Integer programming for building robust surgery schedules.

This paper proposes and evaluates a number of models for building robust cyclic surgery schedules. The developed models involve two types of constraints. Demand constraints ensure that each surgeon (or surgical group) obtains a specific number of operating room (OR) blocks. Capacity con- straints limit the available OR blocks on each day. Furthermore, the number of operated patients per block and the length of stay (LOS) of each operated patient are dependent on the type of surgery. Both are considered stochas- tic, following a multinomial distribution. We develop a number of MIP-based heuristics and a metaheuristic to minimize the expected total bed shortage and present computational results.Constraint; Demand; Distribution; Expected; Heuristic; Integer programming; Model; Models; Resource leveling; Surgery scheduling;

A mathematical programming approach for dispatching and relocating EMS vehicles.

We consider the problem of dispatching and relocating EMS vehicles during a pandemic outbreak. In such a situation, the demand for EMS vehicles increases and in order to better utilize their capacity, the idea of serving more than one patient by an ambulance is introduced. Vehicles transporting high priority patients cannot serve any other patient, but those transporting low priority patients are allowed to be rerouted to serve a second patient. We have considered three separate problems in this research. In the first problem, an integrated model is developed for dispatching and relocating EMS vehicles, where dispatchers determine hospitals for patients. The second problem considers just relocating EMS vehicles. In the third problem only dispatching decisions are made where hospitals are pre-specified by patients not by dispatchers. In the first problem, the objective is to minimize the total travel distance and the penalty of not meeting specific constraints. In order to better utilize the capacity of ambulances, we allow each ambulance to serve a maximum of two patients. Considerations are given to features such as meeting the required response time window for patients, batching non-critical and critical patients when necessary, ensuring balanced coverage for all census tracts. Three models are proposed- two of them are linear integer programing and the other is a non-linear programing model. Numerical examples show that the linear models can be solved using general-purpose solvers efficiently for large sized problems, and thus it is suitable for use in a real time decision support system. In the second problem, the goal is to maximize the coverage for serving future calls in a required time window. A linear programming model is developed for this problem. The objective is to maximize the number of census tracts with single and double coverage, (each with their own weights) and to minimize the travel time for relocating. In order to tune the parameters in this objective function, an event based simulation model is developed to study the movement of vehicles and incidents (911 calls) through a city. The results show that the proposed model can effectively increase the system-wide coverage by EMS vehicles even if we assume that vehicles cannot respond to any incidents while traveling between stations. In addition, the results suggest that the proposed model outperforms one of the well-known real time repositioning models (Gendreau et al. (2001)). In the third problem, the objective is to minimize the total travel distance experienced by all EMS vehicles, while satisfying two types of time window constraints. One requires the EMS vehicle to arrive at the patients\u27 scene within a pre-specified time, the other requires the EMS vehicle to transport patients to their hospitals within a given time window. Similar to the first problem, each vehicle can transport maximum two patients. A mixed integer program (MIP) model is developed for the EMS dispatching problem. The problem is proved to be NP-hard, and a simulated annealing (SA) method is developed for its efficient solution. Additionally, to obtain lower bound, a column generation method is developed. Our numerical results show that the proposed SA provides high quality solutions whose objective is close to the obtained lower bound with much less CPU time. Thus, the SA method is suitable for implementation in a real-time decision support system

Heuristiken im Service Operations Management

This doctoral thesis deals with the application of operation research methods in practice. With two cooperation companies from the service sector (retailing and healthcare), three practice-relevant decision problems are jointly elicited and defined. Subsequently, the planning problems are transferred into mathematical problems and solved with the help of optimal and/or heuristic methods. The status quo of the companies could be significantly improved for all the problems dealt with.Diese Doktorarbeit beschäftigt sich mit der Anwendung von Operation Research Methoden in der Praxis. Mit zwei Kooperationsunternehmen aus dem Dienstleistungssektor (Einzelhandel und Gesundheitswesen) werden drei praxisrelevante Planungsprobleme gemeinsam eruiert und definiert. In weiterer Folge werden die Entscheidungsmodelle in mathematische Probleme transferiert und mit Hilfe von optimalen und/oder heuristischen Verfahren gelöst. Bei allen behandelten Problemstellungen konnte der bei den Unternehmen angetroffene Status Quo signifikant verbessert werden

A layout design decision-support framework and concept demonstrator for rural hospitals using mixed methods

Thesis (MEng)--Stellenbosch University, 2017.ENGLISH ABSTRACT: Layout design is an ever-present problem that has a significant effect on the operations of an organisation, especially in the context of healthcare which deals with the lives of patients. It is a complex problem that has long-term consequences and oftentimes competing objectives. Literature has focused almost exclusively on using either quantitative or qualitative layout design methods for designing layouts. This study develops a generic framework using both quantitative and qualitative layout design methods that will guide the user to design a near optimal layout for a rural hospital while taking into consideration the relevant laws and standards as well as the health outcomes of the surrounding rural community. Rural and urban lifestyles, health, and illnesses differ in many ways. General hospital design methods are therefore not necessarily appropriate for hospitals in these areas. There is thus a need for a framework to be tailored for a rural community. Following a mixed methods methodology, a systematic literature review of quantitative and qualitative layout design methods along with hospital design considerations were conducted in order to determine the most adequate methods for designing a hospital layout at the block diagram level of detail. Furthermore, the commonalities and differences between rural and urban hospitals were investigated including laws and standards relevant to hospital layouts. The qualitative layout design methods involved different layout procedures and Muther’s Systematic Layout Planning Procedure was found to be most adequate. Furthermore, hospital design considerations such as patient-centeredness, efficiency, flexibility and expandability, sustainability, and therapeutic environment were identified and linked with the quantitative layout methods. It was also found that rural communities have different needs to urban ones with regard to access to medical care, prominent illnesses, and attitudes towards health. The healthcare personnel shortages are particularly problematic for rural communities. The quantitative layout design methods involved layout models, solution methods (exact methods, metaheuristics, and hybrid metaheuristics), and layout software. Using criteria of objectives, assumptions, inputs, outputs, and hospital design considerations, the Quadratic Set Covering Problem was determined to be the most appropriate model for designing a rural hospital block diagram layout. It was deemed possible to integrate the quantitative and qualitative methods by embedding the qualitative data into this quantitative model. The rural hospital design framework was developed using Excel VBA and RStudio. The framework was validated via two routes. Firstly, semi-structured interviews were conducted with experts in the field, i.e. expert analyses. Secondly a case study of the Semonkong Hospital Project was employed wherein the framework was applied successfully. The framework was deemed valid according to both the expert analyses and the case study.AFRIKAANSE OPSOMMING: Die uitleg van ‘n gebou het ‘n belangrike impak op die bedrywighede van ‘n organisasie – veral in die konteks van gesondheidsorg waar daar met pasiënte se lewens gewerk word. Dit is ‘n ingewikkelde probleem wat oor langtermyneffekte beskik en dikwels teenstrydige doelwitte. Die literatuur vir uitleg ontwerpsmetodes het meestal gefokus op óf kwantitatiewe óf kwalitatiewe uitleg ontwerpsmetodes. Hierdie studie ontwikkel ‘n generiese raamwerk wat beide van hierdie metodes gebruik om ‘n gebruiker te lei om die uitleg van ‘n plattelandse hospital te ontwerp wat die gepaste wette en standaarde en die gesondheid van die omliggende gemeenskap in ag neem. Landelike- en stedelike gemeenskappe verskil in terme van hul lewenstyl, gesondheid en tipe siektes. Algemene uitleg ontwerpsmetodes is dus nie noodwendig geskik vir ‘n plattelandse hospitaal nie. Daar is dus ‘n behoefte om ‘n raamwerk te ontwikkel wat spesifiek is vir die uitleg van ‘n plattelandse hospitaal. Hierdie studie volg ‘n gemengde metode benadering en ‘n sistematiese literatuurstudie is gevolglik afsonderlik gedoen op kwantitatiewe- en kwalitatiewe uitleg ontwerpsmetodes met die doel om die mees geskikte ontwerpsmetodes vir ‘n hospitaal uitleg te bepaal. Die verskille en ooreenkomste tussen landelike- en stedelike hospitale was ook ondersoek. Hierdie sluit in wette en standaarde wat van toepassing is op hospitaal uitlegte. Die kwalitatiewe uitleg ontwerpsmetodes het verskillende uitleg prosedures ondersoek en dit is gevind dat Muther se Sistematiese Uitleg Prosedure die mees geskik is vir die probleem van hierdie studie. Daar is gevind dat die hoof ontwerpsoorwegings vir die uitleg van ‘n hospitaal pasiënt-gesentreerdheid, doeltreffendheid, aanpasbaarheid, volhoubaarheid en terapeutiese omgewing is. Daar is gevind dat landelike- en stedelike gemeenskappe verskil in terme van hul toegang tot mediese sorg, prominente siektes, en hul houdings teenoor gesondheid. Een van die grootste probleme in landelike hospitale was hul tekort aan personeel. Die kwantitatiewe uitleg ontwerpsmetodes sluit uitleg modelle, oplossingsmetodes (presiese metodes, metaheuristieke en hibriede metaheuristieke) en uitleg sagteware in. ‘n Kriteria van doelwitte, aannames, insette, uitsette en hospitaal ontwerpsoorwegings was gebruik om die mees geskikte uitleg model te kies naamlik: die ‘Quadratic Set Covering Problem’. Dit is gevind dat die kwantitatiewe- en kwalitatiewe uitleg ontwerpsmetodes deur middel van ‘embedding’ geïntegreer kan word. Die uitleg ontwerp raamwerk vir plattelandse hospitale was ontwikkel met behulp van Excel VBA en RStudio. Die raamwerk is bekragtig deur twee roetes. Eerstens, semi-gestruktureerde onderhoude was gevoer met kundiges in die velde van gesondheidsorg, plattelandse gemeenskappe en uitleg ontwerp. Tweedens, die raamwerk is toegepas op ‘n gevallestudie van die Semonkong Hospitaal Projek. Albei roetes dui daarop dat die raamwerk geldig is

Stochastic Goal Programming and a Metaheuristic for Scheduling of Operating Rooms

Health care systems in Canada provide benefits to patients but have issues with costs and wait lists. Long wait lists negatively affect patients’ welfares. This in turn can increase costs because conditions can develop into more complicated ones over time. Operating rooms in a hospital are responsible for a significant portion of both costs and benefits; therefore, finding ways to use them more efficiently can reduce both the waste of tax dollars and the lengths of wait lists and can improve patients’ welfares. In this research, a stochastic weighted goal programming model is proposed to perform elective surgery scheduling under uncertainty of both surgical durations and patient lengths of stay. The model generates a Master Surgical Schedule that schedules surgical teams in operating room blocks in a way that minimizes four objectives, which are the deviations between the targeted number of surgeries and the actual number of surgeries performed, the deviations between the targeted number of hours for surgeries and the actual number of hours used for surgeries, the maximum expected number of patients in the recovery ward over the course of the planning horizon, and the difference between the maximum and minimum expected numbers of patients in the recovery ward over the course of the planning horizon. In addition, the impact of cancellations on the schedule is taken into account. A simulated annealing metaheuristic is developed to find near-optimal solutions. Discrete event simulation is used for validation and to demonstrate the system of operating rooms and recovery ward beds to relevant stakeholders in the health care sector

An Optimisation-based Framework for Complex Business Process: Healthcare Application

The Irish healthcare system is currently facing major pressures due to rising demand, caused by population growth, ageing and high expectations of service quality. This pressure on the Irish healthcare system creates a need for support from research institutions in dealing with decision areas such as resource allocation and performance measurement. While approaches such as modelling, simulation, multi-criteria decision analysis, performance management, and optimisation can – when applied skilfully – improve healthcare performance, they represent just one part of the solution. Accordingly, to achieve significant and sustainable performance, this research aims to develop a practical, yet effective, optimisation-based framework for managing complex processes in the healthcare domain. Through an extensive review of the literature on the aforementioned solution techniques, limitations of using each technique on its own are identified in order to define a practical integrated approach toward developing the proposed framework. During the framework validation phase, real-time strategies have to be optimised to solve Emergency Department performance issues in a major hospital. Results show a potential of significant reduction in patients average length of stay (i.e. 48% of average patient throughput time) whilst reducing the over-reliance on overstretched nursing resources, that resulted in an increase of staff utilisation between 7% and 10%. Given the high uncertainty in healthcare service demand, using the integrated framework allows decision makers to find optimal staff schedules that improve emergency department performance. The proposed optimum staff schedule reduces the average waiting time of patients by 57% and also contributes to reduce number of patients left without treatment to 8% instead of 17%. The developed framework has been implemented by the hospital partner with a high level of success

Optimization models for patient allocation during a pandemic influenza outbreak.

Pandemic influenza has been an important public health concern. During the 20th century, three major pandemics of influenza occurred in 1918, 1957, and 1968. The pandemic of 1918 caused 40 to 50 million deaths worldwide and more than 500,000 deaths in the United States. The 1957 pandemic, during a time with much less globalization than now, spread to the U.S. within 4 to 5 months of its origination in China, causing more than 70,000 deaths in the U.S., and the 1968 pandemic spread to the U.S. from Hong Kong within 2 to 3 months, causing 34,000 deaths. Pandemic influenza is considered to be a relatively high probability event, even inevitable by many experts. During a pandemic influenza outbreak, some key preparedness tasks cannot be accomplished by hospitals individually; regional resource allocation, patient redistribution, and use of alternative care sites all require collaboration among hospitals both in planning and in response. The research presented in this dissertation develops optimization models to be used by decision makers (e.g. hospital associations, emergency management agency, etc.) to determine how best to manage medical resources as well as suggest patient allocation among hospitals and alternative healthcare facilities. Both single-objective and multi-objective optimization models are developed to determine the patient allocation and resource allocation among healthcare facilities. The single-objective optimization models are developed to optimize the patient allocation in terms of minimizing the travel distance between patients and healthcare facilities while considering medical resource capacity constraints. During the pandemic, the surge demand most likely would exhaust all the medical resources, at which time the models can help predict the potential resource shortage so an appropriate contingency plan can be developed. If additional resource quantities become available, the models help to determine the best allocation of these resources among healthcare facilities. Various methods are proposed to conduct the sensitivity analysis to help decision makers determine the impact of different level of each type resource on the patient service. The multi-objective optimization model not only considers the objective of minimization of the total travel distance by patients to healthcare facilities, but also considers the minimization of maximum patient travel distance. A case study from Metro Louisville, Kentucky is presented to demonstrate how the models would aid in patient allocation and resource allocation during a pandemic influenza outbreak. A web-based application based on the optimization models developed in this dissertation is presented as an initial tool for decision makers