Reduced peak load by scheduling based on length of stay |instead of on an admission quota

Red Cross Hospital and ChipSoft do research together

"For us, a relatively small hospital, scheduling based on the length of stay is better than based on a quota. Just imagine how much this will mean to larger hospitals with a lot more variations in the length of stay." says Vincent van Ham, capacity manager for the Red Cross Hospital (Rode Kruis Ziekenhuis, RKZ). He was somewhat surprised by the results of the graduate research by Jeroen Staakman. For ChipSoft, he compared scheduling based on a quota with scheduling based on the patient's length of stay and came to a conclusion that is very interesting for a lot of hospitals.

Strategic value

Well performed scheduling of admissions, operations and turnovers has a high strategic value. For one, optimised use of care capacity enables the staff to care for as many patients as possible. In addition, it also leads to a more comfortable work load for the nursing staff. They are then, as a group, more adaptable. They would rather care for ten patients each day instead of caring for five on one day and for fifteen the other day. On top of that, they only know a short time beforehand whether there are five or fifteen patients on the department that day. In addition, a more stable work load allows them to better safeguard the quality of care.

During the implementation of the OR Scheduler, a question arose among the RKZ staff whether this tool would be implemented on the basis of the length of stay or the scheduling quota. The question that was at the base of this was: which method will cause the lowest variability in the outflow to the ward? RKZ currently uses a scheduling quota; when a scheduler registers an OR session, they will immediately see how many patients can be scheduled with outflow to a specific department. The hospital created this quota based on experience. Hospitals often opt to use scheduling quota because OR schedulers can more easily use it as footing when they have to consider available beds for the first time.

Scheduling quotas are based on averages. A quota works well for entire hospitals, but it's a bit more tedious when looking at departments and individual patients, according to Yke van Dijk, manager of ChipSoft's Capacity management team. "The chances of a patient being 'average' are not high. When multiple patients are on the waiting list with a high surgery duration, the hospital staff can operate on less people in the operation rooms which means that the hospital won't meet the quota. It can also be the case that there are a lot of patients with a higher expected length of stay on the waiting list. When using quotas, this will cause problems in the eventual occupation on the departments."

Collective curiosity

The RKZ took the position that scheduling based on quotas sufficed. Yke van Dijk opened that position up to discussion. Van Dijk: "Then we got the idea to research this, driven by a collective curiosity. The RKZ wants to know whether the peak load of their nursing staff can be reduced and whether they can better control the capacity in the clinic. We want to be able to scientifically support whether scheduling with a quota is better. "

Jeroen Staakman compared, as graduate research for his Master's degree in Industrial Engineering & Management at the University of Twente, the two methods of scheduling. He researched this in ChipSoft's Capacity management team in close cooperation with RKZ's Vincent van Ham. He simulated scheduling based on length of stay by creating a Mixed Integer Linear Program. In order to compare the results of planning based on quota with the length of stay scheduling, he developed the Length of Stay model which consists of two steps. First, a Mixed Integer Quadratic Program determines which waiting list session the patient should be assigned to. Secondly, a Mixed Integer Linear Program is used to sort the operations within the sessions.

"Didn't expect this much of a difference"

After numerous simulations and analysing several scenarios, Staakman came to the conclusion that the Length of Stay model will lead to less variability for the RKZ than the quota model. According to the models, the difference in the peak load for each day will be reduced by 70%. For the day treatment department, the load will have dropped  by 15%. That means that the work load on these departments is better distributed over the week days if the length of stay is taken into account during the scheduling process. Naturally, for some of the simulations in the research, assumptions have been made. Capacity manager Vincent van Ham (RKZ) was nonetheless surprised. "Honestly, I didn't expect this much of a difference for a smaller hospital, because differences in the length of stay are smaller. It's possible the difference is even higher for a larger hospital with more variation in the length of stay. If this can be properly configured HiX, hospitals are able to more effectively control bed occupation on the ward. That will lead to more productivity and better use of the capacity of the nursing staff."

If the RKZ chooses to switch to scheduling based on length of stay, several adjustments wil need to be made, according to Staakman. "A hospital will need to accurately assess the patient's length of stay. Besides, the scheduler will need to learn to think differently, because they will no longer look at the maximum amount of patients. They will have to see whether beds are vacant." Van Ham adds: "Scheduling 0 to 5 patients is fairly easy; looking in a graph where you'll have to take limitations into account is more difficult."

Research in practice

RKZ is expected to start with a pilot in 2021 in order to test whether practice corresponds with theory. Staakman couldn't wish for a better follow-up to his research. "The research is based on an algorithm and assumptions, for example that certain patients will stay for a set amount of days. In practice, this is more unpredictable. That's why it's useful to try it out in practice first."

Capacity manager Van Ham has a vision of how the pilot is going to work: "We'll choose one department that will make a schedule for the OR, based on the length of stay for a certain period of time. Subsequently, we'll analyse the process. The main challenge is that we treat patients of different specialties on the same department. That means that several schedulers will be scheduling beds for those patients. They might use different scheduling horizons – one might plan further ahead than the other. This will have to be coordinated properly. It might become a complex pilot, but this project will serve as a base for other projects. You might be able to use the results of this project to help observe the provisional discharge data."