Operating Room Allocation Using MIP
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Transcript of Operating Room Allocation Using MIP
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Public hospitals are non-profit organizations,and their prime operational objective is toprovide medical services to their patients at a
reasonable cost. In such an environment, asignificant amount of time and resources areinvested in operating theatres. If optimumallocation strategies are devised for the same,
worthy savings can be achieved.
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Priority for Surgery:
1. Emergency Patients
2. Inpatients
3. Outpatients
Separate Operating Rooms for Emergency cases.
Emergency Operating rooms are equipped so that it can handle all
kinds of surgeries.
Non-Emergency Operating rooms are separate for each specialty.
Emergency cases can be done in Non-Emergency rooms but vice-versa is not possible.
Only one operating room is used for emergency surgeries each day.
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I: Set of Room types.
J: Set of Medical specialties. D: Set of Days.
i: Index for Room type.
j: Index for specialty.
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 specialty j on day k (hours).
Ojk: Non-Emergency patients surgery demand for specialtyj 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 met in themodel.
: Penalty rate for undersupply of OR hours to a specialty. It serves the purpose ofsmoothing the OR capacity. Value is
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Minimize
( ) +
+
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Patients length of stay caused by the delay in meeting
surgery demand within specified day.
Total Penalty caused by Undersupply of
OR hours for each specialty.
Unmet non-emergency demand on day k.
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=
,
Guarantees that all the operating rooms are allocated to
some specialty each day.
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+
,
Ensures that on any day, each specialty has at least the OR capacity
to meet the sum of its emergency demand on that day and non-
emergency demand decided to be postponed to that day.
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( + ) + + = ,
Specialtyjs non-emergency surgery demand on day k must meteither on that day, some remaining day in the current week, or
unmet (that is met days late).
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=
Defines h as the sum of idle hours of all the non-emergency ORs over
one week.
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Guarantees that at most s hours of emergency demand is
met in the emergency OR each day.
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,Guarantees the daily emergency OR capacity
allocated to each specialty does not exceed their
emergency demand.
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, , , , , 0, , , ,
Non-Negativity constraint in all the decision variables.
integer,
,,
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After obtaining the template from the MIPmodel, a simulation model is used to assessthe quality of the template generated by MIP.
The optimum value can be determined bytesting the template in the simulation model.
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Each specialty has two queues waiting for the surgery: Inpatients and
Outpatients.
There is a single queue for all emergency patients who need surgery.
All Operating Rooms are modeled as servers in the queue system.
The number of Non-Emergency Operating Rooms available to each
specialty changes throughout the week as determined by the template.
All types of patient arrivals are modeled as renewal processes.
Pre-surgery set-up time and post-surgery operating room cleaning
time, if significant, is also added to the model. Each specialtys inpatient, outpatient, and emergency patients surgery
lengths are random variables fit from historical data.
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Hospital: Los Angeles County General Hospital.
Operating Rooms: 19.
Specialties: 18.
Emergency Operating Rooms: 1.
Data used: January 2005.
Values of smoothing constant(
): 0, 0.5, 0.75, 1.
Softwares used: CPLEX 9.0(Solver), AweSim! Version 3(Simulation).
Computer Hardware used: 3.2 GHz CPU with 2GB RAM.
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Unit: OR hour Template i Template ii Template iii Template iv Template v
Emergency 40 40 40 40 40
Burns 32 32 32 32 24
Cardiac 48 40 40 40 40
Colorectal 24 40 32 24 24
Foregut 16 16 16 16 16
HNS 88 80 88 88 88
Neuro 40 40 40 40 40
Ortho 192 160 168 176 184Trauma 8 24 24 24 24
Tumor 24 24 24 24 24
Urology 40 40 40 40 40
GSNTE 16 40 40 40 40
Plastics 24 24 24 24 24
Hepatobiliary 24 24 24 24 24
Ophthalmology 80 72 72 72 72
OMFS 32 32 32 32 32
Vascular 24 32 24 24 2422
OPERATINGROOMCAPACITYALLOCATEDTOEACHSPECIALTYPERWEEK
Templatei:ActualA
llocation
Templateii:
=
0
Templateiii:=
0.5
Templateiv:=
0.7
5
Templatev:=
1
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Template ii iii iv v
0 0.5 0.75 1Patients Average Wait (Day) 1.64 1.81 1.90 1
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Template i v
Emergency Patients Average Wait(day) 0.62 0.51
Emergency Operating Room Utilization(%) 48.35 47.28
Inpatients Average Wait(day) 1.86 1.54
Outpatients Average Wait(day) 0.34 0.33
Average Non-Emergency Operating Room Utilization(%) 63.39 65.91
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+
,
The sum of the total non-emergency demand and thedemand that has been postponed to day k from lminus the non emergency demand that has beenpostponed from day k for a specialtyj must be less
than or equal to the number of hours available onpost-operative care.
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