operating room allocation using milp
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I: Set of Room types.
J: Set of Medical specialities.
D: Set of Days.
i: Index for Room type.
j: Index for speciality.
k, l: Indices for days.
s: amount of staffed hours per day.
ai: Number of operating rooms of type i.
ejk: Emergency patients surgery demand for speciality j on day k (hours).
ojk: Non-Emergency patients surgery demand for speciality j on day k (hours).
cjk: The maximum number of operating rooms that speciality j can utilise on
day k (hours).
kl: Number of days delayed if the surgery is postponed from day k to day l.
: The equivalent number of days delayed if some surgery demand is not metin the model.
: Penalty rate for undersupply of OR hours to a speciality.
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xijk: Number of Operating Rooms of type i allocated to speciality jon day k.
yjk: Amount of Emergency ORs staffed hours allocated to speciality jon day k.
zjkl: Specialityjs non-emergency demand postponed from day k today l.
ujk: Specialityjs unmet non-emergency demand on day k.
bjk: Amount of idle time of the OR allocated to speciality j on day k.
h: Total amount of idle time of all non-emergency ORs.
pj: oversupply of OR hours to speciality j relative to its desired level.
qj: Undersupply of OR hours to speciality j relative to its desiredlevel.
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(kl zjkl) + ujk + qjkD lD jJ jJ kD jJ
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Patients length of stay caused by the delay in meeting
surgery demand within specified day.
Unmet non-emergency demand on day k.
Total Penalty caused by Undersupply of
OR hours for each speciality.
Minimize
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xijk = ai For all i,kjJ
s xijk zilk For all j,k
iI iI
s xijk bjk + ujk =Ojk For all j,kiI
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h = bjkjJ kD
xijk cjk For all j,kiI
h, pj, qj, xijk,bjk, yjk, zjkl, ujk 0
Xijk is an integer.
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h ojk bjk - kD = pj qjkD
ojkjJ kD
For all j
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Number of operating theatres types, i: 2
Number of staffed hours, s: 8 hrs
Delay for Unmet demand, : 1 day
Number of Operating days, D: 5 Number of specialities, J: 2
Penalty rate, : 0.1
Maximum no. of Operating Rooms for Speciality 1, ci1: 3
Maximum no. of Operating Rooms for Speciality 2, ci2: 3
No. of Operating Rooms of type 1, a1: 3
No. of Operating Rooms of type 2, a2: 2
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xijk = ai For all i,kjJ
s xijk ejk yjk + zilk For all j,k
iI iI
s xijk (ejk yjk + zjlk) bjk +iI lD
zjkl+ ujk = Ojk For all j,klD
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h = bjkjJ kD
yjk s For all kjJ
xijk cjk For all j,kiI
yjk ejk for all j,k
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xijk = ai For all j,kjJ
s xijk ejk yjk + zi
lk For all j,kiI iI
s xijk (ejk yjk + zjlk) bjk +iI lD
zjkl+ ujk = Ojk For all j,klD
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h ojkkD = pj qj For all j. bjk -
kD ojkjJ kD
ojk + zijk ujk POC hours For all j,ki I
h, pj, qj, xijk,
bjk
, yjk, zjkl, ujk 0
Xijk is an integer.
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Here working of operation theatre departmenthas been modeled using ARENA.
Inter arrival time of patients is seen to followExponential Random distribution with a meanof 45 minutes.
All operations are assumed to follow Uniform
distribution with minimum of 1 hour andmaximum of 3 hours.
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Dinh-Nguyen Pham,Andreas Klinkert Surgical Case Scheduling as generalized job
shop scheduling problem, European Journal of operation Research 185 (2008),pp1011-1025.
Aida Jebali,Atidel B. Hadj Alouane,Pierre Ladet Operating rooms scheduling,
Int.J.Production Economics 99(2006), pp 52-62.
Bo Zhang, PavanKumar Murali, Maged Dessouky, and David Belson. A Mixed Integer
Programming Approach For Allocating Operating Room Capacity, Daniel J. EpsteinDepartment of Industrial and Systems Engineering, University of Southern
California,2006.
Brecht Cardoen, Erik Demeulemeester, Optimizing a multiple objective surgical case
sequencing problem, Int. J. Production Economics 119 (2009), pp 354-366.
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H.Fei, N.Meskens, A planning and scheduling problem for an
operating theatre using an open scheduling strategy, Computers
& Industrial Engineering 78(2009), pp 144-54.
AlainGuinet, Sondes Chaabane, Operating Theatre Planning,
Int.J.Production Economics 85 (2003) 6981.
Vincent Augusto, Xiaolan Xie, Operating theatre scheduling withpatient recovery in both operating rooms and recovery beds.,
Computers & Industrial Engineering 45 (2009), pp 112-124.
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Brian R Hunt, A Guide to MATLAB - For Beginners and
Experienced Users, Cambridge University Press, 2006.
Stephan J Chapman, MATLAB Programming forbeginners, Bookware Companion Series, 2008.
Brian D Hahn, Essential MATLAB for scientists and
Engineers, Elsevier, 2006.
David J Anto, A guide to optimization using CPLEX, Dave
guide series, 2008.
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