A surgical procedure type schedule for general surgery : a robust tactical surgery scheduling approach to manage elective- and semi-urgent patient uncertainty

The specialty General Surgery at HagaZiekenhuis (Haga) is struggling to keep access time for elective patients below the national set limits while keeping operating room (OR) availability for semi-urgent patients high. Scheduled elective patients are cancelled at the last moment for semi-urgent and emergency patients that require surgery. An analysis of current General Surgery performance shows an average utilization of 68% in elective surgical schedules with an overtime frequency of 38%. For semi-urgent patients, the probability of access to surgery within a week is currently 47%. For elective patients, Haga achieves a five week access time probability of 37% compared to the national allowed limit of 80%. The access time probability within seven weeks is 75% compared to the national allowed limit of 100%. We identify a number of underlying causes of poor performance and determined that these mainly originate on tactical and operational offline levels. We determine that on these levels, the current scheduling approach fails to properly manage uncertainties related to surgical demand and duration. For example, nearly 86% of the surgery duration estimates that OR planners use when scheduling are off more than 10 minutes. Therefore, our research objective is: To develop an OR scheduling approach which manages surgical demand and duration uncertainty for elective and semi-urgent patients. Solution approach Based on a theoretical framework, we propose a robust cyclic surgical schedule aimed on managing surgical demand and duration uncertainty. To manage this uncertainty, we decompose the solution approach into several steps. We apply a clustering approach proposed by van Oostrum et al. [1] as a method to combine individual surgical procedures into homogenous surgical procedure types in terms of duration. This allows us to reduce demand uncertainty through a pooling effect. To manage semi-urgent demand uncertainty we apply the discrete time slot queuing theory approach presented by Kortbeek et al [2]. The queuing model determines the probability of access within a week based on a chosen number of slots. We determine the number of slots to be the weekly demand for semi-urgent patients that we should cover to provide timely access and to prevent the current frequent elective patient cancellations. With elective and semi-urgent demand input known, we apply a mathematical programming approach with column generation approach based on van Oostrum et al. [3] to create a surgical procedure type schedule (SPTS). In this SPTS, we select operating room days (ORDs), which are ORs filled with surgical procedure types from an implicit set and assign these to specific dates and operating rooms. Implicit refers to the fact that we iteratively expand the set with potential ORDs. New ORDs are iteratively generated in a sub-model that offer an improvement to this set. This sub-model incorporates surgical slack and the portfolio effect by described by Hans et al. [4] for both Gaussian and log-normal distributed surgical duration procedures to manage overtime probability. For all sub-specialties, we select as many ORDs required to balance elective waiting lists to an acceptable level. The result is a schedule where surgical cases can be planned into the first available surgical procedure type slots that they are part off. Only semi-urgent procedures should be scheduled in slots reserved for semi- urgent procedure types.