Session Item

At our dedicated one-stop-shop (OSS) outpatient clinic for palliative RT, each day 4 patients are scheduled from intake to treatment in one working day. Patients arrive in the morning  and are treated at the end of the day, spending roughly 6 hours from start of intake to start of treatment (SIST). It is expected that by optimizing the sequence of the 12 preparation steps per patient (48 in total, in combination referred to a schedule) the average SIST (aSIST) over the 4 patients could be reduced considerably. However, minimizing the aSIST increases the vulnerability of the process for unexpected delays and therefore risk of overtime (RoO). Hence our goal was to develop a method to automatically optimize schedules to balance aSIST and RoO.

The OSS is ran by 1 dedicated RO and 2 all-round RTTs. The mean execution times of the 12 different steps were extracted for 663 patients treated between October 2019 and October 2020 (Table 1). A Kolmogorov-Smirnov test determined execution time distributions for the 12 steps, which were randomly sampled 250 times for the 48 steps.

First, 200 schedules were generated at random (1^st generation) as input for a non-dominated sorting genetic algorithm (NSGA-II). For each schedule a linear program found the optimal starting time of each step, lunch time and optimal operator by minimizing the expected aSIST. To calculate RoO, each schedule was evaluated 250 times for pre-sampled execution times. From the 1^st generation, the 100 most promising parents were selected based on tradeoff fronts between expected aSIST and RoO. Next, the NSGA-II algorithm created 100 offspring (i.e. novel schedules) by random point cross-over and mutation (1-5 pairs, randomly picked) and the expected aSIST and RoO were calculated. The 100 parents and their 100 offspring formed the next generation. The NSGA-II was run for 2000 generations. The expected aSIST and RoO were also calculated for the current clinical schedule.

Figure 1 shows the tradeoff front between expected aSIST and RoO and how it converges with increasing generations. The expected aSIST was smallest (189 min) for Schedule 1 but would lead to 100% RoO. Decreasing RoO to 5% could be achieved but at large increase in expected aSIST of 103 min (Schedule 3). Schedule 2 represented an acceptable balance between RoO of 14% with expected aSIST of 242 min (53 min more than schedule 1). Note that schedule 2 outperformed the clinical schedule (RoO and aSIST) both in RoO and aSIST.