Abstract:
Every day, palliative care nurses in Melbourne’s south-east visit people living with life-limiting illness, guided by clinical recommendations on how often each client should be seen. Most days, demand outstrips the roster and clients are seen late. This summer I built a mathematical model to better understand what is driving these delays.
Blog:
It’s Monday morning, mid-July 2025. A team of nurses from Palliative Care South East (PCSE) are preparing to head out across Melbourne’s south-east, visiting people living with life-limiting illnesses, and supporting the families caring for them. Each client has a recommended visit frequency based on their condition, but on Monday, like most weekdays, there are more clients needing visits than nurses available. As the day unfolds, sudden deteriorations only add further pressure. Additional staff get pulled in to cover the shortfall, but some clients inevitably end up waiting longer than recommended for their next visit, and by Tuesday the cycle begins anew.
This is often the reality of delivering palliative care at scale, where resources are limited and client needs can change quickly. Which raises a natural question: is the challenge simply a shortage of nurses, or could the way visits are scheduled also be part of the problem?
Working with PCSE to address this question, I built an optimisation model that takes seven weeks of historical client visit data and searches for the best possible schedule; one that respects daily nursing capacity and clinical guidelines while minimising how long clients wait beyond their recommended visit window. Comparing these assignments against what actually happened gives us insight into whether the lateness was driven by staffing, scheduling, or both. However, to simplify the problem we had to give the model one big unfair advantage: a crystal ball. It knows in advance which clients will deteriorate and when.
Even before the model got to work, the real schedule revealed a surprising pattern. Stable clients were often being visited more frequently than the guidelines recommended, while some deteriorating clients, who need weekly contact, were falling behind. By adjusting the timing of stable visits to align with guidelines and redirecting that capacity towards clients with greater needs, the model reduced average visit lateness per client from 9 to 6.4 days.
Despite this meaningful improvement, it’s clear that scheduling changes alone don’t solve the entire problem. Moreover, even with its crystal ball, the model struggled under baseline staffing levels. When run without the additional staff that PCSE routinely pulls in, lateness increased sharply, and some clients were dropped from the schedule entirely. More nurses are genuinely needed, though perhaps not as many as Monday might suggest. The model found that adding one to two nurses per weekday above planned levels would bring lateness down considerably. At the same time, it highlighted lower-cost levers that could free up additional capacity: streamlining the admissions process for new clients had a significant impact, while making better use of existing weekend capacity offered a more modest benefit.
So, is the problem staffing or scheduling? As is often the case, it’s both. More considered scheduling can reduce delays by making better use of the capacity that already exists. But even the best schedule cannot overcome genuine shortages of nurses. Addressing one without the other only goes so far.
Thomas Caldecott
Monash University
