Recent optimization models and trends in location,relocation, and dispatching of emergency medical vehicles

Over the past 10 years, a considerable amount of research has been devoted to the development of models to support decision making in the particular yet important context of Emergency Medical Services (EMS). More specifically, the need for advanced strategies to take into account the uncertainty and dynamism inherent to EMS, as well as the pertinence of socially oriented objectives, such as equity, and patient medical outcomes, have brought new and exciting challenges to the field. In this context, this paper summarizes and discusses modern modeling approaches to address problems related to ambulance fleet management, particularly those related to vehicle location and relocation, as well as dispatching decisions. Although it reviews early works on static ambulance location problems, this review concentrates on recent approaches to address tactical and operational decisions, and the interaction between these two types of decisions. Finally, it concludes on the current state of the art and identifies promising research avenues in the field.     

A branch and bound based heuristic for makespan minimization of washing operations in hospital sterilization services

In this paper, we address the problem of parallel batching of jobs on identical machines to minimize makespan. The problem is motivated from the washing step of hospital sterilization services where jobs have different sizes, different release dates and equal processing times. Machines can process more than one job at the same time as long as the total size of jobs in a batch does not exceed the machine capacity. We present a branch and bound based heuristic method and compare it to a linear model and two other heuristics from the literature. Computational experiments show that our method can find high quality solutions within short computation time.     

Facilitated modelling with discrete-event simulation: Reality or myth?

Is it possible for discrete-event simulation to be used in a facilitated workshop environment? Over the last decade there have been various attempts to use simulation in this way, but we argue here that none have been successful in achieving a fully facilitated mode where the model is both developed and used in the workshop. We attempt to use a discrete-event simulation in a facilitated mode as part of a lean improvement workshop in a hospital setting. The model was successfully developed and used within the 3 day period of the workshop. Although the intervention was successful, we still had to build the model in the ‘back-office’, meaning that a fully facilitated mode was not achieved. The paper concludes by discussing how fully facilitated modelling with discrete-event simulation might be made possible; the answer is more about changing mind-sets than about technological challenge.     

Combining discrete-event simulation and system dynamics in a healthcare setting: A composite model for Chlamydia infection

This paper presents a composite model in which two simulation approaches, discrete-event simulation (DES) and system dynamics (SD), are used together to address a major healthcare problem, the sexually transmitted infection Chlamydia. The paper continues an on-going discussion in the literature about the potential benefits of linking DES and SD. Previous researchers have argued that DES and SD are complementary approaches and many real-world problems would benefit from combining both methods. In this paper, a DES model of the hospital outpatient clinic which treats Chlamydia patients is combined with an SD model of the infection process in the community. These two models were developed in commercial software and linked in an automated fashion via an Excel interface. To our knowledge this is the first time such a composite model has been used in a healthcare setting. The model shows how the prevalence of Chlamydia at a community level affects (and is affected by) operational level decisions made in the hospital outpatient department. We discuss the additional benefits provided by the composite model over and above the benefits gained from the two individual models.     

Development and implementation of a real time statistical control method to identify the start and end of the winter surge in demand for paediatric intensive care

Winter surge management in intensive care is hampered by the annual variability in the winter surge. We aimed to develop a real-time monitoring system that could promptly identify the start, and accurately predict the end, of the winter surge in a paediatric intensive care (PIC) setting. We adapted a statistical process control method from the stock market called “Bollinger bands” that compares current levels of demand for PIC services to thresholds based on the medium term average demand. Algorithms to identify the start and end of the surge were developed for a specific PIC service: the North Thames Children's Acute Transport Service (CATS) using eight winters of data (2005–12) to tune the algorithms and one winter to test the final method (2013/14). The optimal Bollinger band thresholds were 1.2 and 1 standard deviations above and below a 41-day moving average of demand respectively. A simple linear model was found to predict the end of the surge and overall demand volume as soon as the start had been identified. Applying the method to the validation winter of 2013/14 showed excellent performance, with the surge identified from 18th November 2013 to 4th January 2014.An Excel tool running the algorithms has been in use within CATS since September 2014. There were three factors which facilitated the successful implementation of this tool: the perceived problem was pressing and identified by the clinical team; there was close clinical engagement throughout and substantial effort was made to develop an easy-to-use Excel tool for sustainable use.     

Mid-term and short-term planning support for home health care services

In this paper we are looking at routing and scheduling problems arising in the context of home health care services. Many small companies are working in this sector in Germany and planning is still done manually, resulting in long planning times and relatively inflexible solutions.     

Selfish routing in public services

It is well observed that individual behaviour can have an effect on the efficiency of queueing systems. The impact of this behaviour on the economic efficiency of public services is considered in this paper where we present results concerning the congestion related implications of decisions made by individuals when choosing between facilities. The work presented has important managerial implications at a public policy level when considering the effect of allowing individuals to choose between providers. We show that in general the introduction of choice in an already inefficient system will not have a negative effect. Introducing choice in a system that copes with demand will have a negative effect.     

Competition under different reimbursement systems: The concept of an internet-based hospital management game

We have developed an internet-based management game to illustrate the economic and organisational decision-making process in a hospital by using discrete event simulation. Up to six hospitals compete against each other for inpatients with different disease categories and budget depending on hospital mission, regional health policy, inpatient reimbursement system (day-, case- and global-budget based) as well as labour and radiology technology market for 12 decision periods. Players can evaluate alternative actions for capacity planning as well as patient scheduling and control problems depending on different game situations. The uniqueness of COREmain hospital game consists of the internet-based framework, the combination of resource, process and financial result management, the competition of hospitals within a region and the consideration of different inpatient reimbursement systems. The deployment of this game in teaching, policy and research might improve policy making both at a hospital, regional and national level and also induce further research in these fields.     

Modelling activities at a neurological rehabilitation unit

A queuing model of a specialist neurological rehabilitation unit is studied. The application is to the Neurological Rehabilitation Centre at Rookwood Hospital (Cardiff, UK), the national rehabilitation unit for Wales. Due to high demand this 21-bed inpatient facility is nearly always at maximum occupancy, and with a significant bed-cost per day this makes it a prime candidate for mathematical modelling. Central to this study is the concept that treatment intensity has an effect on patient length of stay. The model is constructed in four stages. First, appropriate patient groups are determined based on a number of patient-related attributes. Second, a purpose-built scheduling program is used to deduce typical levels of treatment to patients of each group. These are then used to estimate the mean length of stay for each patient group. Finally, the queuing model is constructed. This consists of a number of disconnected homogeneous server queuing systems; one for each patient group. A Coxian phase-type distribution is fitted to the length of time from admission until discharge readiness and an exponential distribution models the remainder of time until discharge. Some hypothetical scenarios suggested by senior management are then considered and compared on the grounds of a number of performance measures and cost implications.     

Discrete Conditional Phase-type models utilising classification trees: Application to modelling health service capacities

Discrete Conditional Phase-type models (DC-Ph) consist of a process component (survival distribution) preceded by a set of related conditional discrete variables. This paper introduces a DC-Ph model where the conditional component is a classification tree. The approach is utilised for modelling health service capacities by better predicting service times, as captured by Coxian phase-type distributions, interfaced with results from a classification tree algorithm. To illustrate the approach, a case-study within the healthcare delivery domain is given, namely that of maternity services. The classification analysis is shown to give good predictors for complications during childbirth. Based on the classification tree predictions, the duration of childbirth on the labour ward is then modelled as either a two or three-phase Coxian distribution. The resulting DC-Ph model is used to calculate the number of patients and associated bed occupancies, patient turnover, and to model the consequences of changes to risk status.     

Behavioural modelling of career progression in the European Commission

Though manpower planning models have been part of OR for many years, and simulation has always been acknowledged as a potential approach, there are few reported applications of its use. In this case-based study we report on a micro-simulation model that exploits the structure of the European Commission’s appraisal and promotion rules, and includes regression-based sampling schemes which allow for non-Normal error terms to represent behavioural factors that led to the need for a new system. With a suitably parsimonious formulation the 20,000 person model runs very effectively, and the transparency associated with simulation proves an important factor in the successful use of the model as the basis for designing a promotion box system that was implemented across the Commission in 2009. The simulation modelling incorporates many Markov-type elements, and we reflect on important lessons learned from this combined use of micro-simulation and Markov-based approaches to manpower modelling.     

Simulation modeling for emergency bed requirement planning

Due to its highly stochastic nature and complex interaction between services involved, health care has been a demanding area of application for computer simulation. This paper includes details and results of a simulation study realized in the Surgical Emergency Department at Istanbul University School of Medicine. The purpose is to suggest new bed capacities to improve the current system, and also to provide the management with guidelines for their expansion plans. For this aim, arrival rates, treatment procedures, inpatient admittance, and service durations have been carefully analyzed and modeled. The model, coded in SLAM-II simulation language, has been run under several bed capacity scenarios, and resulting queueing and waiting patterns have been discussed in detail.Dedictated to Professor Nusret Fiek     

Solving the dynamic ambulance relocation and dispatching problem using approximate dynamic programming

Emergency service providers are supposed to locate ambulances such that in case of emergency patients can be reached in a time-efficient manner. Two fundamental decisions and choices need to be made real-time. First of all immediately after a request emerges an appropriate vehicle needs to be dispatched and send to the requests’ site. After having served a request the vehicle needs to be relocated to its next waiting location. We are going to propose a model and solve the underlying optimization problem using approximate dynamic programming (ADP), an emerging and powerful tool for solving stochastic and dynamic problems typically arising in the field of operations research. Empirical tests based on real data from the city of Vienna indicate that by deviating from the classical dispatching rules the average response time can be decreased from 4.60 to 4.01 minutes, which corresponds to an improvement of 12.89%. Furthermore we are going to show that it is essential to consider time-dependent information such as travel times and changes with respect to the request volume explicitly. Ignoring the current time and its consequences thereafter during the stage of modeling and optimization leads to suboptimal decisions.     

Simulation optimization for an emergency department healthcare unit in Kuwait

This paper integrates simulation with optimization to design a decision support tool for the operation of an emergency department unit at a governmental hospital in Kuwait. The hospital provides a set of services for different categories of patients. We present a methodology that uses system simulation combined with optimization to determine the optimal number of doctors, lab technicians and nurses required to maximize patient throughput and to reduce patient time in the system subject to budget restrictions. The major objective of this decision supporting tool is to evaluate the impact of various staffing levels on service efficiency. Experimental results show that by using current hospital resources, the optimization simulation model generates optimal staffing allocation that would allow 28% increase in patient throughput and an average of 40% reduction in patients’ waiting time.     

SimLean: Utilising simulation in the implementation of lean in healthcare

Discrete-event simulation (DES) and lean are approaches that have a similar motivation: improvement of processes and service delivery. Both are being used to help improve the delivery of healthcare, but rarely are they used together. This paper explores from a theoretical and an empirical perspective the potential complementary roles of DES and lean in healthcare. The aim is to increase the impact of both approaches in the improvement of healthcare systems. Out of this exploration, the ‘SimLean’ approach is developed in which three roles for DES with lean are identified: education, facilitation and evaluation. These roles are demonstrated through three examples of DES in action with lean. The work demonstrates how the fusion of DES with lean can improve both stakeholder engagement with DES and the impact of lean.     

The impact of managerial and organizational aspects on hospital wards’ efficiency: Evidence from a case study

In spite of its acknowledged relevance, the impact of managerial and organizational aspects on hospital wards’ efficiency has been so far overlooked by the literature. In order to explore this issue, this paper presents a model of the relations between the decision making process of a hospital ward and its technical efficiency. In order to test the model, a two-step approach has been adopted. In the first step the technical efficiency of wards belonging to a large Italian Hospital Enterprise has been calculated using DEA. In the second step, efficiency scores have been regressed on a set of variables capturing managerial goals and actions internal to the ward, as well as re-organizations imposed by the hospital central management. Responses to a questionnaire administered to the heads of ward were used to build the independent variables. Results show that both decisions internal to the ward and exogenous re-organizations affect the ward’s efficiency, and suggest that these variables are more significant in explaining efficiency than environmental ones.     

A branch-and-price approach for integrating nurse and surgery scheduling

A common problem at hospitals is the extreme variation in daily (even hourly) workload pressure for nurses. The operating room is considered to be the main engine and hence the main generator of variance in the hospital. The purpose of this paper is threefold. First of all, we present a concrete model that integrates both the nurse and the operating room scheduling process. Second, we show how the column generation technique approach, one of the most employed exact methods for solving nurse scheduling problems, can easily cope with this model extension. Third, by means of a large number of computational experiments we provide an idea of the cost saving opportunities and required solution times.     

Efficiency of the medical care industry: Evidence from the Italian regional system

What might be the relation between clinical research and efficiency of medical care suppliers? Is the hypothesis of a positive relation consistent? Considering efficiency as the supplier’s ability to maximize the number of patients hospitalized in a mobility process among regions (i.e. mobility balance), this work aims at highlighting the existence of a positive externality of pharmaceutical clinical research on that kind of efficiency. In other words, an externality is able to affect the patients’ perception of good/bad quality of outputs supplied by the medical care industry, leading their mobility process. Taking Italy and the mobility of patients among regions into account, an Operational Research study will be performed in order to support this assumption.The goal of this work is to show an alternative way to increase the efficiency of medical care suppliers on the market of health care, that is to say, through their competitiveness on the market of human experimentation.     

A closer look at the economic-environmental disparities for regional development in China

Although China has harvested the fruits of its rapid economic growth over a period of several decades, it has encountered serious environmental problems, an important one being air pollution in the form of soot, dust, and sulfur dioxide. In considering the concept of ‘green-GDP’, this paper analyzes China’s regional development by examining its economic performance while taking into account various environmental factors. In addition to computing technical efficiency for 31 regions in China, a cross-efficiency measure is applied to differentiate the genuine DMUs. ‘Overall’ efficient regions and ‘false positive’ ones are recognized by a false positive index (FPI). It is found that the coastal regions perform on average better than the inland regions both economically and environmentally. For inefficient regions, the benchmark should be those regions with high cross-efficiency mean scores (e.g., Guangdong) rather than those with high self-appraisal scores (e.g., Shanghai). A cross-tabulation illustrating the difference between GDP-oriented performance and Pollution-oriented performance shows that the coastal regions make up the dominant proportion in terms of the benchmarks for economic-environmental optimization.     

Dynamic job assignment: A column generation approach with an application to surgery allocation

We consider the assignment of jobs to heterogeneous agents in a dynamic system with a rolling time horizon. An example is a hospital operating theatre where the jobs are surgeries and the agents are the surgeons. The paper is presented in the context of surgery allocation and the system is characterized as follows: Patients are grouped into categories and they arrive continually following a stochastic process. Patients in each group have specific time limits within which they need treatment and if it cannot be accommodated then the patients are outsourced. The service level is the percentage of patients in each group treated within the time limit. Surgery durations are stochastic and depend on the surgeon conducting the surgeries. Each surgeon has limited time available and expected overtime is penalized by a non-decreasing convex function. We develop a column generation approach for the assignment of already arrived patients and tentative future patients to surgeons on specific days. It balances the conflicting objectives of including as many arrived patients as possible within their time limits, maximizing the service level of future patients, and minimizing the expected overtime of surgeons. A computational study is conducted with the model embedded in a rolling time horizon frame. The study indicates that the assignment of patients based on our model increases system performance in terms of service level and reduced overtime compared to a First-Come-First-Served (FCFS) policy when the arrival rates of patients are medium to high compared to the capacity of the system.