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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 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

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
  • 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

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.

Topic attachments
I Attachment History Action Size Date 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
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Topic revision: r7 - 2010-12-06 - AmeliaWhite
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