Control of Safe Ordinary Petri Nets Using Unfolding

International audienceIn this paper we deal with the problem of controlling a safe place/transition net so as to avoid a set of forbidden markings "F" . We say that a given set of markings has property REACH if it is closed under the reachability operator. We assume that all transitions of the net are controllable and that the set of forbidden markings "F" has the property REACH. The technique of unfolding is used to design a maximally permissive supervisor to solve this control problem. The supervisor takes the form of a set of control places to be added to the unfolding of the original net. The approach is also extended to the problem of preventing a larger set "F" of impending forbidden marking. This is a superset of the forbidden markings that also includes all those markings from which—unless the supervisor blocks the plant—a marking in "F" is inevitably reached in a finite number of steps. Finally, we consider the particular case in which the control objective is that of designing a maximally permissive supervisor for deadlock avoidance and we show that in this particular case our procedure can be efficiently implemented by means of linear algebraic techniques

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

Planning oncologists of ambulatory care units

International audienceThis paper addresses the problem of determining the work schedule, called medical planning, of oncologists for chemotherapy of oncology patients at ambulatory care units. A mixed integer programming (MIP) model is proposed for medical planning in order to best balance bed capacity requirements under capacity constraints of key resources such as beds and oncologists. The most salient feature of the MIP model is the explicit modeling of specific features of chemotherapy such as treatment protocols. The medical planning problem is proved to be NP-complete. A three-stage approach is proposed for determining good medical planning in reasonable computational time. From numerical experiments based on field data, the three-stage approach takes less than 10 min and always outperforms the direct application of MIP solvers with 10 h CPU time. Compared with the current planning, the three-stage approach reduces the peak daily bed capacity requirement by 20 h to 45 h while the maximum theoretical daily bed capacity is 162 h

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

Implementation strategies of a contract-based MRI examination reservation process for stroke patients

International audienceTimely imaging examinations are critical for stroke patients due to the potential life threat. We have proposed a contract-based Magnetic Resonance Imaging (MRI) reservation process [1] in order to reduce their waiting time for MRI examinations. Contracted time slots (CTS) are especially reserved for Neural Vascular Department (NVD) treating stroke patients. Patients either wait in a CTS queue for such time slots or are directed to Regular Time Slot (RTS) reservation. This strategy creates "unlucky" patients having to wait for lengthy RTS reservation. This paper proposes and analyzes other contract implementation strategies called RTS reservation strategies. These strategies reserve RTS for NVD but do not direct patients to regular reservations. Patients all wait in the same queue and are served by either CTS or RTS on a FIFO (First In First Out) basis. We prove that RTS reservation strategies are able to reduce the unused time slots and patient waiting time. Extensive numerical results are presented to show the benefits of RTS reservation and to compare various RTS reservation strategies

Dynamic Surgery Assignment of Multiple Operating Rooms With Planned Surgeon Arrival Times

International audienceThis paper addresses the dynamic assignment of a given set of surgeries to multiple identical operating rooms (ORs). Surgeries have random durations and planned surgeon arrival times. Surgeries are assigned dynamically to ORs at surgery completion events. The goal is to minimize the total expected cost incurred by surgeon waiting, OR idling, and OR overtime. We first formulate the problem as a multi-stage stochastic programming model. An efficient algorithm is then proposed by combining a two-stage stochastic programming approximation and some look-ahead strategies. A perfect information-based lower bound of the optimal expected cost is given to evaluate the optimality gap of the dynamic assignment strategy. Numerical results show that the dynamic scheduling and optimization with the proposed approach significantly improve the performance of static scheduling and First Come First Serve (FCFS) strategy

A two-phase approach for periodic home health care planning

International audienceIn this paper, we study the problem of periodic vehicle routing encountered in Home Health Care (HHC). The problem can be considered as a Periodic Vehicle Routing Problem with Time Windows (PVRPTW). It consists in establishing a planning of visits to patients over a given time horizon so as to satisfy the adherence to the care plan while optimizing the routes used in each time period. One two-stage mathematical formulation of this problem is proposed. We then propose a Tabu Search (TS) and a MIP-based Neighborhood Search method to compute the weekly and daily plan, respectively. These approaches are tested on large size instances

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

Performance analysis of a transfer line with unreliable machines and finite buffers

This paper examines the performance analysis of a transfer line with unreliable machines and finite buffers. All machines have the same processing times. We propose a new decomposition method which decomposes a line into a set of two-machine lines. A sufficient set of equations is established to find performance measures such as production rate and average buffer levels. A simple iterative algorithm is then proposed to solve these equations. We also prove that the set of decomposition equations has a unique solution and that the proposed algorithm converges to that unique solution. Experimental results show that the proposed algorithm leads to a good solution