A queueing theoretic approach to set staffing levels in time-dependent dual-class service systems

This article addresses the optimal staffing problem for a nonpreemptive priority queue with two customer classes and a time-dependent arrival rate. The problem is related to several important service settings such as call centers and emergency departments where the customers are grouped into two classes of “high priority” and “low priority,” and the services are typically evaluated according to the proportion of customers who are responded to within targeted response times. To date, only approximation methods have been explored to generate staffing requirements for time-dependent dual-class services, but we propose a tractable numerical approach to evaluate system behavior and generate safe minimum staffing levels using mixed discrete-continuous time Markov chains (MDCTMCs). Our approach is delicate in that it accounts for the behavior of the system under a number of different rules that may be imposed on staff if they are busy when due to leave and involves explicitly calculating delay distributions for two customer classes. Ultimately, we embed our methodology in a proposed extension of the Euler method, coined Euler Pri, that can cope with two customer classes, and use it to recommend staffing levels for the Welsh Ambulance Service Trust (WAST)

Time-dependent stochastic methods for managing and scheduling Emergency Medical Services

Emergency Medical Services (EMS) are facing increasing pressures in many nations given that demands on the service are rising. This article focuses in particular on the operations of the Welsh Ambulance Service Trust (WAST), which is the only organisation that provides urgent paramedical care services on a day-to-day basis across the whole of Wales. In response to WAST’s aspiration to improve the quality of care it provides, this research investigates several interrelated advanced statistical and operational research (OR) methods, culminating in a suite of decision support tools to aid WAST with capacity planning issues. The developed techniques are integrated in a master workforce capacity planning tool that may be independently operated by WAST planners. By means of incorporating methods that seek to simultaneously better predict future demands, recommend minimum staffing requirements and generate low-cost rosters, the tool ultimately provides planners with an analytical base to effectively deploy resources. Whilst the tool is primarily developed for WAST, the generic nature of the methods considered means they could equally be applied to any service subject to demand that is of an urgent nature, cannot be backlogged, is heavily time-dependent and highly variabl

Time-dependent stochastic modelling for predicting demand and scheduling of emergency medical services

As the prominence of the service sector is increasing in developed nations, new and exciting opportunities are arising for operational researchers to develop and apply models which offer managers solutions to improve the quality of their services. The development of time-dependent stochastic models to analyse complex service systems and generate effective personnel schedules are key to this process, enabling organisations to strike a balance between the provision of a good quality service whilst avoiding unnecessary personnel costs. Specifically within the healthcare sector, there is a need to promote efficient management of an Emergency Medical Service (EMS), where the probability of survival is directly related to the speed of assistance. Motivated by case studies investigating the operation of the Welsh Ambulance Service Trust (WAST), this thesis aims to investigate how operational research (OR) techniques can be developed to analyse priority service systems subject to demand that is of an urgent nature, cannot be backlogged, is heavily time-dependent and highly variable. A workforce capacity planning tool is ultimately developed that integrates a combination of forecasting, queueing theory, stochastic modelling and optimisation techniques into a single spreadsheet model in order to predict future demand upon WAST, set staffing levels, and optimise shift schedules and rosters. The unique linking together of the techniques in a planning tool which further captures time-dependency and two priority classes enables this research to outperform previous approaches, which have generally only considered a single class of customer, or generated staffing recommendations using approximation methods that are only reliable under limited conditions. The research presented in this thesis is novel in several ways. Primarily, the first section considers the potential of a nonparametric modelling technique known as Singular Spectrum Analysis (SSA) to improve the accuracy of demand forecasts. Secondly, the main body of work is dedicated to adapting numerical queueing theory techniques to accurately model the behaviour of time-dependent multi-server priority systems across shift boundaries and evaluate the likelihood of excessive waits for service for two customer classes. The final section addresses how shifts can be optimally scheduled using heuristic search techniques. The main conclusions are that in addition to offering a more flexible approach, the forecasts generated by SSA compare favourably to those obtained using traditional methods, and both approximate and numerical modelling techniques may be duly extended to set staffing levels in complex priority systems

ACTIVE RELOCATION AND DISPATCHING OF HETEROGENEOUS EMERGENCY VEHICLES

An emergency is a situation that causes an immediate risk to the property, health, or lives of civilians and can assume a variety of forms such as traffic accidents, fires, personal medical emergencies, terrorist attacks, robberies, natural disasters, etc. Emergency response services (ERSs) such as police, fire, and medical services play crucial roles in all communities and can minimize the adverse effects of emergency incidents by decreasing the response time. Response time is not only related to the dispatching system, but also has a very close relationship to the coverage of the whole network by emergency vehicles. The goal of this dissertation is to develop a model for an Emergency Management System. This model will dynamically relocate the emergency vehicles to provide better coverage for the whole system. Also, when an emergency happens in the system the model will consider dispatching and relocation problem simultaneously. In addition, it will provide real-time route guidance for emergency vehicles. In summary, this model will consider three problems simultaneously: area coverage, vehicle deployment, and vehicle routing. This model is event-based and will be solved whenever there is an event in the system. These events can be: occurrence of an emergency, change in the status of vehicles, change in the traffic data, and change in the likelihood of an emergency happening in the demand nodes. Three categories of emergency vehicle types are considered in the system: police cars, ambulances, and fire vehicles. The police department is assumed to have a homogeneous fleet, but ambulances and fire vehicles are heterogeneous. Advanced Life Support (ALS) and Basic Life Support (BLS) ambulances are considered, along with Fire Engines, Fire Trucks, and Fire Quints in the fire vehicle category. This research attempts to provide double coverage for demand nodes by non-homogenous fleet while increasing the equity of coverage of different demand nodes. Also, the model is capable of considering the partial coverage in the heterogeneous vehicle categories. Two kinds of demand nodes are considered, ordinary nodes and critical nodes. Node demands may vary over time, so the model is capable of relocating the emergency fleet to cover the points with highest demand. In addition, an attempt is made to maintain work load balance between different vehicles in the system. Real-world issues, such as the fact that vehicles prefer to stay at their home stations instead of being relocated to other stations and should be back at their home depots at the end of the work shift, are taken into account. This is a unique and complex model; so far, no study in the literature has addressed these problems sufficiently. A mathematical formulation is developed for the proposed model, and numerical examples are designed to demonstrate its capabilities. Xpress 7.1 is used to run this model on the numerical examples. Commercial software like Xpress can be used to solve the proposed model on small-size problems, but for large-size and real-world problems, an appropriate heuristic is needed. A heuristic method that can find good solutions in reasonable time for this problem is developed and tested on several cases. Also, the model is applied to a real-world case study to test its performance. To investigate the model's behavior on a real-world problem, a very sophisticated simulation model that can see most of the details in the system has been developed and the real case study data has been used to calibrate the model. The results show that the proposed model is performing very well and efficient and it can greatly improve the performance of emergency management centers

City of Willowick, Ohio Fire and EMS Department Feasibility Study

The City of Willowick, Ohio, (Mayor and City Council), commissioned Cleveland State University, Center for Emergency Preparedness to conduct this “Willowick Fire and EMS Department Feasibility” study. The summary of findings and recommendations highlights some of the major issues, which require discussion. The main focus of this study is on efficient and sustainable staffing for the Willowick Fire and EMS Department; however, there are a number of factors which must be addressed to meet the National Fire Protection Association and Insurance Service Office “best practices,” ones which public safety entities strive to achieve. In addition, this study will provide staffing alternatives, identify financial and legal information and identify funding opportunities that may be available for hiring personnel. A thorough background literature review of the Insurance Service Office “Fire Suppression Rating Schedule,” “Emergency Medical Services” and “Fire and Rescue Services” are provided to assist in the understanding Fire and EMS service activities, which are mentally challenging, physically demanding and labor intensive. This study investigated the current Willowick Fire and EMS Department staffing status, solicited information from contiguous jurisdictional Fire and EMS Departments, and identified staffing models which the Willowick Mayor and City Council may select as the “best fit” for their jurisdiction. Recognizing that expenditures must be matched by revenue and system improvement should be constructed in service delivery increments, building from the current service delivery level through four possible models, with the fourth model being optimal

Developing a resource allocation model for the Scottish Patient Transport Service

The Patient Transport Service is a vital component of many healthcare systems. However, increasing demand and constrained resources impose great challenges, especially in Scotland where there is a substantial remote and rural population. This case study describes the development of a decision support tool for strategic resource allocation decisions. The tool had to be relevant to management's practical needs including transparency to a range of stakeholders and a flexible speedy response to help management explore various operational and policy options. However, the tool also had to demonstrate rigour and identify an efficient allocation of resources. In response to these requirements, the decision support tool was constructed from simple models, verified in comparisons with more rigorous and sophisticated approaches, notably a Dial-a-Ride genetic algorithm and an open vehicle routing simulation. Using this tool, management were able to: identify a more rational, strategic allocation of resources; quantify the remote and rural effect; examine trade-offs between service level and resource requirements within various scenarios for future demand

Optimization approaches to the ambulance dispatching and relocation problem

In the Emergency Medical Service (EMS) context, the decision-making process plays a very important role since some decisions highly impact patients’ health. This thesis focuses on the operational level by solving the dispatching and relocation ambulance problems. Dispatching decisions assign ambulances to emergencies, and the relocation problem decides to which base ambulances should be (re)assigned. Two optimization approaches are proposed to improve the effectiveness and efficiency in the EMS response: a mixed-integer linear programming (MILP) model and a pilot method heuristic. The aim is to maximize the system’s coverage using a time-preparedness measure allowing relocations to any base. Experiments are performed using EMS data from Lisbon, Portugal, where solving these problems is still a handmade task. Different ambulance types are considered, which should be used according to the severity of each emergency. The proposed approaches are tested under different scenarios: varying the period size, varying the number of emergencies, and simulating a whole day. Furthermore, they are adapted to compare the proposed strategy with the current Portuguese EMS strategy, which dispatches the closest available ambulance for each emergency and always relocates ambulances to their home bases. Results highlight the potential of the mathematical model and of the proposed strategy to be applied in realtime contexts since a reduction of 10% is obtained in the average response time to emergencies in the simulation scenario. The heuristic should be used when more emergencies occur in the same time period since a solution can be obtained almost immediately in contrast to the MILP usage. To help EMS managers in the decision-making process, we propose an ambulance management tool using Geographic Information Systems, which embeds the proposed approaches. It can be used in real-time or for simulation purposes. It incorporates a map visualization that analyzes ambulances’ movements on the map and the emergencies’ location