## 2 Related Work  
In literature, many researchers studied the problem of planning and scheduling of elective patients (see [8,13] and the references herein for an overview while for an overview of the problems see [14]). Almost all the works consider criterion \(C1\) presented before. Criterion \(C2\) (of using chance constraints for the scheduling) is considered also in some contributions presented in the last years. For example, in [15], integer stochastic formulations are proposed for two sub-problems in which the original problem is decomposed. The approach to solve them is based on neighborhood search techniques and Monte Carlo simulation. In [16], a two-stage robust optimization model is proposed that is solved based on a column-and-constraint generation method. A similar method is used by the authors in [17] to deal with uncertain surgery duration and emergency demand, while, in [18], the authors use particle swarm optimization for the scheduling of surgeries. The approaches presented in [19,20] are the most related to the one presented in this paper. The authors in [19] present an optimization framework for batch scheduling within a block booking system that maximizes the expected utilization of ORs subject to a set of probabilistic capacity constraints. They propose an algorithm that iteratively solves a series of mixed-integer programs that are based on a normal approximation of cumulative surgery duration. In [20], constructive and local search heuristics for maximization of ORs utilization and minimization of the overcoming risk are proposed. In their model, to address the randomness of surgery processing times, a planned time slack is reserved in each scheduling block, which is a function of total mean and variance of surgeries assigned to the corresponding block. When determining an appropriate size of the planned slacks, the authors assume that the sum of surgery duration follows a normal distribution. Both approaches in [19,20] require setting in advance the patients that are going to be scheduled in the next blocks. Therefore, in these approaches, all considered patients must be scheduled in one of the available blocks. For this, both approaches start with an initial scheduling obtained through the scheduling rule: _first-fit probabilistic_. Following this rule, sequentially each surgery is assigned to the first available block for which the probabilistic capacity constraint is satisfied after the assignment. Once the initial scheduling is obtained, the expected occupation rate of the first blocks is improved by rescheduling the surgeries. In this way, the last blocks are totally or partially released. Unlike [19,20], the approach presented in this paper does not require to know in advance the set of patients that should be scheduled in the next surgical blocks, since any patient on the waiting list may or may not be scheduled. Another big difference with [19,20] consists of the usage of two balanced terms in the cost function that favor patients to be scheduled in an orderly manner at the same time that the expected occupation rate of the OR is maximized. An exhaustive numerical comparison using realistic data is performed and analyzed showing that the approach presented in this manuscript provides better solutions to the considered problem than the one in [19,20]. In particular, even if the results show similar occupation rates and similar confidence levels, the approach presented in this paper respect the preference order of the patients in the waiting list more. Therefore, criterion \(C3\) is better considered. In the case of the hospital in which the approach is implemented, the number of available time blocks per week for each medical team is equal to two, while, on average, three patients are scheduled in a time block, making it very important to keep, if possible, the order of patients in the waiting lists. This is one of the main differences of the approach presented in this paper with the other approaches.