Long term policiesfor operating room

planningA. Agnetis1, A. Coppi1, G. Dellino2, C. Meloni3, M.

Pranzo1

1 Dept. of Information Engineering, University of Siena, Italy2 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

4

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____________________

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Decision problems in OT management

Mon Tue Wed Thu FriOR

1OR

2OR

3OR

4OR

5OR

6

Orthopedic

surgeryUrology

MSSP

SCAP

ESSP

Gynecology

Day surgery

General surgery

Otolaryn-gology

5

Organizational complexity vs. MSS variation

• Staffing and shift planning– MSS fixed over time ↑ stability, ↓

flexibility– MSS different every week ↓ stability,

↑ flexibility

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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

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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

classWaiting time

(days) Due date

6210 15/06/201028 B 27 15/08/2010

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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 timebased on case surgeries duration and a score,

related to:1. case surgery waiting time and priority class2. case surgery slack time

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Optimization models

ILP mathematical formulations, solved by CPLEX1. Unconstrained MSS model

Determines MSS and SCA every week, based on the actual waiting list for each specialty

2. Constrained MSS modelDetermines MSS and SCA, bounding the number of changes in OR session assignments to different surgical specialties w.r.t. a reference MSS

3. Fixed MSS modelDetermines SCA, given an MSS

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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)

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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

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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

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Heuristic methods

MSSP

OR sessions = bins; Surgeries = items1. Candidate OR sessions (half-day/full-

day) for each specialty → first-fit-decreasing rule

2. Selection of candidate sessions assigned to OR

3. MSS is retained, discarding all surgical cases filling it

SCAP

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Planning policies

UnconstrainedMSS model

ConstrainedMSS model

FixedMSS model

MSSP

Exactlysolved

Heuristically

solved

SCAP

Exactlysolved

Heuristically

solved

Δ = 1, block = 1Δ = 2, block = 4

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

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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

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Preliminary resultsBase scenario

f1

f2

18

Preliminary resultsStressed scenario

f1

f2

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Preliminary results

• Stability of the MSS– The unconstrained MSS model has an

average distance between two adjacent MSS of 12-13 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

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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 modelMathematical formulation

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22

Constrained MSS

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• One constraint added to the previous model, bounding such a distance between the new MSS and the reference MSS

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23

Fixed MSS modelMathematical formulation

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