Ordonnancement de bloc opératoire avec intégration des soins intensifs

Our project aims at developing a decision tool for the scheduling of operating rooms at the administrative level of the hospital. Ultimately, this tool's objective is to optimize the use of available resources of the hospital while prioritizing the interventions on patients who have been waiting for the longest time. Above consideration of the operating block, our model integrates the intensive care unit. This allows us to have a better vision of the postoperative part of the patient care and, thus, to fludify it within the hospital. Indeed, not taking this part into account may lead to the cancellation of some interventions since a patient needing to be admitted in the ICU cannot be operated on unless a bed is made available to him. A decision tool is useful for several reasons. Firstly, it accelerates the schedule generating process. This is interesting since the scheduling task is a very complex one and that, having several objectives, makes it almost impossible to reach an optimal solution by hand. Secondly, taking more information into account -such as some patients' characteristics or staff availabilities- is useful and a fine-tuned decision tool may allow us to do so more easily and efficiently. This has a positive impact on both the hospital and the patients. Indeed, optimizing the processes of such a costly section of the hospital in order to make a better use of the available resources may represent substantial savings for the hospital, and a valuable improvement in the quality of care of the patients, whose main concern is their waiting time. Furthermore, reducing the cancellation risk and sharing its occurence probability with the patients might in turn diminish the stress incurred by the intervention. Thus, one of our main challenges is to study the intensive care unit activity in order to implement a well suited solution. Firstly, we will present a basic model and, secondly, we will explore two ways of improving it : integrating the uncertainty in the durations of the interventions and upgrading our level of decision by chosing which surgeon to schedule instead of respecting the constraints already imposed by the hopistal. Our main modelling method is programming 0-1, i.e. with binary variables. The objective function of our program aims at maximizing the total duration of interventions scheduled and will give a more important weight to the patients who have been waiting the longest time. Our method to integrate the intensive care unit is inspired from a Markovian Decision Process and the idea is to impose an upper bound on the daily probabilities of cancellation. All the models used in this project are linear. The obtained results show it is possible to prioritize the patients in an interesting way with a minimal decrease in rooms occupation rates. Indeed, we observe that an improvement concerning the selection of patients can be made: the patients selected with our solution were waiting for a longer time in average than those selected by the hospital. This model yields a rapid, near optimal solution but does not take the urgent and semi-urgent cases into account. Thus, in order for our tool; to be useful to the hospital, a solution might be to book only 75% of the time available with it so that the other 25% are left to be completed by hand with more urgent cases or according to the preferences of the surgeons. The model that takes the uncertainty of the durations of intervention into account shows promising results in terms of preventing rooms from going overtime. Moreover, letting our progam decide which surgeon to schedule is also interesting in the sense that it allows us to enhance prioritization of returning patients. However, this model would require further operational constraints to be fully and accurately implemented by the hospital. Last but not least, the results concerning the postoperative section show that our model schedules more patients who need an admission in the intensive care unit during the summer period. This goes in line with the observations made a priori by the staff working in the unit.