A Mathematical Model for Scheduling Elective Surgeries for Minimizing the Waiting Times in Emergency Surgeries

Document Type : Original Article


1 Department of Industrial Engineering, Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran

2 Department of Industrial Management, Management and Accounting Faculty, Shahid Beheshti University, Tehran, Iran

3 Faculty of Industrial Engineering, Golpayegan University of Technology, Golpayegan, Iran


The ever-increasing demands for surgeries and the limited resources force hospitals to have efficient management of resources, especially the expensive ones like operating rooms (ORs). Scheduling surgeries including sequencing them, assigning resources to them and determining their start times is a complicated task for hospital managers. Surgery referrals usually include elective surgeries that are admitted before the planning horizon of the schedule and emergency surgeries that arrive during this horizon and require fast services. In this paper, we presented a mathematical model for scheduling electives and emergencies. In our model, we considered surgeries as projects with multi-activities. We implemented the Break-in-Moments (BIMs) technique in this structure, which to our best knowledge has not been implemented in the literature before. We examined this method with real data from a medium-sized Norwegian hospital and observed that this method reduces the waiting time of emergencies to be inserted into the schedule without dedicating any OR merely to emergencies. In such a way, this method counterbalances between efficient OR usage and responsiveness for emergency surgeries.


In other words, adjusting the BIM intervals during 
the schedule of elective projects is a successful method
for decreasing the waiting time in emergency projects.
Although, the cost of this success is paid by longer
makespan (finishing the schedule later) and increasing
the number of unscheduled elective projects, when this
method is compared by ordinary scheduling of elective
projects. Decreasing the waiting time for emergency
surgeries is a very important result because of the
responsibility of the hospitals in saving lives. On the
other hand, this is considered that this success is
obtained while all the ORs are utilized for serving the
elective surgeries. In such a way, the profit-making
aspect of the ORs is also considered. These results are
obtained when arrival rate of emergency surgeries is
supposed a normal rate of 20 percent of the number of
elective surgeries. However, when this rate increases
significantly and hospital encounters lots of emergency
surgery referrals, dedicating some ORs to emergencies
is suggested.

In this paper, we introduced a new way of implementing
the method of adjusting the BIM intervals for project
scheduling model and this is our main contribution. We
examined our method with the real data from a
Norwegian hospital. This method is successful for
decreasing the waiting times of emergency projects for
inserting to the schedule of elective projects. However,
this method increases the number of unscheduled
elective projects that is the drawback of this method.
The importance of decreasing the waiting time in
emergency projects without dedicating any OR to
emergency projects and withdrawing this OR from
serving elective projects can be a sufficient reason for
making this method attractive for OR managers. We
propose using this method in surgery units with very
high-profit ORs and low rate of emergency arrivals. 
In this research, we suppose that after the arrival of
any surgery referral, an expert based on his or her
previously experiments determines the feasible modes
for activities and their duration times. Failure of
resources and unpredictable unavailability of resources
and changing the duration of activity modes are not
considered in this paper. As future work, we suggest
covering more uncertainties in this model. 
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