Scheduling surgery cases is a complex task because of the significant uncertainty that exists in the OR system. Variability in surgery procedure duration, multiple surgery types, and the arrival of emergency cases complicate the design of effective schedules. This paper develops surgery scheduling policies for elective and emergency surgeries with the objective of reducing patient waiting time, surgeon idle time and surgery overtime. Simulation models are created to study multiple operating rooms’ schedule for a given session. Using the data from previous literature and from Canadian Institute for Health Information (CIHI), the three cases with three different scenarios (three allocation rules) each are simulated. Two different interval rules, six different sequencing policies, different levels of cost coefficient, two probabilities of emergency case arrival rate are simulated within each case to identify the scheduling policy that results in the best overall performance. The two interval rules consist of a set of fixed interval rules and variable interval rules. Six sequencing rules are also tested including longest processing time first (LPT), shortest processing time first (SPT), alternate rule 1 (AR 1), alternate rule 2 (AR 2), alternate rule 3 (AR 3) and alternate rule 4 (AR 4) in Table 6.
When only one type of procedure is performed in an OR, the trade-off between the surgeon and patient priority should be considered. A hospital usually considers surgeon satisfaction more important because the cost of the surgeon is usually higher than that of the patient. Therefore, if the cost coefficients of idle time and overtime are higher than that of patient waiting time, decreasing the interval length between cases can reduce surgeon idle time and overtime. This finding is consistent with research findings in other papers focusing on outpatient clinic scheduling and surgery scheduling (Klassen and Yoogalingam, 2009; Gul et al. 2011). In addition, the study
and Dome Rule in getting the lowest expected total cost with no emergency cases or 10% emergency case arrival rate. The Decreasing Interval Rule and Reverse Dome Rule always have worse performance.
When different types of procedures are performed in an OR, sequencing of these procedures is important. With no emergency cases, the SPT rule is found to be the best strategy that results in improving overall performance. This finding is consistent with research findings in other articles (Sciomachen et al., 2005; Testi et al., 2007; Olsen, 2015; Gul et al. 2011). The reason why the SPT rule outperforms other rules is because short procedures have less variability than longer procedures. The short procedures have smaller standard deviations. It would allow an OR scheduler to have a more accurate prediction in an OR schedule. ORs that start with short procedures have a higher chance that followed procedures will start on time (Lebowitz, 2003). If they are not started on time, there are less waiting times than ORs that begin with long procedures. In addition, this study has different cases with different surgery mean durations and it could provide a more detail analysis of the impact from different mean durations to sequencing rules.
In general, the SPT rule always reduces patient waiting time, which results in the lowest expected total cost with no emergency cases when surgery mean duration is relatively short. For the LPT rule, even though it always results in lowest idle time and overtime compared to other rules, an ideal sequencing policy needs to minimize the tradeoff between waiting time, idle time and overtime, making the LPT rule not an ideal policy. For the four alternated rules, most of the results indicate that there is no significant difference between them, and the SPT rule outperforms the four alternated rules.
For the arrival of emergency cases, previous studies mainly focused on operating room resource planning (Wullink et al., 2007; Azeri-Rad et al., 2014; Persson and Persson, 2010), but
they did not consider the impact of emergency cases on sequencing rules. With 10% emergency case arrival rate, if the surgery mean duration is relatively long and fewer surgeries are scheduled, there is no significant difference between the SPT rule and other rules. When the surgery mean duration is relatively short, the SPT rule still improves the overall performance only when the cost coefficients of idle time and overtime is 5. It should be noted that, after incorporating the third procedure type, changing rules would not have a statistical difference in overall performance since none of the rules can offset the increase in the cost from both waiting time and overtime resulting from the arrival of emergency cases. The reason why most of the sequencing rules would not make an improvement on performance after the arrival of emergency cases is because the utilization is already very high due to the allocation rules in this study. Therefore, the arrival of emergency case would affect the performance of sequencing rules.
This study considers the impact from different cost coefficients of idle time and overtime to the best rule. Prior literature also focused on testing different cost coefficients in operating rooms (Denton et al., 2007; Astaraky and Patrick, 2015), but none of them studied its impact to
sequencing rules while considered the arrival of emergency cases. With no emergency cases, if the surgery mean duration is relatively long, the SPT rule only has significant improvement when the cost coefficient of idle time and overtime is 5. When the surgery mean duration is relatively short and more procedures are scheduled, the SPT rule always has a significant impact on decreasing the expected total cost. The cost coefficients of idle time and overtime can be low (5) or high (15). With emergency arrival rate is 10%, the improvement from the SPT rule might not be significant.
In the comparison of three allocation rules in three different cases, different cases have the different best option. When surgery mean duration is relatively long, “Partially Shared ORs”,
priority is concerned. In “Partially Shared ORs”, it dedicates some ORs to a single procedure type and remaining ORs to multiple surgery types. Surgeries can be grouped by their durations first, and then similar duration surgeries are put in part of the ORs. The rest of the ORs can schedule different types of surgery. The scheduler can use the mean of surgery durations as the interval between cases to set up the OR schedule in the ORs that only have one procedure type. In the ORs that have more than one procedure type, the relatively shorter procedures should be processed first. When surgery mean duration is relatively short and more cases can be scheduled, the “Shared ORs”, which uses all ORs to multiple surgery types improve overall performance compared to other scenarios. Prior literature mainly used analytical methods to find the best combination of different procedure types (Ozkarahan, 2000; Kuo et al., 2003; Ogulata and Erol, 2003), but the allocation rules in this study that are based on surgery mean duration may also provide a different insight in surgery allocation rules.