Dispatching Fire Trucks under Stochastic Driving Times

In this paper we discuss optimal dispatching of fire trucks, based on a particular dispatching problem that arises at the Amsterdam Fire Department, where two fire trucks are send to the same incident location for a quick response. We formulate the dispatching problem as a Markov Decision Process, and numerically obtain the optimal dispatching decisions using policy iteration. We show that the fraction of late arrivals can be significantly reduced by deviating from current practice of dispatching the closest available trucks, with a relative improvement of on average about $20\%$, and over $50\%$ for certain instances. We also show that driving-time correlation has a non-negligible impact on decision making, and if ignored may lead to performance decrease of over $20\%$ in certain cases. As the optimal policy cannot be computed for problems of realistic size due to the computational complexity of the policy iteration algorithm, we propose a dispatching heuristic based on a queueing approximation for the state of the network. We show that the performance of this heuristic is close to the optimal policy, and requires significantly less computational effort.Comment: Submitted to Computers and Operations Research (December 08, 2018

Analysing the police patrol routing problem : a review

Police patrol is a complex process. While on patrol, police officers must balance many intersecting responsibilities. Most notably, police must proactively patrol and prevent offenders from committing crimes but must also reactively respond to real-time incidents. Efficient patrol strategies are crucial to manage scarce police resources and minimize emergency response times. The objective of this review paper is to discuss solution methods that can be used to solve the so-called police patrol routing problem (PPRP). The starting point of the review is the existing literature on the dynamic vehicle routing problem (DVRP). A keyword search resulted in 30 articles that focus on the DVRP with a link to police. Although the articles refer to policing, there is no specific focus on the PPRP; hence, there is a knowledge gap. A diversity of approaches is put forward ranging from more convenient solution methods such as a (hybrid) Genetic Algorithm (GA), linear programming and routing policies, to more complex Markov Decision Processes and Online Stochastic Combinatorial Optimization. Given the objectives, characteristics, advantages and limitations, the (hybrid) GA, routing policies and local search seem the most valuable solution methods for solving the PPRP

Optimization models and methods for real-time transportation planning in forestry

Lors du transport du bois de la forêt vers les usines, de nombreux événements imprévus peuvent se produire, événements qui perturbent les trajets prévus (par exemple, en raison des conditions météo, des feux de forêt, de la présence de nouveaux chargements, etc.). Lorsque de tels événements ne sont connus que durant un trajet, le camion qui accomplit ce trajet doit être détourné vers un chemin alternatif. En l’absence d’informations sur un tel chemin, le chauffeur du camion est susceptible de choisir un chemin alternatif inutilement long ou pire, qui est lui-même "fermé" suite à un événement imprévu. Il est donc essentiel de fournir aux chauffeurs des informations en temps réel, en particulier des suggestions de chemins alternatifs lorsqu’une route prévue s’avère impraticable. Les possibilités de recours en cas d’imprévus dépendent des caractéristiques de la chaîne logistique étudiée comme la présence de camions auto-chargeurs et la politique de gestion du transport. Nous présentons trois articles traitant de contextes d’application différents ainsi que des modèles et des méthodes de résolution adaptés à chacun des contextes. Dans le premier article, les chauffeurs de camion disposent de l’ensemble du plan hebdomadaire de la semaine en cours. Dans ce contexte, tous les efforts doivent être faits pour minimiser les changements apportés au plan initial. Bien que la flotte de camions soit homogène, il y a un ordre de priorité des chauffeurs. Les plus prioritaires obtiennent les volumes de travail les plus importants. Minimiser les changements dans leurs plans est également une priorité. Étant donné que les conséquences des événements imprévus sur le plan de transport sont essentiellement des annulations et/ou des retards de certains voyages, l’approche proposée traite d’abord l’annulation et le retard d’un seul voyage, puis elle est généralisée pour traiter des événements plus complexes. Dans cette ap- proche, nous essayons de re-planifier les voyages impactés durant la même semaine de telle sorte qu’une chargeuse soit libre au moment de l’arrivée du camion à la fois au site forestier et à l’usine. De cette façon, les voyages des autres camions ne seront pas mo- difiés. Cette approche fournit aux répartiteurs des plans alternatifs en quelques secondes. De meilleures solutions pourraient être obtenues si le répartiteur était autorisé à apporter plus de modifications au plan initial. Dans le second article, nous considérons un contexte où un seul voyage à la fois est communiqué aux chauffeurs. Le répartiteur attend jusqu’à ce que le chauffeur termine son voyage avant de lui révéler le prochain voyage. Ce contexte est plus souple et offre plus de possibilités de recours en cas d’imprévus. En plus, le problème hebdomadaire peut être divisé en des problèmes quotidiens, puisque la demande est quotidienne et les usines sont ouvertes pendant des périodes limitées durant la journée. Nous utilisons un modèle de programmation mathématique basé sur un réseau espace-temps pour réagir aux perturbations. Bien que ces dernières puissent avoir des effets différents sur le plan de transport initial, une caractéristique clé du modèle proposé est qu’il reste valable pour traiter tous les imprévus, quelle que soit leur nature. En effet, l’impact de ces événements est capturé dans le réseau espace-temps et dans les paramètres d’entrée plutôt que dans le modèle lui-même. Le modèle est résolu pour la journée en cours chaque fois qu’un événement imprévu est révélé. Dans le dernier article, la flotte de camions est hétérogène, comprenant des camions avec des chargeuses à bord. La configuration des routes de ces camions est différente de celle des camions réguliers, car ils ne doivent pas être synchronisés avec les chargeuses. Nous utilisons un modèle mathématique où les colonnes peuvent être facilement et naturellement interprétées comme des itinéraires de camions. Nous résolvons ce modèle en utilisant la génération de colonnes. Dans un premier temps, nous relaxons l’intégralité des variables de décision et nous considérons seulement un sous-ensemble des itinéraires réalisables. Les itinéraires avec un potentiel d’amélioration de la solution courante sont ajoutés au modèle de manière itérative. Un réseau espace-temps est utilisé à la fois pour représenter les impacts des événements imprévus et pour générer ces itinéraires. La solution obtenue est généralement fractionnaire et un algorithme de branch-and-price est utilisé pour trouver des solutions entières. Plusieurs scénarios de perturbation ont été développés pour tester l’approche proposée sur des études de cas provenant de l’industrie forestière canadienne et les résultats numériques sont présentés pour les trois contextes.When wood is transported from forest sites to mills, several unforeseen events may occur, events which perturb planned trips (e.g., because of weather conditions, forest fires, or the occurrence of new loads). When such events take place while the trip is under way, the truck involved must be rerouted to an alternative itinerary. Without relevant information on such alternative itineraries, the truck driver may choose a needlessly long one or, even worse, an itinerary that may itself be "closed" by an unforeseen event (the same event as for the original itinerary or another one). It is thus critical to provide drivers with real-time information, in particular, suggestions of alternative itineraries, when the planned one cannot be performed. Recourse strategies to deal with unforeseen events depend on the characteristics of the studied supply chain, such as the presence of auto-loaders and the management policy of forestry transportation companies. We present three papers dealing with three differ- ent application contexts, as well as models and solution methods adapted to each context. In the first paper, we assume a context where truck drivers are provided a priori with the whole weekly plan. In this context, every effort must be made to minimize the changes in the initial plan. Although the fleet of trucks is homogeneous, there is a priority ranking of the truck drivers. The priority drivers are ensured the highest work- loads. Minimizing the changes in their plans is also a priority. Since the consequences of unforeseen events on transportation are cancellations and/or delaying of some trips, the proposed approach deals first with single cancellations and single delayed trips and builds on these simple events to deal with more complex ones. In this approach, we try to reschedule the impacted trips within the same week in such a way that a loader is free at the truck arrival time both at the forest site and at the mill. In this way, none of the other trips will be impacted or changed. This approach provides the dispatchers with alternative plans in a few seconds. Better solutions could be found if the dispatcher is allowed to make more changes to the original plan. In the second paper, we assume a context where only one trip at a time is communicated to the drivers. The dispatcher waits until the truck finishes its trip before revealing the next trip. This context is more flexible and provides more recourse possibilities. Also, the weekly problem can be divided into daily problems since the demand is daily and the mills are open only for limited periods in the day. We use a mathematical programming model based on a time-space network representation to react to disruptions. Although the latter can have different impacts on the initial transportation plan, one key characteristic of the proposed model is that it remains valid for dealing with all the unforeseen events, regardless of their nature. Indeed, the impacts of such events are reflected in the time-space network and in the input parameters rather than in the model itself. The model is solved for the current day each time an unforeseen event is revealed. In the last paper, the fleet of trucks is heterogeneous, including trucks with onboard loaders. The route configuration of the latter is different than the regular truck routes, since they do not have to be synchronized with the loaders. We use a mathematical model where the columns can be easily and naturally interpreted as truck routes. We solve this model using column generation. As a first step, we relax the integrality of the decision variables and consider only a subset of feasible routes. The feasible routes with a potential to improve the solution are added iteratively to the model. A time-space network is used both to represent the impacts of unforeseen events and to generate these routes. The solution obtained is generally fractional and a heuristic branch-and-price algorithm is used to find integer solutions. Several disruption scenarios were developed to test the proposed approach on case studies from the Canadian forest industry and numerical results are presented for the three contexts

A survey of simulation techniques in commerce and defence

Despite the developments in Modelling and Simulation (M&S) tools and techniques over the past years, there has been a gap in the M&S research and practice in healthcare on developing a toolkit to assist the modellers and simulation practitioners with selecting an appropriate set of techniques. This study is a preliminary step towards this goal. This paper presents some results from a systematic literature survey on applications of M&S in the commerce and defence domains that could inspire some improvements in the healthcare. Interim results show that in the commercial sector Discrete-Event Simulation (DES) has been the most widely used technique with System Dynamics (SD) in second place. However in the defence sector, SD has gained relatively more attention. SD has been found quite useful for qualitative and soft factors analysis. From both the surveys it becomes clear that there is a growing trend towards using hybrid M&S approaches

AGENT-BASED DISCRETE EVENT SIMULATION MODELING AND EVOLUTIONARY REAL-TIME DECISION MAKING FOR LARGE-SCALE SYSTEMS

Computer simulations are routines programmed to imitate detailed system operations. They are utilized to evaluate system performance and/or predict future behaviors under certain settings. In complex cases where system operations cannot be formulated explicitly by analytical models, simulations become the dominant mode of analysis as they can model systems without relying on unrealistic or limiting assumptions and represent actual systems more faithfully. Two main streams exist in current simulation research and practice: discrete event simulation and agent-based simulation. This dissertation facilitates the marriage of the two. By integrating the agent-based modeling concepts into the discrete event simulation framework, we can take advantage of and eliminate the disadvantages of both methods.Although simulation can represent complex systems realistically, it is a descriptive tool without the capability of making decisions. However, it can be complemented by incorporating optimization routines. The most challenging problem is that large-scale simulation models normally take a considerable amount of computer time to execute so that the number of solution evaluations needed by most optimization algorithms is not feasible within a reasonable time frame. This research develops a highly efficient evolutionary simulation-based decision making procedure which can be applied in real-time management situations. It basically divides the entire process time horizon into a series of small time intervals and operates simulation optimization algorithms for those small intervals separately and iteratively. This method improves computational tractability by decomposing long simulation runs; it also enhances system dynamics by incorporating changing information/data as the event unfolds. With respect to simulation optimization, this procedure solves efficient analytical models which can approximate the simulation and guide the search procedure to approach near optimality quickly.The methods of agent-based discrete event simulation modeling and evolutionary simulation-based decision making developed in this dissertation are implemented to solve a set of disaster response planning problems. This research also investigates a unique approach to validating low-probability, high-impact simulation systems based on a concrete example problem. The experimental results demonstrate the feasibility and effectiveness of our model compared to other existing systems

Fire truck relocation during major incidents

The effectiveness of a fire department is largely determined by its ability to respond to incidents in a timely manner. To do so, fire departments typically have fire stations spread evenly across the region, and dispatch the closest truck(s) whenever a new incident occurs. However, large gaps in coverage may arise in the case of a major incident that requires many nearby fire trucks over a long period of time, substantially increasing response times for emergencies that occur subsequently. We propose a heuristic for relocating idle trucks during a major incident in order to retain good coverage. This is done by solving a mathematical program that takes into account the location of the available fire trucks and the historic spatial distribution of incidents. This heuristic allows the user to balance the coverage and the number of truck movements. Using extensive simulation experiments we test the heuristic for the operations of the Fire Department of Amsterdam‐Amstelland, and compare it against three other benchmark strategies in a simulation fitted using 10 years of historical data. We demonstrate substantial improvement over the current relocation policy, and show that not relocating during major incidents may lead to a significant decrease in performance

A Framework for Developing and Integrating Effective Routing Strategies Within the Emergency Management Decision-Support System, Research Report 11-12

This report describes the modeling, calibration, and validation of a VISSIM traffic-flow simulation of the San José, California, downtown network and examines various evacuation scenarios and first-responder routings to assess strategies that would be effective in the event of a no-notice disaster. The modeled network required a large amount of data on network geometry, signal timings, signal coordination schemes, and turning-movement volumes. Turning-movement counts at intersections were used to validate the network with the empirical formula-based measure known as the GEH statistic. Once the base network was tested and validated, various scenarios were modeled to estimate evacuation and emergency vehicle arrival times. Based on these scenarios, a variety of emergency plans for San José’s downtown traffic circulation were tested and validated. The model could be used to evaluate scenarios in other communities by entering their community-specific data