OPTIMIZE OR−SCHEDULE TO REDUCE NUMBER OF REQUIRED BEDS Theresia van Essen, Joël Bosch

Reduce number of required beds:  Less admissions  Reduce length of stay  Level bed utilization Optimize OR-Schedule to Reduce Number of Required Beds 2/26 CONTEXT

Optimize OR-Schedule to Reduce Number of Required Beds 3/26 BED UTILIZATION PatientLOSOption 1Option 2 13MondayTuesday 23 Wednesday 32ThursdayWednesday

Optimize OR-Schedule to Reduce Number of Required Beds 4/26 BED UTILIZATION PatientLOSOption 1Option 2 13MondayTuesday 23 Wednesday 32ThursdayWednesday

Optimize OR-Schedule to Reduce Number of Required Beds 5/26 BED UTILIZATION PatientLOSOption 1Option 2 13MondayTuesday 23 Wednesday 32ThursdayWednesday

Optimize OR-Schedule to Reduce Number of Required Beds 6/26 BED UTILIZATION PatientLOSOption 1Option 2 13MondayTuesday 23 Wednesday 32ThursdayWednesday

Optimize OR-Schedule to Reduce Number of Required Beds 7/26 BED UTILIZATION PatientLOSOption 1Option 2 13MondayTuesday 23 Wednesday 32ThursdayWednesday

 Beliën and Demeulemeester (2007)  Stochastic length of stay  Optimization  Minimize sum required beds  Van Oostrum et al. (2008)  Mean length of stay  Optimization  Vanberkel et al. (2011)  Stochastic length of stay  Evaluation Optimize OR-Schedule to Reduce Number of Required Beds 8/26 RELEVANT LITERATURE

 Generate OR blocks  Maximize OR utilization  Satisfy overtime probability  Assign OR blocks to OR-day  Minimize number beds  Satisfy OR availability  Satisfy surgeon availability  Satisfy capacity instrument sets Optimize OR-Schedule to Reduce Number of Required Beds 9/26 MODEL

 Blocks are assigned to one specialist  Maximize sum of expected duration  Sum expected duration plus slack is less than capacity  Solve with Column Generation Optimize OR-Schedule to Reduce Number of Required Beds 10/26 GENERATE OR BLOCKS 08:00 16:00

 Planning horizon  Days with OR and surgeon availability  OR blocks  Number of patients of each type  Required instruments  Probability distribution LOS Optimize OR-Schedule to Reduce Number of Required Beds 11/26 ASSIGN OR BLOCKS TO OR-DAY INPUT LOS12345 Probability

Optimize OR-Schedule to Reduce Number of Required Beds 12/26 ASSIGN OR BLOCKS TO OR-DAY DISTRIBUTION BEDS

Simulated Annealing  Swap two OR blocks from two different days  If swap is feasible, determine number required beds  Better solution: accept  Worse solution: accept with probability Optimize OR-Schedule to Reduce Number of Required Beds 13/26 ASSIGN OR BLOCKS TO OR-DAY MODEL

Optimize OR-Schedule to Reduce Number of Required Beds 14/26 ASSIGN OR BLOCKS TO OR-DAY MODEL OR 1OR 2 Day 112 Day 234

Optimize OR-Schedule to Reduce Number of Required Beds 15/26 ASSIGN OR BLOCKS TO OR-DAY MODEL OR 1OR 2 Day 142 Day 231

 Assignment of OR blocks to OR-days  Number required beds per day Optimize OR-Schedule to Reduce Number of Required Beds 16/26 ASSIGN OR BLOCKS TO OR-DAY OUTPUT

Optimize OR-Schedule to Reduce Number of Required Beds 17/26 RESULT HAGAZIEKENHUIS ORTHOPEDICS

Optimize OR-Schedule to Reduce Number of Required Beds 18/26 RESULT HAGAZIEKENHUIS ORTHOPEDICS

Optimize OR-Schedule to Reduce Number of Required Beds 19/26 RESULT HAGAZIEKENHUIS ORTHOPEDICS

 Applicable to surgical wards  Applicable to nonsurgical wards  No OR blocks, but individual patients  Emergency patients can be incorporated  Add distribution of emergency patients per day Optimize OR-Schedule to Reduce Number of Required Beds 20/26 APPLICATIONS

 Number beds can be reduced  Even when OR utilization increases  Costs can be reduced  Information for nurse rostering provided  Develop iterative approach  Close wards during weekend Optimize OR-Schedule to Reduce Number of Required Beds 21/26 CONCLUSIONS & FUTURE RESEARCH

Questions?