1. Long term policies for operating room planning
A. Agnetis1, A. Coppi1, G. Dellino2, C. Meloni3, M. Pranzo1
1 Dept. of Information Engineering, University of Siena, Italy
2 IMT Institute for Advanced Studies, Lucca, Italy
3 Dept. of Electronics and Electrical Engineering, Polytechnic of Bari, Italy

2. Outline Introduction Problem description
Optimization models and heuristics
Case study
Preliminary results
Conclusions

3. Introduction
Operating theatre (OT) among the most critical resources in a hospital
Significant impact on costs
Affects quality of service
Improve the efficiency of the OT management process
Focus on operating room (OR) planning
Health care expenditure
QoS as perceived by patients

4. Decision problems in OT management
Mon
Tue
Wed
Thu
Fri
OR1
OR2
OR3
OR4
OR5
OR6
MSSP
SCAP
ESSP
Gynecology
Urology
Day surgery
General surgery
Otolaryn-gology
Orthopedic surgery
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5. Organizational complexity vs. MSS variation
Staffing and shift planning
MSS fixed over time  ↑ stability, ↓ flexibility
MSS different every week  ↓ stability, ↑ flexibility
Staffing patterns favour staff satisfaction

6. Main contributions
Alternative policies proposed to trade off efficient management of the surgery waiting lists and organizational complexity
MSSP and SCAP solved through mathematical programming models and heuristics
Performance evaluation over one-year time horizon
Assumptions:
Deterministic data
Elective patients only

7. Problem description (1)
Input: waiting list of elective patients for each surgical specialty
Data for each case surgery in the list:
Output: one-week assignment (Mon-Fri) of elective surgeries to ORs
Waiting list – Day surgery
Surgery code
Entrance time
Surgery duration
(min)
Priority class
Waiting time
(days)
Due date
6210
15/06/2010 28 B 27
15/08/2010

8. Problem description (2)
OR sessions: morning/afternoon/full-day
Assignment restrictions
Objectives:
Max ORs utilization, without overtime
Schedule case surgeries within their due-date, reducing patients’ waiting time
based on case surgeries duration and a score, related to:
case surgery waiting time and priority class
case surgery slack time

9. Optimization models ILP mathematical formulations, solved by CPLEX
Unconstrained MSS model
Determines MSS and SCA every week, based on the actual waiting list for each specialty
Constrained MSS model
Determines MSS and SCA, bounding the number of changes in OR session assignments to different surgical specialties w.r.t. a reference MSS
Fixed MSS model
Determines SCA, given an MSS

10. Unconstrained MSS model
‘Unconstrained’ w.r.t. long-term planning
Constraints
Bounds on the number of weekly OR sessions assigned to a specialty
Min number of ORs assigned to a specialty every day (either half-day or full-day sessions)
Max number of parallel OR sessions for each specialty
Restrictions on specialty-to-OR assignments
Max OR session duration (no overtime)

11. Constrained MSS model ‘Constrained’ w.r.t. long-term planning
Block time = # weeks during which the MSS is fixed
Set a reference MSS
Distance (Δ) between two MSSs: # ORs for each day and session type assigned to different surgical specialties in the MSSs
One constraint added to the previous model, bounding such a distance between the new MSS and the reference MSS

12. Fixed MSS model
The MSS has been already determined  OR sessions already assigned to surgical specialties
Assignment of case surgeries to OR sessions; i.e., SCAP is solved

13. Heuristic methods MSSP SCAP OR sessions = bins; Surgeries = items
Candidate OR sessions (half-day/full-day) for each specialty → first-fit-decreasing rule
Selection of candidate sessions assigned to OR
MSS is retained, discarding all surgical cases filling it
SCAP

14. Planning policies MSSP SCAP Unconstrained MSS model Exactly solved
Heuristically
SCAP
Exactly
solved
Heuristically
Constrained
MSS model
Δ = 1, block = 1
Δ = 2, block = 4
Fixed
MSS model

15. Case study: OT characteristics
Medium-size public Italian hospital (Empoli, Tuscany)
OT = 6 operating rooms; two ORs are bigger
6 surgical specialties: general surgery, otolaryngology, gynecology, orthopedic surgery, urology, day surgery
Surgical specialty restrictions
Gynecology must use the same OR for the whole week
Orthopedics needs big ORs
Two parallel OR sessions can be both assigned to general surgery (the same for orthopedics)
Further restrictions
One OR quickly made available, every morning
One OR free every afternoon

16. Case study: experimental design
MSSP and SCAP solved every week
Simulation over one year
Weekly arrivals:
nonparametric bootstrapping from the initial waiting list
sample size from a uniform distribution centered around the average weekly arrival rate
Two scenarios tested: base/stressed scenario

17. Preliminary results Base scenariof1 f2

18. Preliminary results Stressed scenariof1 f2

19. Preliminary results Stability of the MSS
The unconstrained MSS model has an average distance between two adjacent MSS of  20% of the MSS changes from one week to the next
Worst case: 67% changes in the MSS
Trade-off provided by the constrained MSS model
Commentare anche i risultati sulla gestione delle liste d’attesa?

20. Conclusions
Long-term evaluation of alternative policies for OR planning of elective surgeries
Simulation on a real case study (medium-size public hospital in Italy)
Promising results to improve waiting lists’ management
For future research:
Surgeons and resources availability constraints
Different objective functions and policies
Uncertainty on surgery duration and surgery arrivals

21. Unconstrained MSS model Mathematical formulation

22. Constrained MSS ‘Constrained’ w.r.t. long-term planning
Block time = # weeks during which the MSS is fixed
Set a reference MSS
Distance (Δ) between two MSSs: # ORs for each day and session type assigned to different surgical specialties in the MSSs
One constraint added to the previous model, bounding such a distance between the new MSS and the reference MSS

23. Fixed MSS model Mathematical formulation

24. Introduction
Decision problems faced by managers in OR planning/scheduling:
Assigning surgical specialties to OR sessions over time [Master Surgical Schedule problem (MSSP)]
Assigning elective surgeries to OR sessions [Surgical Case Assignment problem (SCAP)]
Sequencing surgeries within OR sessions [Elective Surgery Sequencing problem (ESSP)]
Extensive literature studies on elective patients only
Recent works on uncertainty affecting the system; e.g., due to stochastic surgery duration or urgencies
Add some references!

25. Problem description (2)
INPUT
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Spec. 6
Spec. 2
Spec. 1
Spec. 3
Spec. 4
Spec. 5
Mon
Tue
Wed
Thu
Fri
OR1
OR2
OR3
OR4
OR5
OR6
OUTPUT

26. Mon
Tue
Wed
Thu
Fri
OR1
OR2
OR3
OR4
OR5
OR6
gynecology
urology
day surgery
general surgery
otolaryngo-logy
orthopedic surgery

27. Heuristic Methods
Decomposition scheme, addressing MSSP and SCAP sequentially
MSSP – For each surgical specialty
Sort the waiting list by non-increasing score
Generate a set of candidate OR sessions (both half-day and full-day), by assigning surgical case i to the first available session
Select a subset of candidate sessions for a complete case surgery assignment
The corresponding MSS is retained, discarding all surgical cases filling it
SCAP – For each surgical specialty [da completare]
Oppure pseudo-codice dal paper? Forse diventa più compatto