operating room allocation using milp

8/9/2019 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.

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Programming Approach For Allocating Operating Room Capacity, Daniel J. EpsteinDepartment of Industrial and Systems Engineering, University of Southern

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Brecht Cardoen, Erik Demeulemeester, Optimizing a multiple objective surgical case

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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.

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Brian R Hunt, A Guide to MATLAB - For Beginners and

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operating room allocation using milp

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