# Outpatient Appointment Optimization: A Case Study of a Chemotherapy Service
## 7 Conclusions and Future Works  
This work proposed a novel mathematical model for planning with time-varying resource constraints and strict time-lags, applied in a real-world outpatient chemotherapy service. The model included all four stages of each care session (consultation, installation, monitoring, and drug mixing), thus providing the most mathematically detailed description of the therapy. The formulation can be reused for more complex constraints such as restricting resource access and unavailability of patients to maximize patients' satisfaction.  
Using an empirical test with real-world data, we demonstrated the efficiency of heuristics and meta-heuristics under the objective function of minimizing total completion time. The _Most Total Successor (MTS)_ rule, which prioritizes lengthier sequences of treatment  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Scenario** & \(N_{a}\) & **GA** & **MILP** \\ \hline daily & 15 & **0.54** & 2.64 \\  & 30 & **0.81** & 5.17 \\  & 60 & **1.96** & 481.84 \\  & 90 & **3.67** & 3144.82 \\  & 120 & **8.88** & 3607.37 \\  & 150 & **9.52** & 3605.55 \\  & 180 & **14.99** & 3607.27 \\  & 210 & **13.91** & 3606.57 \\ \hline uniform & 15 & **0.65** & 3.15 \\  & 30 & **0.94** & 6.93 \\  & 60 & **2.01** & 388.04 \\  & 90 & **3.81** & 2560.58 \\  & 120 & 5.84 & 3605.26 \\  & 150 & **10.96** & 3603.58 \\  & 180 & **13.26** & 3607.83 \\  & 210 & **19.85** & 3605.19 \\ \hline weekend & 15 & **0.69** & 1.86 \\  & 30 & **1.07** & 4.17 \\  & 60 & **2.66** & 85.48 \\  & 90 & **5.01** & 1131.40 \\  & 120 & **8.59** & 2892.92 \\  & 150 & **16.28** & 3614.94 \\  & 180 & **19.63** & 3604.99 \\  & 210 & **20.97** & 3606.20 \\ \hline weekly & 15 & **0.54** & 2.86 \\  & 30 & **0.85** & 6.71 \\  & 60 & **1.83** & 420.77 \\  & 90 & **3.81** & 3236.47 \\  & 120 & **6.88** & 3608.38 \\  & 150 & **9.64** & 3608.42 \\  & 180 & **18.29** & 3607.80 \\  & 210 & **15.09** & 3606.19 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Execution time (in seconds) of different approaches. The priority-based heuristics give responses in several milliseconds, which is significantly faster than GA and MILP. We thus do not display them here. The best results are in bold.  
sessions, should bring about practical use in planning management. On the other hand, the genetic algorithm proves to be an excellent candidate to handle complicated constraints as a alternative for commercial solver. In practice, the heuristic can be useful for quick and simple planning tools, while the GA might be useful for long-term and sustainable planning systems.  
Finally, we are moving to an online version of this problem to provide an efficient algorithm that responds to the unpredictable fluctuation of resources and demands while leveraging the system's maximal operation.  
The authors contributed equally to the different steps of this research. All authors have read and agreed to the published version of the manuscript. This research received no external funding.  
The dataset is available at [[https://github.com/qrhant5010/CHT-I](https://github.com/qrhant5010/CHT-I)]([https://github.com/qrhant5010/CHT-I](https://github.com/qrhant5010/CHT-I)) (accessed on 1 November 2021). All the data have been presented in the manuscript. The codes developed for the current study are available from the corresponding author if requested.  
This work was supported by the Centre Hospitalier de Troyes (France), particularly the outpatient chemotherapy service.  
The authors declare no conflict of interest.