OPTIMAL SHARING OF SURGICAL COSTS IN THE PRESENCE OF QUEUES

We deal with a cost allocation problem arising from sharing a medical service in the presence of queues. We use a standard queuing theory model in a context with several medical procedures, a certain demand of treatment and a maximum average waiting time guarantee set by the government. We show that sharing the use of an operating theatre to treat the patients of the different procedures, leads to a cost reduction. Then, we compute an optimal fee per procedure for the use of the operating theatre, based on the Shapley value. Afterwards, considering the post-operative time, we characterize the conditions under which this cooperation among treatments has a positive impact on the average post-operative costs. Finally, we provide a numerical example constructed on the basis of real data, to highlight the main features of our model.Surgical Waiting Lists; Queueing Theory; Cost-Sharing Game.

Cost sharing of cooperating queues in a Jackson network

We consider networks of queues in which the independent operators of individual queues may cooperate to reduce the amount of waiting. More specifically, we focus on Jackson networks in which the total capacity of the servers can be redistributed over all queues in any desired way. If we associate a cost to waiting that is linear in the queue lengths, it is known how the operators should share the available service capacity to minimize the long run total cost. We answer the question whether or not (the operators of) the individual queues will indeed cooperate in this way, and if so, how they will share the cost in the new situation. One of the results is an explicit cost allocation that is beneficial for all operators. The approach used also works for other cost functions, such as the server utilization

Characterizations of Pareto-efficient, fair, and strategy-proof allocation rules in queueing problems

A set of agents with possibly different waiting costs have to receive the same service one after the other. Efficiency requires to maximize total welfare. Equity requires to at least treat equal agents equally. One must form a queue, set up monetary transfers to compensate agents having to wait, and not a priori arbitrarily exclude agents from positions. As one may not know agents’ waiting costs, they may have no incentive to reveal them. We identify the only rule satisfying Pareto-efficiency, a weak equity axiom as equal treatment of equals in welfare or symmetry, and strategy-proofness. It satisfies stronger axioms, as no-envy and anonymity. Further, its desirability extends to related problems. To obtain these results, we prove that even non-single-valued rules satisfy Pareto-efficiency of queues and strategy-proofness if and only if they select Pareto-efficient queues and set transfers in the spirit of Groves (1973). This holds in other problems, provided the domain of quasi-linear preferences is rich enough.queueing problems, efficiency, fairness, strategy-proofness

Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008

Managing Elective and Non-elective Case Assignments for an Operating Room Suite

The success of operating room management depends on all levels of decision making, from strategic to tactical and operational decisions. One key decision in systems with block booking is to assign sufficient amount of block time to surgeons and surgery groups. While the typical method of block assignment identifies the share of surgery groups from OR times based on average of past usage, this method does not count for the difference between cost of under and overtime. One of the goals of this research is to develop a decision framework for block assignment. This work is presented in chapter two. In this part first, I provide with the linear program that finds the length of block assigned to surgery groups while considering the amount of past undertime and overtime. This model then simplifieded through valid assumptions. In addition, a case study is conducted to support the usefulness of the method. The results show that 12 months of past data is sufficient amount of data to use in this method. Also, this method of block allocation out performs the existing time series method in literature. Another key decision in an OR suite is to how manage elective and non-elective surgeries. The short and long term decisions regarding these two surgery types can change the waiting time of patients and the number of turned away surgeries. In order to accommodate elective and non-elective surgeries at lower cost to system and patients, both short and long term decisions play important roles. The long term decisions regarding the combination of rooms to choose in the system as well as the allocation to choose with the selected room combination are important decisions for OR managers. For short time decision making on the day of surgery a policy that indicate how to use share resources among the two surgery types is another important decision that OR managers need to nd an answer to. In this research I try to provide with methods and models that can guide managers in decision making process. In this research using Markov decision processes (MDP), I introduce a model that could be used to find the optimal policy for use of operating rooms that are considered as shared resources while minimizing the overall cost of the system including waiting, turn-away and overtime. For that I focus on the system with a dedicated OR to non-elective surgeries and a flexible (shared) OR. I also model this system using simulation with Arena, by relaxing the MDP assumptions of steady state and the arrival and surgery times to find a policy that can minimize the cost of system. The simulation better reflects the real system of hospitals however it takes a long time to find a policy using taking simulation approach. In addition to that, the policy from simulation does not guarantee optimality. Moreover, the result of case study shows that relaxing MDP assumptions, simulation model finds the same policy as MDP. However, the MDP model could find an optimal policy in seconds. Although MDP could be used to model the most common existing combinations of operating rooms, however, the optimal policy from MDP may be hard to implement. Therefore I use Markov chain to model combinations of operating rooms and define policies to be used on the day of surgery for accommodating elective and non-elective surgeries. I compare the performance of systems under defined policies by considering input parameters at different levels. I also consider several allocations under each system to find the best system and allocation. Results of this work shows that overall system with all flexible ORs has the minimum cost. However, some other systems may perform better in specific situations and scenarios. The best policy (among the studied policies) is depending on the room combinations and the chosen allocation

Analysis of resource pooling games via a new extension of the Erlang loss function

We study a situation where several independent service providers collaborate by pooling their resources into a joint service system. These service providers may represent such diverse organizations as hospitals that pool intensive care beds and ambulances, airline companies that share spare parts, or car rental agencies that pool rental cars. We model the service systems as Erlang loss systems that face a fixed cost rate per server and penalty costs for lost customers. We examine the allocation of costs of the pooled system amongst the participants by formulating a cooperative cost game in which each coalition optimizes the number of servers. We identify a cost allocation that is in the core of this game, giving no subset of players an incentive to split off and form a separate pooling group. Moreover, we axiomatically characterize this allocation rule and show that it can be reached through a population monotonic allocation scheme. To obtain these results, we introduce a new extension of the classic Erlang loss function to non-integral numbers of servers and establish several of its structural properties

Scheduling Elective Surgeries in Multiple Operating Rooms

This thesis focuses on the problem of designing appointment schedules in a surgery center with multiple operating rooms. The conditions under which overlapping surgeries in the surgeons’ schedule (i.e. parallel surgery processing) at the lowest cost are investigated with respect to three components of the total cost: waiting time, idle time, and overtime. A simulation optimization method is developed to find the near-optimal appointment schedules for elective surgical procedures in the presence of uncertain surgery durations. The analysis is performed in three steps. First, three near-optimal operating room schedules are found for different cost configurations based on the secondary data of surgery durations obtained from the Canadian Institute for Health Information. Second, these near-optimal appointment schedules are used to test a parallel scheduling policy where each surgeon has overlapping surgeries scheduled in two operating rooms for the entire session (480 minutes) and only attends the critical portions of surgeries in the two operating rooms. Lastly, another parallel scheduling policy is tested where each surgeon has overlapping surgeries scheduled for half of the session duration (240 minutes) and only has surgeries scheduled in one operating room for the remaining time. These two policies are tested using simulation with scenarios for parallelizable portions of surgeries varying from 0.1 to 0.9 at 0.1 increments and three cost configurations. In the simulated scenarios, the total cost is calculated as the weighted sum of patient waiting time, surgeon idle time, surgeon overtime, operating room idle time, and operating room overtime. Out of the nine scenarios for each policy and each cost configuration, the parallelizable portion of surgeries that result in the lowest total cost is identified. The results from both policies indicate that implementing parallel scheduling policies for surgery types with higher parallelizable portions results in surgeons remaining idle for longer periods during the session. This idle time cost is justified by a decrease in other cost components for surgeries with parallelizable portions 50% or less; however, the total cost is higher for surgeries with parallelizable portions over 50%. In addition, it has been observed that overlapping surgeries with lower parallelizable portions is more expensive than overlapping those over with 50%. Therefore, it is concluded that the surgery types that allow parallel surgery scheduling policies to be implemented at the lowest cost have 50% of their duration parallelizable

How stochasticity and emergencies disrupt the surgical schedule

In health care system, the operating theatre is recognized as having an important role, notably in terms of generated income and cost. Its management, and in particular its scheduling, is thus a critical activity, and has been the sub ject of many studies. However, the stochasticity of the operating theatre environment is rarely considered while it has considerable effect on the actual working of a surgical unit. In practice, the planners keep a safety margin, let’s say 15% of the capacity, in order to absorb the effect of unpredictable events. However, this safety margin is most often chosen sub jectively, from experience. In this paper, our goal is to rationalize this process. We want to give insights to managers in order to deal with the stochasticity of their environment, at a tactical–strategic decision level. For this, we propose an analytical approach that takes account of the stochastic operating times as well as the disruptions caused by emergency arrivals. From our model, various performance measures can be computed: the emergency disruption rate, the waiting time for an emergency, the distribution of the working time, the probability of overtime, the average overtime, etc. In particular, our tool is able to tell how many operations can be scheduled per day in order to keep the overtime limited.health care, surgical schedule, emergencies, Markov chain.

Control de Congestión TCP y mecanismos AQM

En los últimos años se ha ido poniendo énfasis particularmente en la importancia del retraso sobre la capacidad. Hoy en día, nuestras redes se están volviendo más y más sensibles a la latencia debido a la proliferación de aplicaciones y servicios como el VoIP, la IPTV o el juego online donde un retardo bajo es esencial para un desempeño adecuado y una buena experiencia de usuario. La mayor parte de este retraso innecesario se debe al mal funcionamiento de algunos búferes que pueblan internet. En vez de desempeñar la tarea para la que fueron creados, absorber eventuales ráfagas de paquetes con el fin de prevenir su pérdida, hacen creer al mecanismo de control de congestión que la ruta hacia el destino actual tiene más ancho de banda que el que posee realmente. Cuando la pérdida de paquetes ocurre, si es que lo hace, es demasiado tarde y el daño en el enlace, en forma de tiempo de transmisión adicional, ya se ha producido. En este trabajo de fín de grado intentaremos arrojar luz sobre una solución específica cuyo objetivo es el de reducir el retardo extra producido por esos hinchados búferes, la Gestión Avanzada de Colas o Active Queue Management (AQM). Hemos testeado un grupo de estos algoritmos AQM junto con diferentes modificaciones del control de congestión de TCP con el fín de entender las interacciones generadas entre esos dos mecanismos, realizando simulaciones en varios escenarios caracterísiticos tales como enlaces transoceánicos o enlaces de acceso a red, entre otros.In recent years, the relevance of delay over throughput has been particularly emphasized. Nowadays our networks are getting more and more sensible to latency due to the proliferation of applications and services like VoIP, IPTV or online gaming where a low delay is essential for a proper performance and a good user experience. Most of this unnecessary delay is created by the misbehaviour of many bu ers that populate Internet. Instead of performing the task for what they were created for, absorbing eventual packet bursts to prevent loss, they deceive the sender's congestion control mechanisms into believing that the current path to the destination has more bandwidth than it really has. When the loss event occurs, if it does, it's too late and the damage on the path, in terms of additional transmission time, has been done. On this bachelor thesis we will try to throw light over an speci c solution that aims to reduce the extra delay produced by these bloated bu ers: Active Queue Management. We have tested a bunch of AQM algorithms with di erent TCP modi cations in order to understand the interactions between these two mechanisms. We performed simulations testing various characteristic scenarios like Transoceanic links or Access link scenarios, among other.Ingeniería Telemátic