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Transcript of Dynamic Daily Surgery Scheduling Department of Healthcare Engineering Centre for Health Engineering...
Dynamic Daily Surgery Scheduling
Department of Healthcare Engineering
Centre for Health Engineering
Ecole des Mines de Saint Etienne, France
Centre for Healthcare Engineering
Dept. Industrial Engr. & Management
Shanghai Jiao Tong University, China
Xiaolan XIE
- 2 -
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
- 3 -
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.
- 4 -
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
- 5 -
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
- 6 -
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).
- 7 -
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.
- 8 -
Our focus
Multi-OR setting
- 9 -
Our focus
Multi-OR setting
Single-OR
Multi-OR
A1 A2 A3 An
A1/A2 A3 A4 An
No OR assignment
Dynamic OR assignment
- 10 -
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.
- 11 -
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.
- 12 -
Dilemma of promising surgery starting time
Promise too early
Surgery 1
promised start of surgeon 2
Surgery 2
Surgery 1
promised start of surgeon 2
Surgery 2
Promise too late
surgeon waiting
OR idleOR overtime
Easy if known OR time but OR times are uncerain
- 13 -
Data
J set of surgery interventions or surgeons
N number of identical ORs
T length of OR session
pi() random OR time of surgery i in scenario
bi unit time waiting cost of surgeon i
c1 unit OR idle time cost
c2 unit OR overtime cost
- 14 -
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
- 15 -
Plan
Promising surgery starting times
Real time OR assignment strategies
Some numerical results
Conclusion and perspective
- 16 -
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() completion time of surgery i on OR r
Ir() idle time of OR r
Or() overtime of OR r
Wi() waiting time of surgeon i
- 17 -
Model for promising surgery starting times
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() ≤ Cir ()
Cir () ≤ M xir
Cjr () Cir () + pj() - M (1- yij) - M(2- xir - xjr )
Scenario-dependent OR idle time Cir () ≤ Ir () + iJ xir pi()
Scenario-dependent OR overtime Or () Cir () - T
Scenario-dependent surgeon waiting time rE Cir() = si + Wi() + pi()
OR idle costOR overtime
costsurgeon
waiting cost
min E{c1 ∑r Ir() + c2 ∑r Or() + ∑i biIi()}
- 18 -
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
- 19 -
Plan
Promising surgery starting times
Real time OR assignment strategies
Some numerical results
Conclusion and perspective
- 20 -
Dynamic surgery assignment optimization
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*
An Event-Based Framework
- 21 -
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*
- 22 -
Two-stage stochastic programming approximation
• At k-th surgery completion event at time tk
where J\J(k-1) is the set of remaining surgeries
• The first stage cost is the OR-
idle or surgeon waiting cost induced by surgery l
• lk is the second stage cost, i.e. the total cost induced by
remaining surgeries plus OR overtimes.
\ 1mink lk
l J J klkV g
ˆlk l k l k ls t t sg
- 23 -
The second stage cost
\ 1 \minlk jlk
j J J k l
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.
One-period look-ahead (OPLA) approximation
- 24 -
The second stage cost (cont'd)
Min. cost of two dynamic assignment rules:
• Rule 1: Remaining surgeries assigned in the scenario-independent 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.
Multi-period look-ahead (MPLA) approximation
- 25 -
Lower bound of the dynamic surgery assignment
• Based on perfect information, i.e. all surgery duration realizations
pj() 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() and sequencing
yij()
- 26 -
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
- 27 -
Plan
Background and motivation
Problem setting
Promising surgery starting times
Real time OR assignment strategies
Some numerical results
Conclusion and perspective
- 28 -
Optimality gap
Observations
•Optimality gap is relatively small
•High surgery duration variation degrades the optimality gap
•High workload reduces the optimality gap
•MPLA better than OPLA
GAP = (costX- LB) / LB
(,)GAPI(%) GAPII(%)
Ave. Min. Max. Ave. Min. Max.(0.3,0.75) 7.4 0.1 14.7 6.3 0.1 12.8(0.7,0.75) 8.5 5.1 14.8 7.7 3.8 18.4(0.3,1.25) 5.6 1.3 11.2 4.1 1.0 8.3(0.7,1.25) 7.8 1.9 17.3 6.0 1.6 9.6
(80 3-OR instances)
- 29 -
Value of dynamic scheduling
OR# (,)VDS (%)
Ave. Min. Max.
3 (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
6 (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
12 (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
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.
: variation parameter of surgery time: workload
VDS = (costStatic - costDyna) / costStatic
- 30 -
Value of dynamic scheduling optimization
Observations
•VOS increases as OR# increases.
•VOS increases as increases, i.e. the variance of surgery durations increases.
•VOS decreases as increases, i.e. the workload of OT increases.
OR# (,)VOS (%)
Ave. Min. Max.
3 (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
6 (0.3,75) 5.4 -0.1 13.6
(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
12 (0.3,75) 7.0 5.8 7.8
(0.7,75) 9.3 6.1 11.8
(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
: variation parameter of surgery time: workload
VOS = (costFIFO - costDynaOpt) / costFIFO
- 31 -
Value of proactive decisions
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.
VOS = (costX - costX) / costX
where costX is the average cost of the strategy X but with promised start times determined with deterministic surgery duration.
(,)VPSI(%) VPSII(%)
Ave. Min. Max. Ave. Min. Max.(0.3,0.75) 7.2 -15.2 23.3 7.0 -20.9 22.6(0.7,0.75) 6.8 -11.1 20.4 6.4 -14.4 20.4(0.3,1.25) 9.8 1.1 23.1 10.0 0.9 21.6(0.7,1.25) 10.1 1.1 19.2 10.1 3.2 17.9
- 32 -
Plan
Promising surgery starting times
Real time OR assignment strategies
Some numerical results
Conclusion and perspective
- 33 -
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?
Open issues
- 34 -
Simulation-based Optimization of Surgery Appointment Scheduling
Zheng Zhang, Xiaolan Xie
To appear in IIE Transactions
- 35 -
Outline
• BACKGROUND AND MOTIVATION
• SURGERY APPOINTMENT SCHEDULING PROBLEM
• SAMPLE PATH ANALYSIS
• STOCHASTIC APPROXIMATION
• NUMERICAL EXPERIMENTS
• CONCLUSION AND PERSPECTIVE
- 36 -
Our focus
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 r1An
FCFS assignment
r2 A4
Surgeon appointment optimization for a given sequence of
surgeries assigned to ORs on a FIFO basis.
- 37 -
Outline
• BACKGROUND AND MOTIVATION
• SURGERY APPOINTMENT SCHEDULING PROBLEM
• SAMPLE PATH ANALYSIS
• STOCHASTIC APPROXIMATION
• NUMERICAL EXPERIMENTS
• CONCLUSION AND PERSPECTIVE
- 38 -
Modeling
• Parameters
n surgeries\surgeons and m ORs with capacity T for each OR
pi(): surgery duration with known distribution
/ /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
- 39 -
Modeling
• Sample path cost function
ri(): the i-th OR releasing time.
ri() is a dependent variable of A and and can be solved using a simple
recursion.
1
1 0
( , )n m
i i m i i i m n pi m p
f A r A A r r T
Waiting cost Idling cost Overtime cost
- 40 -
Modeling
• Expected cost function
• Objective
( ) ,g A E f A
1
min ( )
0, 1,...,
, ,..., 1
A
i
i i
g A
A i mA
A A i m n
- 41 -
Outline
• BACKGROUND AND MOTIVATION
• SURGERY APPOINTMENT SCHEDULING PROBLEM
• SAMPLE PATH ANALYSIS
• STOCHASTIC APPROXIMATION
• NUMERICAL EXPERIMENTS
• CONCLUSION AND PERSPECTIVE
- 42 -
Sample path analysis
LEMMA 1. The sample path cost function f(A,) is differentiable on with probability 1.
PROOF: The non-differentiable points exist at
1.Ai = ri-m()
2.ri()= Ai+m + pi+m() = ri+1()
As pi is in continuous distribution, the probability of pi() = a or pi() -pj() = a is
zero where a is a given constant.
- 43 -
Sample path analysis
LEMMA 2. If Ai has an increment of ∆, the OR releasing time rj() has an increment
at most ∆ for j > i-m. (Lipshitz continuity of OR release times)
PROOF: Ri() = ri() for j ≤ i-m. Let ci() / Ci() to be the old / new completion time.
For ∆ ≥ 0, we have ci() ≤ Ci() ≤ ci()+ ∆,
1.For j = i-m+1, rj() ≤ Rj() ≤ rj()+∆,
2.If 1 holds, rj() ≤ Rj() ≤ rj()+∆ holds for any j = j+1 by induction.
Similarly, Lemma 2 holds for ∆ < 0.
- 44 -
Sample path analysis
LEMMA 3. The sample path cost function f(A,) is Lipschitz-
continuous throughout and the Lipschitz constant K is finite.
PROOF: Rewrite f(A,) as
Leading to
where
1 1
1 0 0 1
( , )n m m n
i i m i n p n p ii m p p i
f A r A r T r p
12
max , 1n
m ii m
K m
1 2 1 2 1 2( , ) ( , ) , ,f A f A K A A A A
- 45 -
Sample path analysis
THEOREM 1 (unbiasednes of sample path gradient). The
objective function g(A) is continuously differentiable on ,and the
gradient of g(A) exists for all A∈with
, ,A AE f A E f A
- 46 -
Sample path analysis : partial derivative at interior point
\{ }
\{ }
\{ }
A:
B:
C: 1
D: 1
i
i
i
i
jj BP i
ji j BP i
jj BP i
f
A
Ai
i BP2(i) j
A.
B.
i
Ai waiting
i BP2(i) BP3(i)C.
Ai
i BP2(i) BP3(i)D.
Ai
waiting
waiting waiting
waiting waiting overtime
[i-m]1 …
[i-m]1 …
[i-m]1 …
[i-m]1 … BP4(i)
waiting
= unit OR idling cost
overtime cost
i = surgeon waiting costBusy Period approach
- 47 -
Sample path analysis : directional derivative at boundary point
- 48 -
Sample path analysis : improving direction
- 49 -
Outline
• BACKGROUND AND MOTIVATION
• SURGERY APPOINTMENT SCHEDULING PROBLEM
• SAMPLE PATH ANALYSIS
• STOCHASTIC APPROXIMATION
• NUMERICAL EXPERIMENTS
• CONCLUSION AND PERSPECTIVE
- 50 -
Stochastic approximation
- 51 -
Outline
• BACKGROUND AND MOTIVATION
• SURGERY APPOINTMENT SCHEDULING PROBLEM
• SAMPLE PATH ANALYSIS
• STOCHASTIC APPROXIMATION
• NUMERICAL EXPERIMENTS
• CONCLUSION AND PERSPECTIVE
- 52 -
Convergence of stochastic approximation
THEOREM 2. There exist sample paths on which the sample path cost function is
not quasiconvex.
DATA: p() = {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,) = 1.5, f(y,) = 3.5, f(0.5x+0.5y,) = 4
- 53 -
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.
- 54 -
Convergence of stochastic approximation
- 55 -
Convergence of stochastic approximation
[i-m] iB. 1 …
shiftingAi
t[i-m]
[i-m]
Ai
A. i
shifting
1 …
t[i-m]
- 56 -
Convergence of stochastic approximation: numerical evidence
Log normal distribution Uniform distribution
var, wkload 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
Initial dispersion
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
Final dispersion
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
Final grad
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
- 57 -
Allowances of Multi-OR vs single OR settings
- 58 -
Allowances of Multi-OR vs single OR settings
Optimal allowance shapedome shape in 1-OR, zigzag shape in 2-OR
2-OR vs 1-ORsmaller allowances, half total allowance, highly uneven
Increasing surgery duration variabilitysmoothing 2-OR allowances, increasing 1-OR allowance variability
Higher waiting costlarger allowances in both settings but rather insensitive in the 2-OR setting
- 59 -
Allowances vs OR#
- 60 -
Allowances vs OR#
- 61 -
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
- 62 -
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
- 63 -
Outline
• BACKGROUND AND MOTIVATION
• SURGERY APPOINTMENT SCHEDULING PROBLEM
• SAMPLE PATH ANALYSIS
• STOCHASTIC APPROXIMATION
• NUMERICAL EXPERIMENTS
• CONCLUSION AND PERSPECTIVE
- 64 -
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.
- 65 -
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
- 66 -
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
- 67 -
Healthcare engineering lab
At
ENSM.SE & SJTU
- 68 -
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
- 69 -
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
- 70 -
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
Dynamic capacity planning and location of hierarchical service networks under service level constraints, IEEE Transactions on Automation Science and Engineering, 2014.
Perinatal Network of North Hauts-de-Seine
(Type-3)
H. Louis Mourier
H. Beaujon
(Type-1)
H. FOCH
(Type-2)
CH Neuilly(Type-
2)
H. Franco Britan
(Type-2)
H. Nanterre(Type-1)
Challenge: •Determine optimum reconfiguration of perinatal networks to meet demographic changes and equal service level of care
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.
- 71 -
Traceability in biobanks
Research questions
Performance evaluation of traceability technologies
Design supply chains of drugs and medical devices with RFID
New operation management problems (re-warehousing of bio-banks, skill/quality monitoring, ...)
Infoerrors
InventoryerrorCurrent situation
Samples stored in nitrogen tanks (77°K)
“Cold Chain” constraints Resistance of the tags?
Hand-made inventories, data-base updates, cryotube numbering or label edition…
Problems: Error probabilities(Hand-copy, inventory, picking, computerization…)
Impacts of Radio-Identification on Cryo-Conservation Centers, TOMACS, 2011.
- 72 -
Engineering health care : Design blood collection systems
Research questions
Human resource capacity planning
Donor appointment scheduling
Annual planning mobile collections
Backgrounds
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
Modeling and simulation of blood collection systems, HCMS, 2012.
Cost-efficiency
- 73 -
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
- 74 -
Optimization of outpatient chemotherapy
ICL Loire Cancer Institute
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
Large variation in bed capacity requirement in actual planning
20% reduction of peak bed requirement in the optimized planning
bed requirement
Planning oncologists of ambulatory care units. Decision Support Systems. (To appear)
- 75 -
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
- 76 -
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)
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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
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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.
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Process Mining (1/3)
6
concept : -Business Process Management-Based on knowlege extracted from an event log (national hospital care data base)
Example: 3 patients Consultation appointment application.
Data Mining
Business Process
Process Mining
1 2
Données BrutesDonnées mises en forme
Découverte du processus sous-jacent
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Process Mining + PMSI (2/3)
7
PMSI Process MiningPathway
patient
Device implementation
01/01/2006 (15j)
Patient- ID = 73
- Age = 45 ans
Heart failure28/03/2006 (4j)
Device infection03/06/2006 (8j)
CHU d’Amiens
Clinique privé d’Amiens
Clinique privé d’Amiens
ID = 98, 101, 106, …
…
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Process Mining + PMSI (3/3)
Brut data : 16,931 hospital stays from 2006 - 2013
Diagramme spaghetti
Implantation
Complication post- opératoire
Suivi régulier
Remplacement
Décès
8
Sortiedu PMSI
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Event clustering +process mining