J. Theresia van Essen
Johann L. Hurink
Center of Healthcare Operations Improvement and Research (CHOIR)
University of Twente, Enschede
The Netherlands[email protected]
Bernd J. van den Akker
Isala Clinics Zwolle
Managing the Operating Room (OR) department is difficult due to the conflicting priorities and preferences of stakeholders. Therefore, planning and scheduling methods are helpful to increase the efficiency in OR departments (see Cardoen et al. and Hulshof et al. for an overview on OR planning and scheduling). In this article, we focus on the rescheduling of surgeries, or more precisely, on the rescheduling of surgeries throughout the day.
On any given day, emergency patients who need surgery arrive in the OR department. In many hospitals, these surgeries are scheduled in one of the elective ORs, which disrupts the OR schedule. Changes in the duration of elective surgeries may also
disrupt the OR schedule. Therefore, the initial OR schedule may have to be adjusted throughout the day to ensure that it is still possible to execute.
The new OR schedule must fulfill quite a number of restrictions, and in addition, there are several stakeholders whose preferences should be taken into account. Since it is hard for an OR-manager to consider all these restrictions and preferences simultaneously, we developed a decision support system (DSS), which supports the OR-manager. The proposed approach is general, but the realisation and used preferences are based on data from a specific hospital in the Netherlands.
In the next section, we discuss the various stakeholders involved and their restrictions and preferences, based on a survey performed at the Isala Clinics, which is the above mentioned hospital in the Netherlands. Although these restrictions and preferences may differ between hospitals, the ideas of the method developed in this paper should be applicable for other hospitals too. Based on the achieved insights, we have developed a mathematical model that incorporates these restrictions and preferences to analyse which changes are preferred. These changes are incorporated as decision rules in the DSS. The developed DSS is tested by means of a simulation study to determine what improvements can be made to the OR schedule when the developed DSS is used in practice.
Restrictions and Preferences
The initial OR schedule is given by the assignment of the elective surgeries to an OR and the initially planned start times of the elective surgeries. Each surgery has an expected duration, however, in practice, the actual duration of a surgery generally deviates from this duration. When a surgery takes less time than expected, the initial OR-schedule is not disrupted. However, it may be beneficial for the OR and other departments to schedule this next surgery earlier. When a surgery takes longer than expected, the next surgery may have to start later. This results in a shift of the not yet started surgeries in this OR. Because of this, some restrictions may be violated. In addition, emergency surgeries may arrive which also disrupt the initial OR-schedule. Therefore, throughout the day, a new OR schedule may have to be created for all elective and emergency surgeries that still have to be performed. In this section, we first consider the overall restrictions for rescheduling surgeries throughout the day. Then, we consider all stakeholders involved when changing the OR schedule and discuss their restrictions and preferences.
Rescheduling is done by assigning a new start time to each surgery. Note that we do not allow the elective surgeries to be assigned to another OR as this might lea to larger disruptions in the processes. Within the rescheduling, it may be necessary to cancel an elective surgery. Note that we do not consider the rescheduling of a cancelled surgery, because we only focus on rescheduling within the day and not from day to day.
The new start time of a surgery should fulfill a number of restrictions. It should be greater than or equal to (i) the ready time of the patient, (ii) the start time of the assigned surgeon , and (iii) the start time of the assigned OR. In addition, there may be some surgeries that should start before a certain time because of medical reasons, and therefore, cannot be cancelled.
The key stakeholder is the patient. For patients it is important that the surgery takes place at the scheduled time. Penalty costs are incurred when the new start time deviates from this preference.
Prior to surgery, patients are admitted to a ward where they are prepared for surgery. The survey showed that when a surgery starts earlier or later than scheduled, the workload on the ward increases. Therefore, penalty costs are incurred when there is a change in the start time of a surgery.
After the preparation on the ward, the patient is transported to the holding department to be further prepared. A limit on the number of patients who can be treated simultaneously is determined by the number of available nurses and beds.
The survey at the Isala Clinics showed that the holding department prefers a levelled amount of patients that are present at each point of time. Therefore, penalty costs, specified by the manager of the holding department, are incurred when the number of patients exceeds a certain threshold.
The anaesthetist is responsible for administering and reversing anaesthesia on one or more ORs. However, during the surgical procedure, the anaesthetist does not have to be present in the OR, because the presence of an anaesthesia nurse is enough. Therefore, we do not allow that more than one anaesthesia is administered or reversed at a time in the ORs to which the anaesthetist is assigned.
However, there are a few exceptions. When a surgery is complex, for example when the patient is younger than six months, the anaesthetist must be present during the complete surgery, including the surgical procedure. This means that during this time no anaesthesia can be administered or reversed in one of the other assigned ORs.
The surgeon is assigned to one OR and only has to perform the surgical procedure. This means that he/she does not have to be present during administering and reversing anaesthesia. The surgeons indicated in the survey that they do not have any preferences concerning a change in the OR-schedule as they consider the patient to be the most important.
The OR-assistants do not impose any restrictions on the OR-schedule. Their only preference is that overtime is minimised. Overtime can occur due to emergency surgeries and surgeries that take longer than expected. Therefore, penalty costs are incurred when there is overtime.
After surgery, the patient is transported to the recovery department to be monitored while recovering from surgery. The limit on the number of patients who can be monitored simultaneously is determined by the number of available nurses and beds.
Like the holding department, the recovery department also prefers a levelled amount of patients that are present at each point of time. Therefore, penalty costs are incurred when the number of patients exceeds a certain threshold.
For some surgeries, an X-ray machine is needed during surgery. For these surgeries a radiology technician should be present during administering anaesthesia and the surgical procedure. This means that he/she does not have to be present during reversing anaesthesia. We restrict the number of required radiology technicians to be smaller than or equal to the number of available radiology technicians.
The survey showed that it is important for the radiology department that their employees at the OR department finish as early as possible so that they can carry out other work in the radiology department. Therefore, penalty costs specified by the radiology department are incurred when a radiology technician finishes later than needed, i.e., when the time the radiology technicians are present is longer than the time the radiology technicians are needed.
During some surgeries, tissue is removed from a patient that needs to be examined by a pathologist. After the surgical procedure, the tissue is transported from the OR to the pathology department. When tissue arrives after closing time and overtime is needed penalty costs are incurred.
The logistic department is responsible for preparing materials needed during surgery. The materials are laid out in the order in which the surgeries are scheduled. When two surgeries are interchanged, penalty costs specified by the logistic department are incurred, because they have to change the order in which the materials are laid out.
All the restrictions and preferences described in the previous section are combined in a mathematical model (Van Essen et al. 2012). The model is used to determine optimal adjustments of the OR-schedule, however, the computation time of this model is too long to make the model applicable in practice. Therefore, the solutions obtained by this model are only used to determine which changes are preferred by the stakeholders in the solutions obtained by the mathematical model.
We tested the model on three scenarios for Isala Clinics. For each of the scenarios, we only considered surgeries that started or arrived after a certain point in time. Table 1 shows that for Isala Clinics, shifting a sur- gery is the most frequent adjustment used, and we also see that often a break is scheduled between two surgeries. The latter may not seem optimal with respect to OR utilisation, however, these breaks can improve the perceived workload of other departments or may be necessary to fulfill the restrictions. Therefore, we incorporate the following two decision rules into our DSS:
1. Shifting a surgery
break between two surgeries
Decision Support System
To make our method applicable in practice, we have developed a DSS which can be used by the OR-manager. We incorporated the two decision rules that are derived in the previous section. The user can indicate for which OR the schedule should be adjusted. Then, the DSS presents the three best options to the user. A screenshot of the DSS is shown in Figure 1.
To determine the effect of using the DSS in practice, we tested the developed DSS on data of Isala Clinics by means of a simulation study. The results in Table 2 show that the DSS provides a much better solution than the original realised OR-schedule of the Isala Clinics as the total penalty costs are reduced by approximately 50%. In addition, the results show that the penalty costs for the patients and wards decrease, however, the penalty costs for the OR-assistants and the recovery, radiology and pathology departments increase. The penalty costs for the mentioned stakeholders increase because surgeries cannot be cancelled or exchanged and thus, more surgeries have to be done in overtime. Concluding, the use of the DSS provides a better trade-off between the preferences of the involved stakeholders and by this reduces the incurred penalty costs significantly.
In this article, we treated the problem of rescheduling surgeries on the day of execution. We formulated a mathematical model that determines the best adjusted OR-schedule at a given point in time. The achieved results show that, with a few exceptions, the only used adjustments are (i) shifting surgeries, and (ii) scheduling breaks between two surgeries. These two decision rules are incorporated in a developed DSS. This system determines the best adjusted schedule for one OR with respect to the given restrictions. The simulation study shows that by using this DSS, fewer surgeries are cancelled and patients and wards are more satisfied, but also that the workload of several departments increases to compensate this.
Further research could focus on including the Central Sterile Supply Department (CSSD) into the model. This department prepares the instrument sets needed for a surgery. When a surgery is added to the OR-schedule during the day, this may influence the workload on the CSSD. In addition, the CSSD may impose some extra restrictions on the OR schedule.
are several ways in which the developed DSS can be used, for example, to reschedule
an OR immediately when it is disturbed or reschedule all ORs at some moments in
time. The last example also raises the question in what order the ORs should be
rescheduled. Therefore, it is interesting to investigate good ways to use the