Surgical scheduling based on Timed Coulored Petri Nets and (max, +) Algebra

― This paper addresses surgical scheduling problem on the operational decision level. The problem consists of assigning an intervention date and operating room (OR) to elective surgeries, taking into account limited resources of OR and surgeons. The Healthcare System (HS) is studied in this paper as a Discrete Event System. The main purpose of our study is to model and analyze the HS using two complementary formalisms Timed Coulored Petri Nets (TCPN) and (max, +) Algebra. To do so, TCPN model is first developed to model and study the patient care flow behavior, in order to evaluate its performances. Based on TCPN model, (max, +) equations are then developed to represent the system behavior by linear models and to calculate the occurrence dates of surgery activities. Owing to the both proposed models it is possible to design a provisional schedule of elective interventions, that will be used to suggest optimization strategies aimed at improving the HS performances. An illustrative example is given to show the effectiveness of the proposed approach.