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.
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.
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