Existence of an unbounded vacant set for subcritical continuum percolation

We consider the Poisson Boolean percolation model in $\mathbb{R}^2$, where the radii of each ball is independently chosen according to some probability measure with finite second moment. For this model, we show that the two thresholds, for the existence of an unbounded occupied and an unbounded vacant component, coincide. This complements a recent study of the sharpness of the phase transition in Poisson Boolean percolation by the same authors. As a corollary it follows that for Poisson Boolean percolation in $\mathbb{R}^d$, for any $d\ge2$, finite moment of order $d$ is both necessary and sufficient for the existence of a nontrivial phase transition for the vacant set.Comment: 9 page

A modelling and simulation framework for health care systems.

International audienceIn this paper, we propose a new modeling methodology named MedPRO for addressing organization problems of health care systems. It is based on a metamodel with three different views: process view (care pathways of patients), resource view (activities of relevant resources), and organization view (dependence and organization of resources). The resulting metamodel can be instantiated for a specific health care system and be converted into an executable model for simulation by means of a special class of Petri nets (PNs), called Health Care Petri Nets (HCPNs). HCPN models also serve as a basis for short-term planning and scheduling of health care activities. As a result, the MedPRO methodology leads to a fast-prototyping tool for easy and rigorous modeling and simulation of health care systems. A case study is presented to show the benefits of the MedPRO methodology

Operating theatre scheduling with patient recovery in both operating rooms and recovery beds

International audienceThis paper investigates the impact of allowing patient recovery in the operating room when no recovery bed is available. Three types of identical resources are considered: transporters, operating rooms and recovery beds. A fixed number of patients must be planned over a term horizon, usually one or two weeks. The surgery process is modelled as follows: each patient is transported from the ward to the operating theatre. Then the patient visits an operating room for surgery operation and is transferred to the recovery room. If no recovery bed is available, the patient wakes up in the operating room until a bed becomes available. The operating room needs to be cleaned after the patient's departure, before starting another operation. Finally, the patient is transported back to the ward after his recovery. We consider several criteria based on patients' completion times. We propose a Lagrangian relaxation-based method to solve this operating theatre scheduling problem. The efficiency of this method is then validated by numerical experiments. A comprehensive numerical experiment is then performed to quantify the benefit of allowing patient recovery in operating rooms. We show that the benefit is high when the workload of the recovery beds is high

Hospitalization admission control of emergency patients using markovian decision processes and discrete event simulation

International audienceThis paper addresses the hospitalization admission control policies of patients from an emergency department that should be admitted shortly or transferred. When an emergency patient arrives, depending on his/her health condition, a physician may decide to hospitalize him/her in a specific department. Patient admission depends on the availability of beds, the length of stay (LOS) and the reward of hospitalization which are both patient-class specific. The problem consists in determining patient admission policies in order to maximize the overall gain. We first propose a Markov Decision Process (MDP) Model for determination of the optimal patient admission policy under some restrictive and necessary assumptions such as exponentially distributed LOS. A simulation model is then built to assess MDP admission policies under realistic conditions. We show that MDP policies significantly improve the overall gain for different types of facilities

Mathematical Programming Models for Annual and Weekly Bloodmobile Collection Planning

International audienceIn this paper, we propose a two-step bloodmobile collection planning framework. The first step is the annual planning to determine weeks of collection at each mobile site in order to ensure regional self-sufficiency of blood supply. The second step is the detailed weekly planning to determine days of collections at each mobile site and to form corresponding transfusion teams. Only key resource requirements are considered for annual planning while detailed resource requirements and transportation times are considered for weekly planning. Two Mixed Integer Programming models are proposed for annual planning by assuming fixed or variable mobile collection frequencies. A new donation forecast model is proposed based on population demographics, donor generosity, and donor availability. A new concept of bloodmobile collection configurations is proposed for compact and efficient mathematical modeling of weekly planning in order to minimize the total working time. Field data from the French Blood Service (EFS) in the Auvergne-Loire Region are used to design numerical experiments and to assess the efficiency of the proposed models

Heuristic algorithms for a vehicle routing problem with simultaneous delivery and pickup and time windows in home health care

International audienceThis paper addresses a vehicle scheduling problem encountered in home health care logistics. It concerns the delivery of drugs and medical devices from the home care company's pharmacy to patients' homes, delivery of special drugs from a hospital to patients, pickup of bio samples and unused drugs and medical devices from patients. The problem can be considered as a special vehicle routing problem with simultaneous delivery and pickup and time windows, with four types of demands: delivery from depot to patient, delivery from a hospital to patient, pickup from a patient to depot and pickup from a patient to a medical lab. Each patient is visited by one vehicle and each vehicle visits each node at most once. Patients are associated with time windows and vehicles with capacity. Two mixed-integer programming models are proposed. We then propose a Genetic Algorithm (GA) and a Tabu Search (TS) method. The GA is based on a permutation chromosome, a split procedure and local search. The TS is based on route assignment attributes of patients, an augmented cost function, route re-optimization, and attribute-based aspiration levels. These approaches are tested on test instances derived from existing VRPTW benchmarks

Modelling and simulation of blood collection systems: improvement of human resources allocation for better cost-effectiveness and reduction of candidate donor abandonment

International audienceFormal Petri net models were used to describe all relevant donor flows of the various blood collection systems; the Petri net models were converted onto discrete-event simulation models, allowing the evaluation of a large number of scenarios and configurations of blood collection systems. Quantitative models were proposed that encompassed all components of the blood collection systems, such as the donor arrival process, resource capacities and performance indicators. Appropriate experimental designs and cost-effectiveness analyses were used to determine the best configurations of human resources and donor appointment strategies

Economic comparison between Hospital at Home and traditional hospitalization using a simulation-based approach

International audienceHospital at Home (HAH) is a concept slowly expanding over time. At first this type of organization was used to accomplish low-technical tasks. The main objective was to increase bed availability in hospitals for new patients. Nowadays, HAH structures are able to undertake more technical complex care such as (but not limited to) end-of-life care, chemotherapy and rehabilitation. The purpose of this paper is to propose a new methodology to make an unbiased economic comparison between HAH structures and traditional hospitalization. This article accomplishes two main objectives: in the first part the authors propose a comprehensive literature review dealing with the comparison between traditional hospital and home care structures from an economic standpoint, showing that results are highly dependent on initial conditions of the study (patient health state, territory settings, bio-medical parameters); in the second part the authors propose an unbiased economic comparison approach between health care provided in traditional hospital and home care network using formal modelling with Petri nets and discrete event simulation. As an example for the comparison a multi-session treatment is proposed. Various scenarios are tested to ensure that results will be maintained even if initial conditions change. Relevant performance indicators used for comparison are economic costs from the point of view of the insurance and economic costs related to the consumption of resources