Hospital Scheduling

1
Hospital Scheduling

• Chandni Verma
• Semonti Sinhaaroy

2
Overview

• Problems faced in hospital scheduling
• Methods used FIFO, SPT or LSO
• Columbia Presbyterian Hospital
• Operation Room Scheduling
• Our solution - Linear Programming
• Scope

3
Problem hospital scheduling

• Many hospitals have difficulty controlling the
  access and throughput times for patients.
• Difficulty arise in using of shared resources
  like Operation Rooms, Ambulances, Clinique etc
• Different healthcare chains are connected through
  the shared resources
• Systemic failure gives rise to blockage and
  increase queues and increases revenues while
  decreasing profits
• Objective is to minimize blockage and use
  available resources completely
• Eliminate need to cancel appointments and
  procedures
• Minimize Revenues and maximize Profit

4
Methods used in general

• First In First Out (FIFO) Priority
• Shortest Processing Time first (SPT)
• Categorize the patients according to their
  illness/disorder
• Assign an expected completion time
• Least Slack per Operation (LSO)
• The due time tolerance for each patient is
  calculated
• (Due time Time of assignment)
• S(Times of all operations to be
  done)For all operations
• Next the due time tolerance is divided by the
  number of remaining operations.
• The outcome of this procedure determines the
  priority (lower numbers have higher priority)

5
Visit to Columbia Presbyterian Hospital

• Visited scheduling department
• Not ready to share data
• They use FIFO to schedule
• They have blocks of times assigned to doctors
• Patients are assigned to their doctors on FIFO
  basis
• Emergency cases are considered

6
The problem we work on

• Instance of scheduling patients in Operation
  rooms in Hospitals
• Same problem can be modified into other
  categories where shared hospital resources are
  used hence broader scope
• Creating an optimal schedule for operating room
• The key was to schedule surgical procedures on
  different days to minimize and balance the number
  of beds required each day
• If we minimize the revenues incurred, we maximize
  the number of operations in the operating rooms
  per day and hence prevent cancellation problem
  faced in many hospitals
• We use Linear Programming to minimize the above
  mentioned using some operation room data found on
  the internet

7
No of particular procedure scheduled for that
particular day
Surgical categories Monday Tuesday Wednesday Thursday Friday Saturday Sunday
A.  Otolaryngology XA1 XA2 XA3 XA4 XA5 XA6 XA7
B.  General XB1 XB2 XB3 XB4 XB5 XB6 XB7
C.  Gynecology XC1 XC2 XC3 XC4 XC5 XC6 XC7
D.  Neurology XD1 XD2 XD3 XD4 XD5 XD6 XD7
E.  Orthopedics XE1 XE2 XE3 XE4 XE5 XE6 XE7
F.  Pulmonary XF1 XF2 XF3 XF4 XF5 XF6 XF7
G.  Urology XG1 XG2 XG3 XG4 XG5 XG6 XG7
H.  Vascular XH1 XH2 XH3 XH4 XH5 XH6 XH7
I.  Day surgery XI1 XI2 XI3 XI4 XI5 XI6 XI7
J.  Other ambula tory surgery and pediatrics XJ1 XJ2 XJ3 XJ4 XJ5 XJ6 XJ7
Capacity (min)
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LP formulation

• Maximize
• (XA1XA2XA3.XA7) 5,600
  (XB1XB2XB3.XB7) 9,400 (XC1XC2XC3.XC7
  ) 3,100 (XD1XD2XD3.XD7)
  13,900(XE1XE2XE3.XE7) 8,200
  (XF1XF2XF3.XF7) 9,200 (XG1XG2XG3.XG7
  ) 8,000 (XH1XH2XH3.XH7) 12,400
  (XI1XI2XI3.XI7) 1,200 (XJ1XJ2XJ3.XJ
  7) 1,000

9

• Subject to
• XA1 XA2XA7 gt 3
• XB1 XB2...XB7 gt 24
• XC1 XC2...XC7 gt 8
• XD1 XD2XD7 gt 1
• XE1 XE2XE7 gt 7
• XF1 XF2.XF7 gt 1
• XG1XG2.XG7 gt 2
• XH1 XH2.XH7 gt 1
• XI1 XI2 XI7 gt 15
• XJ1 XJ2...XJ7 gt 70,

10

• XA1 XA2XA7 lt 6
• XB1 XB2XB7 lt 36
• XC1 XC2XC7 lt 12
• XD1 XD2XD7 lt 3
• XE1 XE2XE7 lt 15
• XF1 XF2.XF7 lt 2
• XG1 XG2XG7 lt 4
• XH1 XH2.XH7 lt 2
• XI1 XI2.XI7 lt 30
• XJ1 XJ2XJ7 lt 150,

11

• XA1 210 XB1 210 XJ190 lt 5880.875
• XA2 210 XB2 210 XJ290 lt 5880.875
• XA3 210 XB3 210 XJ390 lt 5880.875
• XA4 210 XB4 210 XJ490 lt 5880.875
• XA5 210 XB5 210 XJ590 lt 5880.875
• XA6 210 XB6 210 XJ690 lt 5880.875
• XA7 210 XB7 210 XJ790 lt 5880.875
• XAigt0 for i1,2,3,7
• XBigt0 for i1,2,3,7
• XCigt0 for i1,2,3,7
• XDigt0 for i1,2,3,7
• XEigt0 for i1,2,3,7
• XFigt0 for i1,2,3,7
• XGigt0 for i1,2,3,7
• XHigt0 for i1,2,3,7
• XIigt0 for i1,2,3,7
• XJigt0 for i1,2,3,7

12
Result
Scheduling option Limited Saturday/Sunday with 12-bed capacity Scheduling option Limited Saturday/Sunday with 12-bed capacity Scheduling option Limited Saturday/Sunday with 12-bed capacity Scheduling option Limited Saturday/Sunday with 12-bed capacity
Category Monday Tuesday Wednesday Thursday Friday Saturday Sunday Total
Otolaryngology 1 1 1 0 0 0 0 3
General 2 3 2 2 11 2 2 24
Gynecology 6 3 0 0 0 0 0 9
Neurology 0 0 0 0 1 0 0 1
Orthopedics 2 1 1 0 2 1 0 7
Pulmonary 0 0 0 1 0 0 0 1
Urology 0 0 2 0 0 0 0 2
Vascular 0 0 0 0 1 0 0 1
Day surgery 2 2 4 8 0 0 0 16
Other ambulatory surgery and pediatrics 41 46 49 49 14 0 0 150
Total 54 56 60 60 29 3 2 214
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Result Daily OR time used in minutes
Daily OR time used in minutes
Category Monday Tuesday Wednesday Thursday Friday Saturday Sunday
Otolaryngology 210 210 210 0 0 0 0
General 420 630 420 420 2310 420 420
Gynecology 900 450 0 0 0 0 0
Neurology 0 0 0 0 210 0 0
Orthopedics 360 180 180 0 360 180 0
Pulmonary 0 0 0 60 0 0 0
Urology 0 0 300 0 0 0 0
Vascular 0 0 0 0 240 0 0
Day Surgery 240 240 480 960 0 0 0
Other ambulatory surgery and pediatrics 3690 4140 0 4140 1260 0 0
Total 5820 5850 1590 5580 4380 600 420
Capacity in minutes 5880 5880 5880 5880 5880 600 420
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Conclusion and scope

• We analyzed an effective way to Minimize revenue
  and maximize profits while we minimize the
  cancellations
• We can add several other constraints that is
  faced in reality to make the solution more
  optimal
• We can do more analysis by considering number of
  beds
• We can conduct sensitivity analysis and come up
  with different variations

15
References

• Hospitals as complexes of queuing systems
  Godefridus G. Van Merode, Siebren Gruthius
• Distributed patient scheduling in hospitals
  T.O Paulussen, A. Heinzl
• Analysis of real world personnel scheduling
  problem Patrick De Causmaecker
• http//findarticles.com/p/articles/mi_m0FSL/is_3_8
  1/ai_n13471119/
• http//ieeexplore.ieee.org/Xplore/login.jsp?urlht
  tp3A2F2Fieeexplore.ieee.org2Fiel42F56592F151
  642F00699038.pdf3Farnumber3D699038authDecision
  -203