# Hybrid Harmony Search for Stochastic Scheduling of Chemotherapy Outpatient Appointments
## 1 Introduction
Table 1 aims to retrieve the main literary contributions for the optimization of the COS problem and adopts a series of classification criteria to stress the difference between the literature and the proposed study as well. The first two classification criteria refer to the way the medical consultation is run and to the scheduling strategy, respectively. A distinction between deterministic and stochastic approaches (type of model) is also indicated along with the adopted solving method. In each work, it can be observed that the solving methods were compared with the scheduling rule implemented in practice by the oncology unit. The objective function is defined as a Key Performance Indicator (KPI). The kind of resources explicitly involved in the model can be the following: oncologists for the consultation phase (ON), pharmacists for the drug preparation stage (PH) and nurses at the treatment stage (NU). Finally, the last column points out the models capable of running the drug transportation time and the transportation batch as well. \begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline \multirow{2}{*}{**Reference**} & **Medical** & **Scheduling** & \multirow{2}{*}{**Type of Model**} & \multirow{2}{*}{**Solving**} & \multirow{2}{*}{**KPI**} & \multicolumn{2}{c}{**Limited Resources**} & \multirow{2}{*}{**Drug**} \\  & **Consultation** & & & & & **Method** & & **ON** & **PH** & **NU** \\ \hline [PERSON] and [PERSON] & Next-day & Offline & Stochastic & SP & WT, WL & & & ✓ \\ [PERSON] et al. (2017) [15] & Same-day & Offline & Deterministic & MP & WT & ✓ & ✓ & \\ [PERSON] et al. (2016) [23] & Next-day & Offline & Stochastic & SP, HE & WT, TCT & & & ✓ \\ [PERSON] and [PERSON] & Next-day & Offline & Deterministic & MP, T & WT, WL & & ✓ \\ [PERSON] et al. (2021) [10] & Same-day & Offline & Stochastic & SP, HE & WT, CU, OT & & & ✓ \\ [PERSON] (2003) [7] & Next-day & Offline & Deterministic & T & WT, WL & & ✓ \\ [PERSON] et al. (2017) [8] & Next-day & Offline & Deterministic & T & CU, P & & ✓ \\ [PERSON] et al. (2020) [25] & Same-day & Offline & Stochastic & SP, GRASP & M & ✓ & ✓ \\ [PERSON] et al. (2014) [18] & Next-day & Online & Deterministic & CP, DT & & ✓ & ✓ \\ [PERSON] et al. (2019) [2] & Same-day & Online & Deterministic & MP, DT & FW, M & & & ✓ \\ [PERSON] et al. (2017) [11] & Next-day & Offline & Deterministic & MP, CL & TCT & & ✓ \\ [PERSON] et al. (2018) [16] & Next-day & Offline & Deterministic & MP, CL & TCT & & ✓ \\ [PERSON] et al. (2019) [19] & Same-day & Offline & Deterministic & CP, T & WL & & ✓ \\ [PERSON] and [PERSON] (2019) [17] & Next-day & Offline & Deterministic & MP & P & & ✓ \\ [PERSON] and [PERSON] & Same-day & Offline & Deterministic & MP & WT, WL, OT & & ✓ \\ (2016) [14] & Same-day & Offline & Deterministic & MP & WL & ✓ & ✓ \\ [PERSON] et al. & Same-day & Offline & Stochastic & IR & WT, OT & & ✓ \\ (2020) [24] & Same-day & Offline & Deterministic & LR & WT, M & ✓ & ✓ \\ [PERSON] et al. (2011) [9] & Same-day & Offline & Deterministic & LR & WT, M & ✓ & ✓ \\ [PERSON] et al. (2013) [3] & Next-day & Online & Deterministic & HE & CU & & ✓ \\ [PERSON] et al. (2012) [10] & Same-day & Offline & Deterministic & MP & TCT & & ✓ \\
**This study** & **Same-day** & **Offline** & **Stochastic** & **HS** & **F** & ✓ & ✓ & ✓ \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison with the literature. Notably, HS was compared with a specific Greedy Randomized Adaptive Search Procedure (GRASP) algorithm, since this is the unique metaheuristic algorithm already used in the literature for the COS problem. A benchmark of instances was generated and an extended comparison analysis was carried out to demonstrate the outperformance of the proposed optimization technique over the competitor. The rest of the paper is organized as follows. Section 2 describes the problem statement also including the basic assumptions and the objective function. The major components characterizing the proposed hybrid harmony search are dealt with in Section 3.