Lara Wiesche

Time-Dependent Ambulance Allocation Considering Data Driven Empirically Required Coverage

Empirical studies considering the location and relocation of emergency medical service (EMS) vehicles in an urban region provide important insight into dynamic changes during the day. Within a 24-hour cycle, the demand, travel time, speed of ambulances and areas of coverage change. Nevertheless, most existing approaches in literature ignore these variations and require a (temporally and spatially) fixed (double) coverage of the planning area. Neglecting these variations and fixation of the coverage could lead to an inaccurate estimation of the time-dependent fleet size and individual positioning of ambulances. Through extensive data collection, now it is possible to precisely determine the required coverage of demand areas. Based on data-driven optimization, a new approach is presented, maximizing the flexible, empirically determined required coverage, which has been adjusted for variations due to day-time and site. This coverage prevents the EMS system from unavailability of ambulances due to parallel operations to ensure an improved coverage of the planning area closer to realistic demand. An integer linear programming model is formulated in order to locate and relocate ambulances. The use of such a programming model is supported by a comprehensive case study, which strongly suggests that through such a model, these objectives can be achieved and lead to greater cost-effectiveness and quality of emergency care.

Strategies for interday appointment scheduling in primary care

When faced with a medical problem, patients contact their primary care physician (PCP) first. Here mainly two types of patient requests occur: non-scheduled patients who are walk-ins without an appointment and scheduled patients with an appointment. Number and position of the scheduled appointments influence waiting times for patients, capacity for treatment and the utilization of PCPs. As the number of patient requests differs significantly between weekdays, the challenge is to match capacity with patient requests and provide as few appointment slots as necessary. In this way, capacity for walk-ins is maximized while overall capacity restrictions are met. Decisions as to the optimal appointment capacity per day on a tactical decision level has gained little attention in the literature. A mixed integer linear model is developed, where the minimum number of appointments scheduled for a weekly profile is determined. We are thus able to give the answer as to how many appointments to offer on each day in a week in order to create a schedule that takes patient preferences as well as PCP preferences into account. Appointment schedules are often influenced by uncertain demands due to the number of urgent patients, interarrivals and service times. Based on an exemplary case study, the advantages of the optimal appointment schedule on different performance criteria are shown by detailed stochastic simulations.

Time-Dependent Dynamic Location and Relocation of Ambulances

The rescue service is an important part of public health care, which is provided to the general public by the state. A crucial aspect of the rescue service is the first aid of patients provided by the local emergency medical service (EMS). Given a limited budget, the available resources, e. g. ambulances, have to be used efficient in order to ensure a high quality coverage. Empirical studies have shown temporal and spatial variations of emergency demand as well as variations of travel times during the day. Existing models do not sufficiently consider time-dependency of important model parameters as demand and travel times for EMS vehicles. Especially the use of flexible ambulance locations, e.g. hospitals or voluntary fire departments, can be useful to reach a suitable coverage. A mixed-integer linear program is formulated in order to explicitly model time-dependent demand and travel times. On an extensive case study it is shown that the presented dynamic model outperforms existing static models with respect to coverage and utilization of resources.

Optimal Allocation of Operating Hours in Surgical Departments

A large part of revenue in hospitals is generated in surgical departments. In order to use available resources efficiently, we propose an innovative tactical optimization model to optimally allocate operating hours for operating rooms. An extensive simulation study is applied to evaluate the tactical plan with respect to main stakeholders. Results indicate strongly positive effects on staff and patients.

Optimal distribution of operating hours over operating rooms using probabilities

Usually, all operating rooms in a hospital have the same daily capacity although differing operating hours might be advantageous to match the demand. We propose and evaluate an optimization model that tactically distributes the total available operating time over the different operating rooms in order to improve performance. The probability of a perfect day without overtime or cancellations serves as objective criterion. Hence, the solution obtained has a maximum probability of no overtime or cancellations in all operating rooms. Uncertainties handled are mainly the surgery duration of patients and the daily number of patients to treat. To assess the number of patients, a method for sampling from multidimensional distribution functions for health care purposes is introduced. It is demonstrated that optimal operating hours for operating rooms can significantly influence key performance indicators such as overtime, rescheduling of patients and utilization. Implications for research and practical purposes can be deduced from an extensive simulation study with realistic data.

Influence of Appointment Times on Interday Scheduling

In primary care mainly two types of patient requests occur: walk-ins without an appointment and patients with a prescheduled appointment. The number and position of such prescheduled appointments influence waiting times for patients, capacity for treatment and the utilization of physicians. An integer linear model is developed, where the minimum number of appointments prescheduled for a weekly profile is determined. Since the number of patient requests differs significantly between seasons, weekdays and daytime, efficient appointment scheduling has to take different scenarios into account. Using an intensive monte-carlo simulation, we compare appointment strategies with respect to their performance for different scenarios.

Time-Dependent Ambulance Deployment and Shift Scheduling of Crews

For patients requesting emergency medical services (EMS) in a life-threatening emergency, the probability of survival is strongly related to the rapidness of assistance. An especially challenging task for planners is to allocate limited resources while managing increasing demand for services. The provision of sufficient staff resources for the ambulances has great impact on the initial treatment of patients and thus on the quality of emergency services. Data-driven empirically required ambulance location planning as well as the allocation of staff for these vehicles are successively optimized in the proposed approach to support emergency medical service decision makers. According to the identified problem structure, an integer linear programming model is proposed. An exemplary case study based on real-world data demonstrates how this approach can be used within the emergency medical service planning process.

Analysis of Ambulance Location Models Using Discrete Event Simulation

The quality of a rescue service system is typically evaluated ex post by the proportion of emergencies reached within a predefined response time threshold. Optimization models in literature consider different variants of demand area coverage or busy fractions and reliability levels as a proxy for Emergency Medical Service quality. But no comparisons of the mentioned models with respect to their real-world performance are found in literature. In this paper, the influence of these different model formulations on real-world outcome measures is analyzed by means of a detailed discrete event simulation study.

Data Driven Ambulance Optimization Considering Dynamic and Economic Aspects

Providing high quality emergency medical services (EMS) and ensuring accessibility to these services for the general public is a key task for health care systems. Given a limited budget available resources, e.g. ambulances, have to be used economically in order to ensure a high quality coverage. Emergency vehicles have to be positioned and repositioned such that emergencies can be reached within a legal time frame. Empirical studies have shown temporal and spatial variations of emergency demand as well as variations of travel times during a day. The numbers of emergency calls within 24 h differ significantly between night and day and show peaks especially during rush hours. We provide a data driven model considering time and spatial dependent degrees of coverage. This allows a simultaneous optimization of empirically required coverage with minimal number of ambulances, respectively costs. Therefore utilization and quality criteria are to be implemented. An integer linear program is formulated using time periods in order to model time-dependent demand and time-dependent travel times. It is shown on large empirical data records that the presented dynamic model outperforms existing static models with respect to coverage and utilization of resources.

Bedarfsplanung für kommunale Rettungsdienste

Aufgrund der Knappheit der Mittel und der Wichtigkeit kurzfristiger Reaktionen ist es gerade im Rettungswesen von besonderer Bedeutung, verfugbare Rettungsdienstressourcen effizient einzusetzen. Dies ist der Ansatzpunkt des Projektes an der Ruhr-Universitat Bochum, mit dem eine Optimierung der Versorgungsqualitat im Rettungswesen unter Berucksichtigung wirtschaftlicher Gegebenheiten erreicht werden soll. Dazu wurde das prototypisch verfugbare Entscheidungsunterstutzungssystem SPR2 entwickelt, mit dessen Unterstutzung Standorte und Zuteilungen von Rettungsmitteln unter Einsatz innovativer mathematischer Optimierungsansatze optimal im zeitlichen Verlauf ermittelt werden. Wirkungsweise, Einsatzmoglichkeiten und Ergebnisse von SPR2 werden in diesem Beitrag am Beispiel der Stadt Bochum prasentiert. Die Allgemeingultigkeit der verwendeten mathematischen Methoden und die Entwicklung geeigneter Eingabekomponenten erlauben die Anpassung an die Gegebenheiten anderer Stadte und damit einen breiten Einsatz des Tools.