This month, the Centre for Smart Warehousing and Logistics Systems (SWALOS) is taking over the Business and Society blog. The Centre is newly established, and brings together researchers in warehousing and logistics operations looking to improve operations management and decision making. We’ll hear how their members are solving problems in the field, and the business and society implications.
Here Melih Celik details his research on chemotherapy scheduling. He explains how his mathematical models can help improve the efficiency of scheduling decisions, to improve patient waiting times and reduce nurse overtime.
According to Cancer Research UK, around 1,000 people are diagnosed with cancer in the UK every day. Every four minutes someone diagnosed with cancer sadly dies. Breast, prostate, lung, and bowel cancers constitute the majority of cancer cases.
Globally, cancer is one of the leading causes of death, second only to heart disease. The expected increase from 17 to 23.6 million in the number of global cancer patients by 2030 underlines the importance of efficient and effective planning for cancer treatments.
Chemotherapy is the most common way to alleviate or mitigate against the spread of cancer. It may be used to completely cure the cancer (curative), to decrease the risk of cancer coming back following a surgery or radiotherapy treatments (adjuvant) or to reduce the effects of the symptoms if the cancer cannot be cured (palliative). In either case, the patient needs to go through an exhaustive process with many side effects.
Prior to receiving chemotherapy, each patient needs to go through a number of tests including blood tests, X-rays and oncologist evaluations. After arriving for their set appointment time, the patient first waits for an available nurse and a chemotherapy chair. Following blood pressure and fever checks, pre-medication drugs are injected to avert potential side effects (such as fatigue, indigestion or nausea), after which the infusion of chemotherapy drugs commences.
Chemotherapy day units operate with extremely limited resources and under tight schedules. Designing patient schedules plays a crucial role in determining how efficiently these resources are used. To this end, day units take a two-step approach: First, patients are assigned appointment days based on their initial assessment or required infusion frequency. Then, specific appointment times are determined based on the estimated time it will take for the chemotherapy drugs to be fully infused (that is, delivered into each patient’s bloodstream).
In our recent work, we looked at addressing the daily chemotherapy scheduling decisions, in collaboration with the outpatient chemotherapy unit of a university hospital in Turkey, where these decisions were previously made using simple rules-of-thumb.
In determining daily appointment schedules, both provider and patient satisfaction need to be taken into account. From the provider’s perspective, nurse workloads should be balanced, overtime should be avoided to the best extent possible, and chairs should be highly utilised. Patient satisfaction mainly depends on reducing waiting times due to prior patients’ infusions taking longer than expected. These objectives are often in conflict with one another, particularly when simple rules are used for scheduling. For example, when patients are scheduled in decreasing order of estimated infusion times (which was the way they are scheduled in the chemotherapy unit in Turkey), nurse overtime will be decreased at the expense of higher patient waiting times.
The first part of our analysis consisted of a time study of the infusion times for more than 200 patients to see if they were in line with the estimations. The results showed significant deviations from the estimations. For example, of the 39 patients with an estimated infusion time of 150 minutes, actual times ranged between 61 and 196 minutes. We also observed that shorter infusion durations were underestimated, whereas longer ones were overestimated. We realised that we had to incorporate the uncertainties when estimating the infusion times.
The intricacies of resolving the trade-offs between multiple conflicting objectives require building complex mathematical models to find the “best” set of decisions. However, these models need substantial computational times (multiple hours) to arrive at these decisions, which prevents their use in an environment where timely decisions are of the essence. To overcome this, we built a simpler approach which not only provides ‘near-best’ schedules in only a few minutes and also outperforms the existing schedules of the chemotherapy unit by a long margin; patient waiting times were improved by 80%, nurse overtime was reduced by more than 30%, and chair utilisation was increased by 5%.
An interesting aspect of working with different healthcare institutions is that the specifics of their environment – including what is causing problems and delays - may differ significantly. The factors influencing the same decisions may be very different. For example, our collaborating unit applies ‘functional care delivery’, which means that each patient can be assigned to different nurses in each subsequent visit. This means that our model assumes that every nurse can help treat every patient. Functional care delivery is a flexible system where cross-training allows for more efficient treatment. We are currently extending this work to look at primary care delivery, where each chemotherapy nurse has a specific group of patients that only they treat. The benefit of this is that nurses know the specifics of the patients better, but also makes modelling and finding efficient schedules more challenging due to the more constrained environment.
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