Dynamic Daily Surgery Scheduling
Xiaolan XIE
Department of Healthcare Engineering
Centre for Healthcare Engineering
Centre for Health Engineering
Dept. Industrial Engr. & Management
Ecole des Mines de Saint Etienne, France
Shanghai Jiao Tong University, China
xie@emse.fr
xie@sjtu.edu.cn
Field observation of the operating theatre of Ruijin Hospital

Top 1 hospital in Shanghai

+12000 outpatient visits / day

An integrated operating theatre of 21 OR and a second one
under construction

60-70 elective surgery interventions + 10 emergency
surgeries / day
-2-
Field observation of the operating theatre of Ruijin Hospital

No integrated surgery planning but each surgery speciality
is given an amount of total OR time

Each speciality decides the surgeries to perform the next
day

The operating theatre (OT) is responsible for daily OR
assignment and the OR program execution.
-3-
Field observation of the operating theatre of Ruijin Hospital
Special features of the Ruijin Hospital

Queue of elective patients never empty

Availability of patients to be operated in short notice

Availability of surgeons to operate each day

Large variety of surgeons : top surgeons, senior surgeons,
ordinary surgeons

Strong demand to operate at the OT opening in the morning
to avoid endless waiting

Strong concern of OT personal overtime
-4-
Field observation of the operating theatre of Ruijin Hospital
Issues addressed

Promising surgery starting times to meet surgeon's
demand for reliable surgery starting

Surgery scheduling/rescheduling to balance between the
number of OR team working overtime and the total overtime
-5-
Related work
Static scheduling for a single OR

Surgeon appointment scheduling (AS):
Two surgeries: AS solved by a newsvendor model (Weiss, 1990)
A fixed sequence of surgeries: stochastic linear program solved by SAA
and L-shape algo to determine the allowance of each surgery, or
equivalently, the arrival time (Denton 2003).
Others: discrete appointment (Begen et al, 2011), robust appointment
(Kong et al, 2011)

Sequence scheduling: The problem is to jointly determine the position and
arrival time of each surgery (Denton 2007; Mancilla 2012).
-6-
Related work
Dynamic scheduling for a single OR

Arrival scheduling: The demand of surgeries is uncertain, surgeries are
processed as FCFS rule. The problem is to dynamically determine the
arrival time upon each application(Erdogan 2011).

Sequence scheduling: The demand of surgeries is also uncertain. The
problem is to jointly determine the position and arrival time of each
surgery upon each application (Erdogan 2012).
•
S. Erdogan and B. Denton, "Dynamic Appointment Scheduling of a Stochastic Server with Uncertain Demand," INFORMS Journal on Computing, pp. 1-17, 2011.
•
S, Erdogan, A. Gose and B. Denton “On-line Appointment Sequencing and Scheduling”, working paper, Stanford.
-7-
Our focus
Multi-OR setting
-8-
Our focus
Single-OR
A1
A2

Multi-OR setting
A
3
An
No OR assignment
Multi-OR
A1/A2
A3
A4
An
Dynamic OR assignment
-9-
Our focus
Two raised problems:
•
Determining surgeon arrival times by taking into account OR capacities
and random surgery durations.
•
Dynamic surgeon-to-OR assignment of during the course of a day as
surgeries progress by taking into account planned surgeon arrival
times.
- 10 -
Assumptions of our work
Assumption 1: Emergency surgeries are assigned to dedicated
ORs and hence neglected.
Assumption 2: ORs are all identical and each surgery intervention
can be assigned to any OR.
Assumption 3: Each surgeon has at most one surgery
intervention each day.
Assumption 4(Starting time planning or proactive problem): At
the end of each day, each surgeon of the next day is given a
promised surgery starting time or surgeon arrival time.
Assumption 5: Surgeons not available before the promised times.
Assumption 6(Dynamic sugery assignment or scheduling):
During the course of the day, at the completion of any surgery,
a new surgery is selected as the next surgery on the OR.
- 11 -
Dilemma of promising surgery starting time
Promise too early
surgeon waiting
Surgery 1
Surgery 2
promised start of surgeon 2
Promise too late
Surgery 1
Surgery 2
OR idle
OR overtime
promised start of surgeon 2
Easy if known OR time but OR times are uncerain
- 12 -
Data
J
set of surgery interventions or surgeons
N
number of identical ORs
T
length of OR session
pi(w)
random OR time of surgery i in scenario w
bi
unit time waiting cost of surgeon i
c1
unit OR idle time cost
c2
unit OR overtime cost
- 13 -
Dynamic Surgery Assignment of Multiple Operating Rooms with
Planned Surgeon Arrival Times
Zheng Zhang, Xiaolan Xie, Na Geng
In IEEE Trans. Automation Science and Engineering
- 14 -
Plan

Promising surgery starting times

Real time OR assignment strategies

Some numerical results

Conclusion and perspective
- 15 -
Decision variables
si
promised surgery starting time of surgeon i
xir
= 1/0 assignment of surgery i to OR r
yij
= 1 if surgery i precedes j in the same OR
= 0 if not
Auxilliary random variables
Cir(w)
completion time of surgery i on OR r
Ir(w)
idle time of OR r
Or(w)
overtime of OR r
Wi(w)
waiting time of surgeon i
- 16 -
Model for promising surgery starting times
OR idle cost
OR overtime
cost
surgeon
waiting cost
min Ew{c1 ∑r Ir(w) + c2 ∑r Or(w) + ∑i biIi(w)}
Assign each surgery to an OR
∑r xir = 1
Relation between assignment & sequencing
yij + yji ≥ xir + xjr -1
Promised start before the end of the session
si ≤ T
Scenario-dependent completion time
xir pi(w) ≤ Cir (w)
Cir (w) ≤ M xir
Cjr (w)  Cir (w) + pj(w) - M (1- yij) - M(2- xir - xjr )
Scenario-dependent OR idle time
Cir (w) ≤ Ir (w) + iJ xir pi(w)
Scenario-dependent OR overtime
Or (w)  Cir (w) - T
Scenario-dependent surgeon waiting time
rE Cir(w) = si + Wi(w) + pi(w)
- 17 -
Proposed solution
1. Convertion into mixed-integer linear programming
model by Sample Average Approximation by using a
given number of randomly generated samples
2. Heuristic for large size problem based on
a) Local search for surgery-to-OR assignment
optimization
b) Surgery sequencing rule based on optimal
sequencing of the two-surgery case
c) Optimal promised start time by SAA and MIP
- 18 -
Plan

Promising surgery starting times

Real time OR assignment strategies

Some numerical results

Conclusion and perspective
- 19 -
Dynamic surgery assignment optimization
An Event-Based Framework

At time 0, start surgeries planned at time 0

At the completion time t* of a surgery in OR r*,
select a surgery i* to be the next surgery in OR r*
among all remaining ones J*

Surgery i* starts at time max{ t*, si* } in OR r* after the
arrival of the surgeon at time si*
- 20 -
Dynamic surgery assignment optimization
Surgery i* is selected in order to minimize E[ TC(t*, i*, J*)]
where
E[ TC(t*, i*, J*)] is the minimal total cost similar to promised
time planning model

by conditioning on all completed surgeries and ages of
all on-going surgeries

by scheduling i* as the next surgery on OR r*
- 21 -
Two-stage stochastic programming approximation
• At k-th surgery completion event at time tk
Vk 
min
lJ \ J  k 1
glk  Qlk
where J\J(k-1) is the set of remaining surgeries
•

The first stage cost gˆlk   sl  tk   l  tk  sl 

is the OR-idle
or surgeon waiting cost induced by surgery l
• Qlk is the second stage cost, i.e. the total cost induced by
remaining surgeries plus OR overtimes.
- 22 -
The second stage cost
One-period look-ahead (OPLA) approximation
Qlk 
min
jJ \ J  k 1 \l
 jlk
where
• jlk is the expected stage cost induced by surgery j
•
if surgery l is selected at event k and surgery j at event k+1
Jensen's inequality is used to speedup the OPLA rule.
- 23 -
The second stage cost (cont'd)
Multi-period look-ahead (MPLA) approximation
Min. cost of two dynamic assignment rules:
• Rule 1: Remaining surgeries assigned in the scenarioindependent order of minimal expected first stage cost,
i.e. the surgery in selected at event n > k minimizes the stage n
cost induced by in.
• Rule 2: Remaining surgeries are selected in non-decreasing
order of their surgeon arrival times si
Jensen's inequality and another valide inequality are used to
speedup the MPLA rule.
- 24 -
Lower bound of the dynamic surgery assignment
• Based on perfect information, i.e. all surgery duration realizations
pj(w) are known at the beginning of the day
• The lower bound problem is similar to the proactive problem but
with
o given promised surgery start times
o scenario-dependent surgery assignment xir(w) and sequencing
yij(w)
- 25 -
Dynamic surgery assignment policies
Policy Static:
 No real time rescheduling
 OR assignment / sequencing decisions of promised time
planning model are followed
Policy FIFO:
 Dynamic surgery assignment in FIFO order of surgeon
arrival times
Policy I:
 Dynamic surgery assignment optimization with OPLA
Policy II:
 Dynamic surgery assignment optimization with MPLA
- 26 -
Plan

Background and motivation

Problem setting

Promising surgery starting times

Real time OR assignment strategies

Some numerical results

Conclusion and perspective
- 27 -
Optimality gap
(h,r%)
(0.3,0.75)
(0.7,0.75)
(0.3,1.25)
(0.7,1.25)
Ave.
7.4
8.5
5.6
7.8
GAPI(%)
Min.
0.1
5.1
1.3
1.9
Max.
14.7
14.8
11.2
17.3
Ave.
6.3
7.7
4.1
6.0
GAPII(%)
Min.
0.1
3.8
1.0
1.6
Max.
12.8
18.4
8.3
9.6
(80 3-OR instances)
GAP = (costX- LB) / LB
Observations
• Optimality gap is relatively small
• High surgery duration variation degrades the optimality gap
• High workload reduces the optimality gap
• MPLA better than OPLA
- 28 -
Value of dynamic scheduling
Ave.
VDS (%)
Min.
Max.
(0.3,75)
10.6
2.6
22.9
(0.7,75)
14.8
5.5
26.9
(0.3,125)
7.4
3.9
14.1
(0.7,125)
11.1
5.7
15.5
Ave.
11.0
4.4
19.9
(0.3,75)
25.4
18.7
31.6
(0.7,75)
29.2
24.7
39.9
(0.3,125)
11.1
7.1
15.5
(0.7,125)
19.1
12.8
24.1
Ave.
21.2
15.8
27.8
(0.3,75)
33.6
30.1
37.9
(0.7,75)
36.0
28.9
42.1
(0.3,125)
18.6
17.2
20.4
(0.7,125)
26.1
23.9
30.1
Ave.
28.6
25.0
32.6
OR#
(h,r%)
3
6
12
VDS = (costStatic - costDyna) / costStatic
h : variation parameter of surgery time
r : workload
Observations
•
Dynamic surgery scheduling always
helps.
•
The benefit is more important for
larger OT.
•
Dynamic surgery scheduling is able
to cope efficiently with surgery
uncertainties.
•
VDS decreases as the workload of
OT increases.
- 29 -
Value of dynamic scheduling optimization
OR#
(h,r%)
3
6
12
VOS (%)
VOS = (costFIFO - costDynaOpt) / costFIFO
Ave.
Min.
Max.
(0.3,75)
2.8
0.0
14.4
(0.7,75)
5.4
0.0
26.5
(0.3,125)
2.3
0.0
7.0
(0.7,125)
3.1
0.0
10.2
Ave.
3.4
0.0
14.5
Observations
(0.3,75)
5.4
-0.1
13.6
•
VOS increases as OR# increases.
(0.7,75)
6.0
-0.1
11.3
(0.3,125)
2.9
0.0
5.0
•
(0.7,125)
5.0
0.6
8.7
Ave.
4.8
0.1
9.6
VOS increases as h increases, i.e.
the variance of surgery durations
increases.
(0.3,75)
7.0
5.8
7.8
•
(0.7,75)
9.3
6.1
11.8
VOS decreases as r increases, i.e.
the workload of OT increases.
(0.3,125)
5.0
3.4
6.8
(0.7,125)
6.4
4.7
9.2
Ave.
6.9
5.0
8.9
h : variation parameter of surgery time
r : workload
- 30 -
Value of proactive decisions
(h,r%)
(0.3,0.75)
(0.7,0.75)
(0.3,1.25)
(0.7,1.25)
Ave.
7.2
6.8
9.8
10.1
VPSI(%)
Min.
-15.2
-11.1
1.1
1.1
Max.
23.3
20.4
23.1
19.2
Ave.
7.0
6.4
10.0
10.1
VPSII(%)
Min.
-20.9
-14.4
0.9
3.2
Max.
22.6
20.4
21.6
17.9
VOS = (costX - costX) / costX
where costX is the average cost of the strategy X but with promised start
times determined with deterministic surgery duration.
Observations
•
Proactive decision is very important to dynamic assignment scheduling.
•
The arrival times that optimize the proactive model may not be adjustable
to the dynamic assignment scheduling.
•
Joint optimization of promised start times and dynamic assignment policies
is an open research issue.
- 31 -
Plan

Promising surgery starting times

Real time OR assignment strategies

Some numerical results

Conclusion and perspective
- 32 -
Open issues

Optimal surgery promised starting times for a given OR
assignment / sequencing?

Features of surgeries planned to start at OR opening?

Time slacks in promised times vs surgery OR time and
waiting cost?

Design of efficient optimization algorithms for promised time
planning and real time rescheduling?

Promising time planning under starting time reliability
constraints?
- 33 -
Simulation-based Optimization of Surgery Appointment
Scheduling
Zheng Zhang, Xiaolan Xie
To appear in IIE Transactions
- 34 -
Outline
•
BACKGROUND AND MOTIVATION
•
SURGERY APPOINTMENT SCHEDULING PROBLEM
•
SAMPLE PATH ANALYSIS
•
STOCHASTIC APPROXIMATION
•
NUMERICAL EXPERIMENTS
•
CONCLUSION AND PERSPECTIVE
- 35 -
Our focus
Surgeon appointment optimization for a given sequence of
surgeries assigned to ORs on a FIFO basis.
Example : the first released OR is allocated to surgeon 3, the second
released OR is allocated to surgeon 4 and so forth.
Multi-OR
A1/A2
A3
r1
r2 A 4
An
FCFS assignment
- 36 -
Outline
•
BACKGROUND AND MOTIVATION
•
SURGERY APPOINTMENT SCHEDULING PROBLEM
•
SAMPLE PATH ANALYSIS
•
STOCHASTIC APPROXIMATION
•
NUMERICAL EXPERIMENTS
•
CONCLUSION AND PERSPECTIVE
- 37 -
Modeling
• Parameters
n surgeries\surgeons and m ORs with capacity T for each OR
pi(x): surgery duration with known distribution
1 / a /i: unit OR idling cost / overtime cost / surgeon waiting cost
• Decisions
Ai: surgeon arrival time with Ai = 0 for i=1,…,m and Ai ≤ Ai+1
- 38 -
Modeling
• Sample path cost function
f ( A, x ) 
    r x   A    A  r x  
n
i  m 1

i
i m
Waiting cost
i
i
i m
Idling cost

  a  r
m 1
p 0
n p
x   T 

Overtime cost
ri(x): the i-th OR releasing time.
ri(x) is a dependent variable of A and x and can be solved using a simple recursion.
- 39 -
Modeling
• Expected cost function
g ( A)  Ex  f  A, x  
• Objective
min g ( A)
AQ

 Ai  0, i  1,..., m 

Q  A


 Ai  Ai 1 , i  m,..., n  1

- 40 -
Outline
•
BACKGROUND AND MOTIVATION
•
SURGERY APPOINTMENT SCHEDULING PROBLEM
•
SAMPLE PATH ANALYSIS
•
STOCHASTIC APPROXIMATION
•
NUMERICAL EXPERIMENTS
•
CONCLUSION AND PERSPECTIVE
- 41 -
Sample path analysis
LEMMA 1. The sample path cost function f(A,x) is differentiable
on X with probability 1.
PROOF: The non-differentiable points exist at
1.Ai = ri-m(x)
2.ri(x)= Ai+m + pi+m(x) = ri+1(x)
As pi is in continuous distribution, the probability of pi(x) = a or pi(x) -pj(x) = a is
zero where a is a given constant.
- 42 -
Sample path analysis
LEMMA 2. If Ai has an increment of ∆, the OR releasing time rj(x) has an increment
at most ∆ for j > i-m. (Lipshitz continuity of OR release times)
PROOF: Ri(x) = ri(x) for j ≤ i-m. Let ci(x) / Ci(x) to be the old / new completion time.
For ∆ ≥ 0, we have ci(x) ≤ Ci(x) ≤ ci(x)+ ∆,
1.For j = i-m+1, rj(x) ≤ Rj(x) ≤ rj(x)+∆,
2.If 1 holds, rj(x) ≤ Rj(x) ≤ rj(x)+∆ holds for any j = j+1 by induction.
Similarly, Lemma 2 holds for ∆ < 0.
- 43 -
Sample path analysis
LEMMA 3. The sample path cost function f(A,x) is Lipschitz-continuous
throughout Q and the Lipschitz constant K is finite.
PROOF: Rewrite f(A,x) as
f ( A, x ) 
m 1
m 1
   r x   A   a  r x   T    r x   p x 
n
i  m 1

i
i m
i
p 0

n p
p 0
n
n p
i 1
i
Leading to
f ( A1 , x )  f ( A2 , x )  K A1  A2 , A1 , A2  Q
where
n


K  max   m1 , m 1  a    i 
i m 2


- 44 -
Sample path analysis
THEOREM 1 (unbiasednes of sample path gradient). The
objective function g(A) is continuously differentiable on Q ,and the
gradient of g(A) exists for all A∈Q with
 A Ex  f  A, x    Ex  A f  A, x  
- 45 -
Sample path analysis : partial derivative at interior point
A:  i

B:  jBP \{i}  j

i
f


Ai C: 1   jBPi \{i}  j

D: 1  a   jBP \{i}  j

i

Ai
A.
1
…
[i-m]
1
…
1
…
1
…
i
[i-m]
BP2(i)
waiting
i
[i-m]
[i-m]
Busy Period approach
waiting
i
j
waiting
BP2(i)
waiting
Ai
D.
i = surgeon waiting cost
i
Ai
C.
a  overtime cost
waiting
Ai
B.
1 = unit OR idling cost
BP2(i)
BP3(i)
waiting
BP3(i)
waiting
overtime
BP4(i)
- 46 -
Sample path analysis : directional derivative at boundary point
- 47 -
Sample path analysis : improving direction
- 48 -
Outline
•
BACKGROUND AND MOTIVATION
•
SURGERY APPOINTMENT SCHEDULING PROBLEM
•
SAMPLE PATH ANALYSIS
•
STOCHASTIC APPROXIMATION
•
NUMERICAL EXPERIMENTS
•
CONCLUSION AND PERSPECTIVE
- 49 -
Stochastic approximation
- 50 -
Outline
•
BACKGROUND AND MOTIVATION
•
SURGERY APPOINTMENT SCHEDULING PROBLEM
•
SAMPLE PATH ANALYSIS
•
STOCHASTIC APPROXIMATION
•
NUMERICAL EXPERIMENTS
•
CONCLUSION AND PERSPECTIVE
- 51 -
Convergence of stochastic approximation
THEOREM 2. There exist sample paths on which the sample path cost function is not
quasiconvex.
DATA: p(x) = {9, 4, 4, 1}; m=2 ORs with capacity T=10; Idle time penalty is 1; No
overtime penalty; Unit waiting penalty with 3=1, 4=3.
Two sets of arrival times: x=(4, 7.5); y=(6, 8.5).
f(x,x) = 1.5, f(y,x) = 3.5, f(0.5x+0.5y,x) = 4
- 52 -
Convergence of stochastic approximation
By randomly perturbing p around {9, 4, 4, 1}, we implement the stochastic
approximation algorithm.
Evolution of arrival times visited by the stochastic approximation algorithm in
Example 1, when applying it over 200 sample paths.
- 53 -
Convergence of stochastic approximation
- 54 -
Convergence of stochastic approximation
Ai
shifting
A.
1
…
[i-m]
i
t[i-m]
shifting
B.
1
…
[i-m]
Ai
i
t[i-m]
- 55 -
Convergence of stochastic approximation: numerical evidence
Log normal distribution
var, wkload
Initial
dispersion
Final
dispersion
Final grad
Uniform distribution
0.3,0.75
0.7,0.75
0.3,1.25
0.7,1.25
0.3,0.75
0.7,0.75
0.3,1.25
0.7,1.25
3-OR
5.0
4.9
6.5
7.0
5.4
4.8
6.6
6.8
6-OR
6.5
6.7
8.5
9.5
6.5
6.6
10.3
9.8
9-OR
8.0
7.4
11.2
10.5
7.9
7.7
10.5
10.5
3-OR
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
6-OR
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
9-OR
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
3-OR
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
6-OR
0.0
0.0
0.1
0.1
0.0
0.0
0.1
0.1
9-OR
0.0
0.2
0.1
0.3
0.0
0.2
0.2
0.3
- 56 -
Allowances of Multi-OR vs single OR settings
- 57 -
Allowances of Multi-OR vs single OR settings
Optimal allowance shape
dome shape in 1-OR, zigzag shape in 2-OR
2-OR vs 1-OR
smaller allowances, half total allowance, highly uneven
Increasing surgery duration variability
smoothing 2-OR allowances, increasing 1-OR allowance variability
Higher waiting cost
larger allowances in both settings but rather insensitive in the 2-OR setting
- 58 -
Allowances vs OR#
- 59 -
Allowances vs OR#
- 60 -
Value of dynamic assignment and proactive solution
Three strategies
Strategy I : no dynamic surgery-to-OR assignment
Strategy II : same surgeon appointment times, FIFO surgery-to-OR assignment
Strategy III : same surgeon arrival sequence, FIFO surgery-to-OR assignment,
simulation-based optimized appointment times
Value of dynamic assignment (VDA)
percentage improvement of strategy II over strategy I
Value of proactive anticipation and dynamic assignment (VPD)
percentage improvement of strategy III over strategy I
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Value of dynamic assignment and proactive solution
VDA > 0, VPD > 0 , VPD > VDA : dynamic assignment and the proactive anticipation of
dynamic assignments always pay
Higher OR number : increasing VDA and VPD due to scale effect and benefit of well
planned arrivals.
Higher duration variability: increasing VDA and VPD implying the importance of
careful appointment planning and dynamic scheduling.
Higher waiting costs: higher VPD but smaller VDA implying the importance of
appointment time optimization.
Higher workload: smaller VPD and VDA due to unimprovability of overloaded system.
Impact of case-mix:
• larger VPD when surgeries are identical due to their interchangeability.
• smaller VDA when surgeries are identical due to suboptimal appointment times
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Outline
•
BACKGROUND AND MOTIVATION
•
SURGERY APPOINTMENT SCHEDULING PROBLEM
•
SAMPLE PATH ANALYSIS
•
STOCHASTIC APPROXIMATION
•
NUMERICAL EXPERIMENTS
•
CONCLUSION AND PERSPECTIVE
- 63 -
Summary

A more realistic model of AS which has m servers; patients are served
in a pre-determined order but are flexible to any server.

Our aim is to proactively optimize the arrival times under the FCFS
dynamic assignment strategy.

We formulate a simulation-based optimization model to smooth integer
assignments, and derivate a continuous and differentiable cost function.

The proposed stochastic approximation algorithm is able to solve
realistic-sized instances and significantly improve the initial solution.
- 64 -
What next?
Joint optimization of surgery sequence and surgeon
appointment times.


simulation-based discrete optimization + stochastic approximation

Chance constraints of surgery starts

Dynamic control of overtime allocation

Surgeon behavior

Joint scheduling of inpatient and day surgeries
- 65 -
Relevant previous work
Planning operating theatres with both elective and emergency
surgeries

M. Lamiri, X.-L. Xie, A. Dolgui and F. Grimaud. "A stochastic model for operating room
planning with elective and emergency surgery demands", European Journal of Operational
Research, Volume 185, Issue 3, 16 March 2008, Pages 1026-1037

Mehdi Lamiri, Xiaolan Xie and Shuguang Zhang, "Column generation for operating theatre
planning with elective and emergency patients," IIE Transactions, 40(9): 838 – 852, 2008

M. Lamiri, F. Grimaud, and X. Xie. “Optimization methods for a stochastic surgery planning
problem,” International Journal of Production Economics, 120(2): 400-410, 2009
- 66 -
Healthcare engineering lab
At
ENSM.SE & SJTU
- 67 -
Mission statement

Develop quantitative methods for modeling, simulation and
optimization of health care systems & health services

Explore the integration of medical knowledge and patient
health information in operations management of health care
systems

in close collaboration with hospitals
Stochastic modeling and optimization in the face
of random events and changing system dynamics
- 68 -
Theme I : Engineering health care systems & services
To develop scientific methods for performance evaluation and design
of health care delivery systems and new health services.
Examples of work done :
• Performance analysis of patient flows with UML and Petri nets
• Simulation and capacity planning of Emergency departments
• Process improvement of hospital supply chains by RFID
• Health care logistics with mobile service robots
• Designing home healthcare networks
• Design and operations of perinatal care networks
• Permance evaluation of Hospital Information Systems
• Blood collection optimization
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Dynamic perinatal network reconfiguration
Context
• 3 types of neonatal cares (OB = obstetrics care,
Neo = basic Neonatal Care, NICU)
• 3 types of maternity services (OB, OB+Neo,
OB+Neo+NICU)
• Demographic evolution
• Immediate admission of random arrivals
Challenge:
• Determine optimum reconfiguration of perinatal
networks to meet demographic changes and equal
service level of care
H. Louis Mourier
(Type-3)
H. Beaujon
CH Neuilly
(Type-2)
H. Nanterre
(Type-1)
(Type-1)
(Type-2)
H. Franco Britan
H. FOCH
(Type-2)
Perinatal Network of North Hauts-de-Seine
Solution & results:
• Erlang loss-queueing model for admission probability evaluation;
• Original hierarchical service network with nested hierarchy of patients and maternity services
• Network reconfiguration by opening/closing services, capacity transfers, hiring/firing
• Large-scale nonlinear optimization models solved with original linearization techniques
• 5% increase of admissions at the 1st choice hospital.
Dynamic capacity planning and location of hierarchical service networks under service
level constraints, IEEE Transactions on Automation Science and Engineering, 2014.
- 70 -
Traceability in biobanks
Current situation
Samples stored in nitrogen
tanks (77°K)
 “Cold Chain” constraints
 Resistance of the tags?
Hand-made inventories, database updates, cryotube
numbering or label edition…
Problems: Error probabilities
(Hand-copy, inventory,
picking, computerization…)
Inventory
error
Info
errors
Research questions
Performance evaluation of
traceability technologies
Design supply chains of
drugs and medical devices
with RFID
New operation
management problems (rewarehousing of bio-banks,
skill/quality monitoring, ...)
Impacts of Radio-Identification on Cryo-Conservation Centers, TOMACS, 2011.
- 71 -
Engineering health care : Design blood collection systems
Backgrounds
Cost-efficiency
Increasing demand for blood products
Dilemma of donor quality of service &
efficiency of blood collection systems
Uncertain and dynamic donor arrivals
Goal: decision aid tools for design of
blood collection systems
Research questions
Human resource capacity planning
Donor appointment scheduling
Annual planning mobile collections
Modeling and simulation of blood collection systems, HCMS, 2012.
- 72 -
Theme II: Planning and logistics of health care delivery
To develop optimization methods for operations management of
healthcare delivery and its supply chains.
Example of work :
• Planning and scheduling operating theatres subject to uncertainties
• Capacity planning control MRI examinations of stroke patients
• Stochastic optimization for hospital bed allocation
• Inpatient admission control
• Dynamic outpatient appointment scheduling
• Operation management of outpatient chemotherapry
• Capacity planning and patient admission for radiotherapy
• Robust home healthcare planning
• Home healthcare admission planning&control
• Management of winter epidemics (flu, bronchitis, gastroenteritis)
• Long-term care planning & scheduling
- 73 -
Optimization of outpatient chemotherapy
ICL Loire Cancer Institute
bed requirement
Large variation in bed
capacity requirement in
actual planning
20% reduction of peak
bed requirement in the
optimized planning
Major challenges of further research:
• Integration of decisions different levels and different time scales
(medical planning, patient assignment, appointment scheduling)
• Modeling treatment protocols with rich medical knowledge
• Modeling the dynamics of health conditions based on rich patient data
• High uncertainties of patient flow and patient's health care requirement
Planning oncologists of ambulatory care units. Decision Support Systems. (To appear)
- 74 -
Capacity planning of diagnostic equipment (MRI)
MRI examination of stroke patients

Expensive (over 1 million $) -> high utilization

Demand uncertainties and demand diversity (both
elective and emergency)

Goal: Reduce waiting time for stroke patients without
degrading MRI utilization
Actual waiting times
of 30-40 days for
MRI examination
2 - 10 days with the
optimized reservation
and control strategy。
Monte Carlo optimization and dynamic programming approach for managing MRI examinations of
stroke patients. IEEE Transactions on Automatic Control, 2011
- 75 -
Some projects
• Management of winter epidemics (flu, bronchitis, gastroenteritis)
(ANR-TECSAN project HOST)
• Engineering home health care logistics
• Planning home health care admissions (ARC2, Rhone-alps region)
• Planning home health care activities (Labex IMOBS 3)
• Planning home health care logistics (Labex IMOBS3)
• Performance modeling & evaluation of HIS (DGOS-PREPS e-SIS)
• CIFRE-Heva : Patient pathway mining with national database
• Care pathway optimization of elderly people
• CLARA – Procan : Cancer care delivery & chemotherapy at home. 2008• FP6-IST6-IWARD on mobile & reconfigurable robots for hospital logistics.
2007-2010 (1 thesis)
- 76 -
Planning and optimisation of hospital resources

5-year project funded by National Science Foundation of China
(2012-2016)

Consortium: IE, B. School, Ruijin hospital all from SJTU

Four major research tasks:

Planning / scheduling of key clinical resources (human +
beds)

Capacity planning / preventive maintenance of diagnostic &
treatment equipment

Coordination / cooperation mechanism design

Modelling / simulation of hospital emergency responses
- 77 -
Process Mining of patient pathways
PhD thesis funded by HEVA company
(2014-2016)
Goal:
extract the process model with what patients actually
endured instead what is recommended.
- 78 -
Process Mining (1/3)
Data
Mining
Business
Process
Process
Mining
concept :
- Business Process Management
- Based on knowlege extracted from an event log (national hospital care data base)
Example: 3 patients  Consultation appointment application.
Données Brutes
1
6
Découverte du processus sous-jacent
Données mises en forme
2
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Process Mining + PMSI (2/3)
PMSI
Patient
- ID = 73
- Age = 45 ans
Device
implementation
01/01/2006 (15j)
Heart failure
28/03/2006 (4j)
Device infection
03/06/2006 (8j)
7
Pathway
patient
Process
Mining
ID = 98, 101, 106, …
CHU d’Amiens
…
Clinique privé
d’Amiens
Clinique privé
d’Amiens
- 80 -
Process Mining + PMSI (3/3)
Brut data : 16,931 hospital stays from 2006 - 2013
Implantation
Complication
post- opératoire
Diagramme
spaghetti
Suivi régulier
Remplacement
Sortie
du PMSI
8
Décès
- 81 -
Event clustering
+
process mining
- 82 -