10:30 AM - 11:00 AM
Benchmarking Hospital Geriatric Services using Discrete-Event Simulation
The increasing number of geriatric patients is one of the most important problems for the next years. This kind of patients is often dependent and can have difficulties with environment changes so that hospitalization can strongly deteriorate the elderly health state. This study aims at evaluating the added value of integrated care for elderly and focuses on two services of the geriatric department: the Short Stay (Acute Care) and Rehabilitative Care (to prepare the return at home). These services are complementary and a large proportion of patients (approximatively 50%) needs to be transferred to the Rehabilitative Care unit after the Short Stay. We propose a benchmark of four University Hospitals in France (Saint-Etienne, Lyon, Grenoble and Clermont-Ferrand) with different configurations of the two services (integrated and separated). In the integrated configuration (Saint-Etienne and Grenoble) both services are located in the same department and the patient keeps the same bed with the same staff (nurses, doctors…). In the separated configuration (Lyon and Clermont-Ferrand) services are independent and may be located in two different wards. According to doctors, integrated services provide the most coherent pathway for the patient but it can be difficult to implement because each hospital has constraints relevant to its territory. For example both separated case studies have a Rehabilitative Care shared with other services of the hospital and cannot be only allocated to the geriatric department. In addition the bed ratio between Short Stay and Rehabilitative Care is different in the studied hospitals. We use Discrete Event Simulation to compare the efficiency of each organization and measure the impact on indicators such as the occupancy, admissions and the length of stay. According to our results, the integrated configuration is the best solution and separated services are too dependent on other departments.
11:00 AM - 11:30 AM
New Developments in Minimizing Expected Excess Waiting Time in KPI-based Systems
Key Performance Indicators (KPIs) are a measure of service system performance which comprise a delay limit and compliance probability (the chance a patient commences treatment by the delay limit). The primary flaw of a pure KPI approach is that no consideration is given for the consequences of patients whose waiting time exceeds the delay limit. We present an optimization model for such systems which seeks to minimize the weighted average of expected excess waiting time, beyond the treatment time limits, for the various classes. We test the model extensively in an Accumulating Priority Queue (APQ) setting. The Accumulating Priority Queue selects patients for treatment according to a linear priority accumulation function at a rate that depends upon the patient acuity class. It acts as a unifying patient selection discipline, which includes as its extremes the First-come, First-served (FCFS) discipline and the classical priority discipline.
At ORAHS 2014, we presented our insights gained from extensive numerical testing. Most notably, when minimizing expected excess waiting time, we found the optimal accumulation rates were almost invariably close to those suggested by a rule of thumb involving accumulation rates in inverse proportion to the delay limits. We now present mathematical bounds on the optimal accumulation rates in the two class case; in particular, we establish that the rule of thumb always acts as an upper bound on the optimal accumulation rate; thereby providing a quick starting point for a recursive method to converge to the true optimal value.
11:30 AM - 12:00 PM
Multi-Class Accumulating Priority Queues with Heterogeneous Servers
Historically, lengthy waiting time problems have been analyzed using classical priority queuing theory. Classical priority queues serve classes of customers according to their pre-assigned priority, meaning that no customer from a given class can be admitted into service when there are customers from classes with higher priority present in the queue.
Kleinrock (1964) proposed a queue called "time-dependent priority queue", where customers' pre-assigned priority changes dynamically based on how long they have waited. He suggested that customers accumulate priority according to a linear function of their waiting time in the queue, and the rate at which the customer accumulates priority depends on the customer's class. Since the performance of many queues is specified in terms of tails of waiting time distributions and not only the mean waiting times, Stanford et. al. (2014) derived the waiting time distributions of different priority classes in a single server accumulating priority queue (APQ) subject to Poisson arrivals. However, in practice, often there is more than one server to handle the arriving customers in the waiting lines. Sharif et. al. (2014) obtained the waiting time distributions of different priority classes for a multi-server APQ where the service time distributions are assumed to be exponentially distributed with a common parameter for all classes.
Currently, we are developing a more general multi-server model whose service times are exponentially distributed with heterogeneous service rates among different servers. Numerical investigations through simulation are carried out to validate our model.