# Hybrid Harmony Search for Stochastic Scheduling of Chemotherapy Outpatient Appointments
## 1 Introduction  
The Chemotherapy Outpatient Scheduling (COS) problem is a sensitive and challenging issue that is capturing the attention of both scholars and stakeholders in the healthcare landscape. Building an effective schedule of patients allows for reducing their waiting times on the one hand and increasing the number of treatments in the working shift on the other hand. To strengthen this thought, the health wards may exploit an appointment scheduling approach to improve the efficiency of their services, thus increasing patient satisfaction and service rate as well [1]. In brief, the main steps to generate a daily schedule of appointments in an oncology clinic are the following. The oncologists plan the days of treatment for each patient through a specific medium-term care protocol that defines all the necessary information, e.g., date and duration of treatments, type and doses of drugs. Subsequently, the oncology unit communicates to the patients the appointment time for a given day. Since each patient may have a different disease history, thus requiring a different care path, the time he/she needs to receive the oncology treatment, which goes from the medical visit to the end of treatment, can be highly variable and the interaction with the other patients can strongly bias his/her length of stay in the clinic. Hence, an effective method for scheduling patient appointments may positively impact the performance of the clinic and patient satisfaction as well. The literature background reveals that the COS problem can be viewed from two different perspectives, namely offline or online scheduling [2; 3]. As for offline scheduling, the daily list of patients is known in advance and the scheduler usually generates theappointment schedule a few days before the treatments. In this case, a non-templated approach is usually adopted to optimize an objective function based on a priori information [2]. Instead, for online scheduling, the appointment time is communicated to the patient immediately after his request or shortly after (e.g., no later than 24 h) by employing a dynamic template. In general, a template is an appointment timetable in which the total number of slots, the length of each slot, and the characteristics of patients to be scheduled for each slot are specified [4]. In fact, in online scheduling, a series of vacant appointment slots of the designed template, preliminarily generated based on a specific criterion, have to be filled by the patient requests. Another classification criterion concerns the chemotherapy treatment and depends on when the patients undergo the medical consultation. In next-day chemotherapy, the medical consultations are processed the day before the treatment. The scheduling problem consists of allocating patients to chairs, assigning them a nurse and defining the related treatment starting time. This strategy enables pharmacists to prepare the therapy in advance. However, the patient has to go to the clinic on two consecutive days and that could be not so practical if they live far away from the clinic. In the same-day chemotherapy strategy, the medical consultations are carried out on the same day of the infusion therapy. This strategy is quite well-diffused in real-world oncology clinics as it is preferred by patients [5] and prevents any waste of expensive drugs in case of deferral of patients or no-show at the infusion stage [6]. Several solving approaches were employed in the literature to cope with the COS problem. The contribution by [PERSON] [7] can be considered seminal research on the problem under investigation. The author adopted a next-day scheduling method based on a timetable for each day of the week. Similarly, [PERSON] et al. [8] made use of a specific template or ad hoc rules, based on the patient acuity level. From then on, most literature recognized the need to explicitly consider the patient flow to improve the performance of oncology units for solving the COS problem. In this regard, [PERSON] et al.