optimization of surgery delivery systemsbtdenton.engin.umich.edu/wp-content/uploads/sites/... ·...
TRANSCRIPT
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Optimization of Surgery Delivery
Systems
Brian Denton
Edward P. Fitts Department of Industrial & Systems
Engineering
North Carolina State University
May, 2012
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Collaborators
Hari Balasubramanian (University of Massachusetts)
Sakine Batun (University of Pittsburgh)
Bjorn Berg (NCSU)
Todd Huschka (Mayo)
Andrew Miller (University of Bordeaux)
Heidi Nelson (Mayo)
Ahmed Rahman (Mayo)
Andrew Schaefer (University of Pittsburgh)
Supported by National Science Foundation – CMMI 0620573
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Summary
• Surgery process and complicating factors
• Examples:
• Problem 1: Single OR scheduling
• Problem 2: Multi-OR surgery allocation
• Problem 3: Bi-criteria scheduling of a surgery
suite
• Future research
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Surgery Process
• Patient Intake: administrative
activities, pre-surgery exam,
gowning, site prep, anesthetic
• Surgery: incision, one or multiple
procedures, pathology, closing
• Recovery: post anesthesia care
unit (PACU), ICU, hospital bed
Intake Surgery
Recovery
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Mayo Clinic, Rochester MN
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Outpatient Procedure Center
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Surgical Suite Decisions
• Number of cases to schedule
• Number of ORs and staff to activate each day
• Surgery-to-OR assignment decisions
• Scheduling of staff and patients in intake, surgery, and recovery
• How to design the suite (intake rooms, recovery rooms, ORs)
• Selection of equipment resources (surgical kits, diagnostic equipment)
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Complicating Factors
• Many types of resources to be scheduled:
surgery team, equipment, materials
• High cost of resources and fixed time to
complete activities
• Large number of activities to be coordinated
in a highly constrained environment
• Uncertainty in duration of activities
• Many competing criteria
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Surgery Duration Uncertainty
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Surgery Duration Uncertainty
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Problem 1: Single OR Scheduling
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x1 x2 x3 x4 x5
a1 a2 a3 a4 a5
Idling
Planned OR Time
Overtime Waiting
Min{ Idling + Waiting + Overtime}
Single OR Scheduling
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Stochastic Optimization Model
]}[][][min{ **
11
* LECSECWEC Li
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sn
i
iw
i ZZZ
)0,max( 111 iiii xZWW
)0,max( 111 iiii xZWS
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Cost of Waiting Cost of Idling Cost of
Overtime
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Literature Review – Single Server
• Queuing Analysis:
Mercer (1960, 1973)
Jansson (1966)
Brahimi and Worthington (1991)
• Heuristics:
White and Pike (1964)
Soriano (1966)
Ho and Lau (1992)
• Optimization:
Weiss (1990) – 2 surgery news vendor model
Wang (1993) – Exploited phase type distribution property
Denton and Gupta (2003) – General 2-SLP formulation
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Stochastic Linear Program
}][min{2 2
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22332 xZsww
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0,,,...,1,0,0,0 glniswx iii
1122 xZsw s.t.
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Two Stage Recourse Problem
Initial Decision (x) Uncertainty Resolved Recourse (y)
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T T T
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x
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Example
• Comparison of surgery allocations for n=3,
5, 7 with i.i.d. distributions with U(1,2):
X
Patient
2 3 4 5 6 1
µ 1.5
1.2
2
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General Insights
• Simple heuristics often perform poorly
• The value of the stochastic solution (VSS)
is high
• Large instances of this problem can be
solved easily
1) Denton, B.T., Gupta, D., 2003, A Sequential Bounding Approach for
Optimal Appointment Scheduling, IIE Transactions, 35, 1003-1016
2) Denton, B.T., Viapiano, J, Vogl, A., 2007, Optimization of Surgery
Seqencing and Scheduling Decisions Under Uncertainty, Health Care
Management Science, 10(1), 13-24
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Problem 2: Multi-OR Surgery
Allocation
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Multi-Operating Room Scheduling
Decisions:
•How many operating rooms (ORs) to open?
•Which OR to schedule each surgery block in?
Performance Measures:
•Cost of operating rooms opened
•Overtime costs for operating rooms
S 1 S 2 S 3 S n
OR 1 OR 2 OR 3 OR m
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Extensible Bin Packing
0},1,0{,
),(
)(1
),(..
}min{
1
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jjij
n
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jORtoassignediyBlockSurgifyij
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Symmetry • m! optimal solutions:
• Anti-symmetry constraints:
OR1 OR2 OR3 ORm
1
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21
mm xx
xx
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OR Ordering
m
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Surgery
Assignment
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Two-Stage Stochastic MIP
,0)(},1,0{,
),,()()(
)(1
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]})([min{)(
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Integer L-Shaped Method IP0
IP2 IP1
IP4 IP3
IP5 IP6
IP7 IP8
)]([ TxhE
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}min{
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Master Problem:
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Heuristic and Bounds Dell’Ollmo (1998) – 13/12 approximation algorithm for bin packing with
extensible bins
EBP Heuristic:
);(
;1
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repeatend
nn
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nLPT
repeat
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Sort surgeries from longest
to shortest
Sequentially apply
surgeries to emptiest room
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Robust Formulation
0}1,0{,
)(1
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Instance MV_IP LPT_Heu Tau=2 Tau=4 Tau=6 MV_IP LPT_Heu Tau=2 Tau=4 Tau=6
1 0.808 0.806 0.892 0.906 0.933 0.999 0.998 0.880 0.948 0.948
2 0.953 0.966 0.898 0.896 0.970 0.999 0.999 0.999 0.999 0.980
3 0.854 0.852 0.936 0.937 0.970 0.999 0.999 0.929 0.952 0.944
4 0.925 0.972 0.911 0.971 0.917 0.999 0.998 0.930 0.930 0.929
5 0.896 0.946 0.831 0.916 0.892 0.990 0.996 0.932 0.938 0.924
6 0.862 0.853 0.923 0.931 0.938 0.989 0.990 0.886 0.881 0.881
7 0.930 0.936 0.810 0.930 0.817 0.973 0.993 0.844 0.974 0.927
8 0.888 0.966 0.876 0.903 0.904 0.966 0.966 0.966 0.987 0.939
9 0.962 0.966 0.964 0.969 0.964 0.975 0.993 0.847 0.960 0.957
10 0.860 0.924 0.910 0.893 0.918 0.997 0.996 0.900 0.901 0.903
average 0.894 0.919 0.895 0.925 0.922 0.988 0.993 0.916 0.951 0.933
stdev 0.046 0.057 0.047 0.028 0.046 0.013 0.010 0.059 0.045 0.028
max 0.962 0.972 0.964 0.971 0.970 0.999 0.999 1.042 1.040 0.980
min 0.808 0.806 0.810 0.893 0.817 0.966 0.966 0.844 0.881 0.881
15 surgery instances
Variable Cost = 0.033 Variable Cost = 0.0083
Robust IP Robust IP
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General Insights
• A fast LPT based heuristic works well on a
large number of instances
– LPT works well when overtime costs are low
– LPT is better (and easier) than solving MV
problem in most cases
• Robust IP is better than LPT when overtime
costs are high
Denton, B.T., Miller, A., Balasubramanian, H., Huschka, T., 2010,
Optimal Surgery Block Allocation Under Uncertainty, Operations
Research 58(4), 802-816, 2010
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Problem 3: Patient Arrival Scheduling
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Pa
tie
nt C
he
ck-in
Waitin
g A
rea
Preoperative
Waiting Area
Operating Rooms
Recovery Area
Pa
tie
nt A
rriv
als
Pa
tie
nt D
isch
arg
e
Endoscopy Suite
Intake Area
1st Patient
Arrival
nth Patient
Completion
Length of Day
Patient Waiting Time
Schedule
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Intake, Surgery, and Recovery
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Simulation-optimization
• Decision variables: scheduled start times to be
assigned to n patients each day
• Goal: Generate the set of non-dominated schedules to
understand tradeoffs between waiting and length of day
• Schedules generated using a genetic algorithm (GA)
• Non-dominated sorting used to identify the Pareto set
and feedback into GA
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Pareto Set • The non-dominated sorting genetic algorithm
(NSGA-II) of Deb et al.(2000) is used in the
simulation optimization.
1
z 2
Rank 1 Solutions
Rank 2 Solutions
Rank 3 Solutions
z 1
z 2
Rank 1 Solutions
Rank 2 Solutions
Rank 3 Solutions
Rank 1 Solutions
Rank 2 Solutions
Rank 3 Solutions
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Selection Procedure
• Sequential two stage indifference zone ranking and
selection procedure of Rinott (1978) is used to
compute the number of samples necessary to
determine whether a solution i “dominates” j
• Solution i “dominates” j if:
and
][][ ji WEWE ][][ ji LELE
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Genetic Algorithm
• Main features of the GA:
• Randomly generated initial population of schedules
• Selection based on 1) ranks and 2) crowding
distance
• Single point crossover:
• Mutation
z1 z2 z3 ….. zn
y1 y2 y3 ….. yn
z1 z2 - y3 ….. yn
y1 y2 - z3 ….. zn
Parents Children
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Schedule Optimization
330.00
340.00
350.00
360.00
370.00
380.00
390.00
400.00
0.00 10.00 20.00 30.00 40.00
Mean
Sess
ion
Len
gth
Mean Waiting Time
GA
Dominated
Avera
ge L
ength
of D
ay
Average Waiting Time
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General Insights
• The simulation optimization approach provided
significant improvement to schedules used in
practice
• A shortest processing time first (SPT) heuristic
provided a good solution
• Controlling surgery mix among days can
significantly improve patient waiting time and
overtime
Gul, S., Denton, B.T., Fowler, J., 2011 Bi-Criteria Scheduling of Surgical
Services for an Outpatient Procedure Center, Production and Operations
Management, 20(3), 406-417
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Current and Future Research
• Investigating new stochastic programming and
robust optimization formulations and methods
• Dynamic (online) scheduling problems
• Rescheduling
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Questions?
Brian Denton
North Carolina State University
Department of Industrial & Systems Engineering
Email: [email protected]
Website: www.ise.ncsu.edu/bdenton/