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Hospital Scheduling

Hospital Scheduling. Chandni Verma Semonti Sinhaaroy. Overview. Problems faced in hospital scheduling Methods used – FIFO, SPT or LSO Columbia Presbyterian Hospital Operation Room Scheduling Our solution - Linear Programming Scope. Problem – hospital scheduling.

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Hospital Scheduling

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  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) Σ(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 tominimize 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

  8. LP formulation Maximize (XA1+XA2+XA3+…….+XA7)* 5,600+ (XB1+XB2+XB3+…….+XB7)* 9,400+ (XC1+XC2+XC3+…….+XC7)* 3,100 + (XD1+XD2+XD3+…….+XD7)* 13,900+(XE1+XE2+XE3+…….+XE7)* 8,200+ (XF1+XF2+XF3+…….+XF7)* 9,200+ (XG1+XG2+XG3+…….+XG7)* 8,000+ (XH1+XH2+XH3+…….+XH7)* 12,400+ (XI1+XI2+XI3+…….+XI7)* 1,200 + (XJ1+XJ2+XJ3+…….+XJ7)* 1,000

  9. Subject to: XA1+ XA2+……………………+XA7 >= 3 XB1+ XB2+…………………...+XB7 >= 24 XC1+ XC2+…………………...+XC7 >= 8 XD1+ XD2+……………………+XD7 >= 1 XE1+ XE2+……………………+XE7 >= 7 XF1+ XF2+…………………….+XF7 >= 1 XG1+XG2+…………………….+XG7 >= 2 XH1+ XH2+…………………….+XH7 >= 1 XI1+ XI2+……………………… +XI7 >= 15 XJ1+ XJ2+……………………...+XJ7 >= 70,

  10. XA1+ XA2+…………………+XA7 <= 6 XB1+ XB2+…………………+XB7 <= 36 XC1+ XC2+…………………+XC7 <= 12 XD1+ XD2+…………………+XD7 <= 3 XE1+ XE2+…………………+XE7 <= 15 XF1+ XF2+………………….+XF7 <= 2 XG1+ XG2+…………………+XG7 <= 4 XH1+ XH2+………………….+XH7 <= 2 XI1+ XI2+…………………….+XI7 <= 30 XJ1+ XJ2+……………………+XJ7 <= 150,

  11. XA1* 210 + XB1* 210 +……+XJ1*90 <= 5880*.875 XA2* 210 + XB2* 210 +……+XJ2*90 <= 5880*.875 XA3* 210 + XB3* 210 +……+XJ3*90 <= 5880*.875 XA4* 210 + XB4* 210 +……+XJ4*90 <= 5880*.875 XA5* 210 + XB5* 210 +……+XJ5*90 <= 5880*.875 XA6* 210 + XB6* 210 +……+XJ6*90 <= 5880*.875 XA7* 210 + XB7* 210 +……+XJ7*90 <= 5880*.875 XAi>=0 for i={1,2,3,…7} XBi>=0 for i={1,2,3,…7} XCi>=0 for i={1,2,3,…7} XDi>=0 for i={1,2,3,…7} XEi>=0 for i={1,2,3,…7} XFi>=0 for i={1,2,3,…7} XGi>=0 for i={1,2,3,…7} XHi>=0 for i={1,2,3,…7} XIi>=0 for i={1,2,3,…7} XJi>=0 for i={1,2,3,…7}

  12. Result:

  13. Result :Daily OR time used in minutes

  14. 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_81/ai_n13471119/ • http://ieeexplore.ieee.org/Xplore/login.jsp?url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel4%2F5659%2F15164%2F00699038.pdf%3Farnumber%3D699038&authDecision=-203

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