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Roster Redesign Exploration (RRE)

Problem Description

General medicine (GM) regristrars at Auckland Hospital are currently rostered to 'on call' shifts by a 12 week rotating roster. This roster has grown organically over the years and is subject to union rules. The GM registrars on call admit patients to their GM ward from the emergency department and the Acute and Planning Unit (APU). There are 4 GM wards, with 3 registrars attatched to each ward. The types of shifts that are allocated to registrars include 'long day' admitting shifts (0800-2230), and normal admitting shifts (0800-1600). If a registrar is not allocated to an admitting shift then they complete a 'Normal Day' (0800-1600).

The current roster requires development as currently there are high fluctuations in patient numbers across registrars. These flucations result in some registrars being overworked on some days while other registrars have a low number of patients. This affects the standard of care for patients and the quality of life for registrars. Also of importance to consider is 'continuation of care', that is where the same registrar is looking after a patient for the duration of the patient's stay.


The purpose of this project is to investigate how the current roster for General Medicine registrar. The main goal is to implement a working model of an "Idealized roster". The timeline of this project is 10 weeks and as such is not expected to produce a full working roster but to provide the basis for further investigation, possibly as a 4th year project.

The desired outcomes of the summer project are:

  • Develop a detailed understanding of how the roster works and what is required
  • Identify a significant subset of the important constraints to include in the optimization of the roster governing measures of patient care and staff quality-of-life.
  • Develop a code shell for roster generation.
  • Produce example of an improved roster


Initial meeting held 25th November with Andrew Peterson, Tim Denison, Rupert Handy, Nicolas Szecket, Mike O'Sullivan and Amelia White.

From the initial meeting it seems that the main issues is variation in patient numbers across the teams which results in registrars being overworked and can compromise continuation of care for patients. This variation means that on some days a registrar may have to see upwards of 15 patients whereas on other days they may have 2 or 3. This means that on a given day one sub team may be extremely busy whereas another team may be quiet. The important aspect at this stage to address appears to be "smoothing" out the number of patients admitted across the week for each team to reduce variability.

An initial mathematical model was developed in Python. This model simply allocates one shift to every registrar and ensures that the correct number of admitting shifts are allocated each day. Python outputs this as a color-coded schedule into HTML format. This schedule currently is not practical, for example it does not match up night shifts with days off. This model has been set up to generate a schedule for each individual registrar and to develop a schedule for one registrar which is rotated through by each of the registrars. The advantage of the rotating schedule is that it is a smaller problem to solve and thus should solve faster (hopefully). The rotating roster also means that the work load on all registrars is equal as over the 12 weeks they all do the same roster just in different weeks

Current Roster Notes

The current roster is based from historical preferences but it is not known how it was developed. There are 4 GM wards and 4 teams: White, Gold, Red and Black, each consisting of 3 sub-teams. Each team is allocated to a ward.

A and B call each take approximately 1/3 of the new patients each day, C and D call take the remaining 1/3. As of December 13th 2010 this will change so each admitting team will take 1/4 of the incoming patients each. Patients admitted by the night cover registrar are split evenly across all wards.

Patients stay on average 3.5 days, however this is a long tailed distribution with around 50% of the patients being discharged within 24 hours. 40% of the time there are not enough GM beds.

Workload of registrars tends to peak later in the day and thus their shifts are not currently allocated around the peak work demand periods.

Admissions are 10-20% lower on weekends and there is a cap of 30 maximum admissions to the GM wards.

More Post-acute shifts would be beneficial in the weekend if possible.

Current Roster Rules

  • Shifts A B C D call must be allocated to one registrar Mon-Friday
  • Night shift and three days off must be allocated Sunday-Thursday
  • A relief registrar covers the shifts of the registrar on night duty. They can only work one long day (A or B call) in any given 7 day period and do not work weekends.
  • Friday A call must do P shift (post-acute) on Saturday and Sunday
  • Saturday A call must do P shift on Sunday
  • Friday C and D call's patients are covered by the 'P' call on the weekends
  • Registrars must have at least every second weekend off

Shift Rules

  • Shift length must be less than 15 hours
  • Minimum of an 8 hour break between shifts
  • A registrar can do a maximum of one shift per day
  • Registrars are paid from 0730 to 1730, Monday to Friday, regardless of whether they work those hours or not
  • A registrar must be replaced by a RMO of equal or greater standing

Preliminary Formulation

Objective: Produce a schedule


  • Every week day must have shifts 'A B C D' allocated to one and only one sub team
  • Every weekend day must have shifts 'A' and 2 'P' allocated to one and only one sub team
  • Sunday through to Thursday must have 'N' night shift allocated to one and only one sub team.
  • Each sub team can be allocated at most one shift

Addition constraints to add from meeting held 03/12/2010

  • Friday 'A' call does a post acute ('P') shift on Saturday and Sunday.
  • Saturday A call does a post acute ('P') on Sunday

Hospital Visit

To gain further understanding to exactly how things currently run at Auckland hospital, I shadowed several of the staff in General Medicine. I shadowed Dr Janar Sathanathan for several hours around the APU. Patients can be admitted directly to the APU from their GP to avoid double handing by the ED. One thing that I found surprising was the amount of time paper work took compared to the time actually needed to be spent with the patient.

Dr Anthony Jordan Showed me around the APU and Emergency Department (ED) and discussed several of the current issues. One issue brought up is that not all team positions are actually filled and there is currently no-one allocated to the relief roster. This means that that if a ward is short of a registrar, that ward has to stretch to cover the absent registrars work-load. He also mentioned that it may be useful to talk to Sarah Tracey at ARRMOS who currently develop the rosters based on templates in Excel. Apparently usually the first time the rosters come out, there is usually a problem with it not meeting some of the rules such as working two weekends in a row.

The Doctors that are on call admit from the ED and APU. In addition to this they can be allocated the Emergency pager which means they have to respond immediately to any critical cases. They can also be allocated the GP phone, which is the line GP's call in on if they are sending a patient to hospital. It appears having this phone can be highly disruptive to the doctors schedule.

I followed around a locum registrar in the ED for a couple of hours in the evening. The late afternoon to early evening is usually the busiest but the night I was there it was quite quiet. I discovered the next morning that some of the patients he admitted went to the team I was following the next morning. This meant that that no-one on the team that they were admitted to had the next day had seen the patient before morning rounds. In the ED each patient is assessed based on priority and can either be dispatched or, if they are expected to only be in for a short time, admitted to the APU or finally they can be admitted to the wards.

The morning following the evening I was in ED, I attended the GM morning meeting. This meeting occurs at 8am every weekday morning. The purpose is to review patients that have come in over-night and which wards and teams they have been allocated to. Ideally patients are allocated to the ward belonging to the team they have been assigned too. This unfortunately doesn't always happen and part of the meeting is spent 'finding' 'lost' patients. I shadowed Dr Rupert Handy, we first visited the new patients who had been kept in the APU overnight and then saw the new patients who had been allocated to the wards.

Example of patient allocation:

The below tables detail patient allocation before and after patients were moved between teams at the 8am meeting. The reason patients have to be moved between teams is when they have been sent to the wrong ward from ED or the APU.

TeamNew Total Call total ward
B1 511 29
B2 110
B3 18 X
W1 4 X 24
W21 10
W35 10
R11116 33
R2 10
R3 7 X
G1 5 X 24
G2 4
G35 15

Above: Patient allocation before transfers

Below: Patient allocation after transfers

Team New Total Call Total Ward
B1 8 14 32
B2 1 10
B3 1 8 X
W1 4 X 24
W2 1 10
W3 5 10
R1 8 13 31
R2 11
R3 7 X
G1 5 X 23
G2 4
G3 4 14

Next Steps

  • Look at historical data regarding patient admission and verify split of admissions across teams.
  • Shadow a medical team to gain further understanding as to how the roster affects patient care.
  • Mathematically formulate further constraints and incorporate in model

Future things to think about

  • Scheduling public holidays
  • Annual leave
  • 'Blank slate' -- Currently Junior Doctor rules are under negotiation and thus it is possible that a roster may be able to be developed from scratch, focusing on patient needs. Stephen Child spoke about this at the meeting 03/12/2010.
  • If patients are returning patients then they get realloctaed to the previous team they were seen by?

Topic attachments
I Attachment History Action Size DateSorted ascending Who Comment
Microsoft Excel Spreadsheetxlsx Shedule.xlsx r1 manage 26.8 K 2010-12-06 - 01:46 AmeliaWhite Example schedule handed to ADHB as example of initial model implementation
Texttxt roster.py.txt r1 manage 4.7 K 2010-12-06 - 01:47 AmeliaWhite Initial model formulation which generates a full roster
Texttxt roster_solution_rotate.txt r1 manage 0.7 K 2010-12-06 - 01:48 AmeliaWhite Initial model formulation which generates one roster which is then rotated through the registrars
Texttxt roster_rotate_1_4.py.txt r1 manage 6.9 K 2010-12-12 - 20:54 AmeliaWhite latest update with nice comments and displaying schedule in correct order

This topic: ORUA > WebHome > GenMedRoster
Topic revision: r12 - 2010-12-12 - AmeliaWhite
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