Towards a methodology to generate resource assignment rules in healthcare systems

In this work, we present a methodology providing a decision tool for resource assignment problem in healthcare systems. The choice of h i s problem among others is justified on one hand by the hospital environment need to be assisted by decision tools for managing its resources and on the other hand by the human resource rarefaction. Hence, it becomes essential to search for a bener use ofthe existing means in this kind of systems. One of the resource assignment problem specifications in the healthcare systems consistS of the resources intervention mode in operations. Indeed, various resources are used in healthcare operations, their intervention mode is a mixing of the IWO classical modes, series and parallel [Jebali et al., 20011. Evidently not all resources are needed at the beginning of an operation. However, in the healthcare system, once an operation i s started. a resource has to be available at the time it is needed. This is known as a scheduling problem with “ n e wait” consmint. This problem with the objective of minimizing the makespan and with more than IWO resources (two machines) has been proven to be smongly NP-hard [Pinedo, 19951. Many works deal with the resource assigmnent problem in healthcare systems [Vissers, 19941, [Vissm, 19981, [Kim and al., 20001. [Guinet and Chaabane, ZOOI]. They may be broadly classified as being based on analytic or simulation models. However, the most of them do not consider the intervention mode specification. They are limited only to one resource of the healthcare system (for example beds, operating rooms.. .). However, a healthcare operation uses various resources and can begin only if it is guaranteed that all resources will be available at the time they are needed. So, assignment decisions must ensure this specification in healthcare systems by disallowing all kinds of rcsource unavailability after the beginning of the operation. The unavailability of a resource at the time it is needed in an operation generates an undesirable sihlalion in the healthcare system, which we call “forbidden state“. In [Jebali et al.. 20021, we developed an approach for a supervised and optimized resource assignement in healthcare systems centered on this specicification. This approach is made up of three steps : the first step consists of a modelling of heathcare system based on Time Petri Nets (TPN) the second step consists, at first, in synthesizing the TPN behavior using a timed automaton. Then, a timed automaton of supervision is constructed in the objective to forbid the occurrence of a “forbidden stale”. The passages TPN timed automaton timed automaton of supervision are based on algorithms given in [Sava, 20011. ~ the third step consists in transforming the timed automaton of supervision into a directed graph for which each arc has an associated length. The shortest path provides the optimal assignment strategy. Hencefonh, this approach finishes at the level of timed automaton of supervision. Our objective by generating assignment rules is to extend this approach by giving an interpretation to supervisor action. These mles serve to consmct algorithm that determine the SW times of each operation. Another objective by the present methodology is to go past the conslraint of the combinatorial feature of the passage TPN timed automaton. Indeed, the number of timed automaton nodes corresponding lo the TPN explodes with the increase of resource units and patients presenf in the healthcare system represented by tokens in the TPN model. To our mind, it become essential to consider this consmaint, as soon as we think of a real healthcars system where several patients and resource units exist. Our methodology comprises IWO main stages : the first StRgC : it consists in generating resource assignment rules in a heathcare system that works with a minimum amount of resources. the second stage : it consists in generalizing the resource assignment rules found at the fin stage to the case of a healthcare system working with several units of every resource. -