective in obtaining good quality solutions in times that are suitable for operational purposes. This is particularly useful for increasing the tools available to IMT's faced with making deployment decisions crucial to savings lives and critical assets

Battery Management in Electric Vehicles: Current Status and Future Trends

Lithium-ion batteries are an indispensable component of the global transition to zero-carbon energy and are instrumental in achieving COP26's objective of attaining global net-zero emissions by the mid-century. However, their rapid expansion comes with significant challenges. The continuous demand for lithium-ion batteries in electric vehicles (EVs) is expected to raise global environmental and supply chain concerns, given that the critical materials required for their production are finite and predominantly mined in limited regions worldwide. Consequently, significant battery waste management will eventually become necessary. By implementing appropriate and enhanced battery management techniques in electric vehicles, the performance of batteries can be improved, their lifespan extended, secondary uses enabled, and the recycling and reuse of EV batteries promoted, thereby mitigating global environmental and supply chain concerns. Therefore, this reprint was crafted to update the scientific community on recent advancements and future trajectories in battery management for electric vehicles. The content of this reprint spans a spectrum of EV battery advancements, ranging from fundamental battery studies to the utilization of neural network modeling and machine learning to optimize battery performance, enhance efficiency, and ensure prolonged lifespan