# Hybrid Harmony Search for Stochastic Scheduling of Chemotherapy Outpatient Appointments
## 5 Conclusions  
### Final Discussion  
In this research, the same-day offline stochastic chemotherapy outpatient appointment scheduling problem, inspired by a real-world oncology department, was investigated. Differently from the rest of the literature on this topic, we stochastically modeled all the stages provided by the chemotherapy process and, in addition, several sources of uncertainty (e.g., deferrals and medical consultation times) were taken into account. Particularly, since the pharmacy is located far away from the treatment unit, we considered the real-life scenario in which a drug delivery service is a time-consuming task needed to take the therapies to the ward.  
A stochastic scheduling approach was adopted to cope with the uncertainty of the problem. Since the problem under investigation can be assimilated into a hybrid flow shop scheduling problem with resource-related constraints, several idle times may occur among the stages. Therefore, to improve the quality of any appointment schedule, we implemented an LS scheduling strategy in the decoding algorithm for the minimization of the objective function, i.e., the expected total flow time.  
The outpatient scheduling problem is extensively studied in the literature and most authors used mathematical programming applied to relaxed models for the generation of optimal solutions. Since the problem under investigation is NP-hard in the strong sense, we developed a hybrid Harmony Search named HS. To demonstrate both the efficacy  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Instance** & **LPT [\%]** & **HS [\%]** \\ \hline  
\(RPD_{ave}\) & 6.94 & **0.00** \\ \hline \hline \end{tabular}
\end{table}
Table 8: Comparison between LPT rule and HS algorithm.  
and efficiency of the proposed metaheuristic, a comparative analysis involving a GRASP algorithm from the relevant literature on the same topic was carried out.  
The analysis pointed out the effectiveness of the proposed hybrid HS algorithm. There are no instances in which the GRASP algorithm can perform better than HS. Since the GRASP algorithm works by successive constructions of a greedy randomized solution, which in turn is improved by a semi-greedy constructive procedure, the time required to build a solution is considerably high. Therefore, the weakness of GRASP in comparison with the other techniques can be mostly explained by the lower number of solutions it evaluates within _Max_ct_. In fact, the HS algorithm is able to perform almost 5000 evaluations more than GRASP in 2500 s.  
The quality of the solutions assured by the hybrid HS, as well as its computational efficiency, was tested by the staff of the chemotherapy clinic, which decided to replace the LPT appointment strategy adopted so far with the proposed hybrid metaheuristic approach.  
The numerical results demonstrate that the use of the proposed outpatient scheduling method may positively affect oncology units as follows:  
1. The proposed method, which combines efficacy and computational efficiency, assures a significant improvement in terms of total flow time with respect to the LPT rule, which in turn is a scheduling strategy commonly adopted by healthcare managers;
2. From an economic viewpoint, solutions obtained by the hybrid HS allow for reducing the clinics' idle time and the number of patients treated in a day as well;
3. Considering the patient's perspective, the proposed method yields a significant reduction in patient waiting time and on a global service level as well.