operating room allocation using mip

8/8/2019 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

( ) +

+

11

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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operating room allocation using mip

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