Appointment scheduling at a multidisciplinary outpatient clinic using stochastic programming

Abstract

The purpose of this paper is to investigate the problem of constructing an appointment template for scheduling patients at a specific type of multidisciplinary outpatient clinic called an integrated practice unit (IPU). The focus is on developing and solving a stochastic optimization model for a back pain IPU in the face of random arrivals, an uncertain patient mix, and variable service times. The deterministic version of the problem is modeled as a mixed integer program with the objective of minimizing a weighted combination of clinic closing time (duration) and total patient waiting time (length of stay). A two‐stage stochastic program is then derived to account for the randomness and the sequential nature of the decisions. Although it was not possible to solve the two‐stage problem for even a limited number of scenarios, the wait‐and‐see (WS) problem was sufficiently tractable to provide a lower bound on the stochastic solution. The introduction of valid inequalities, limiting indices, and the use of special ordered sets helped to speed up the computations. A greedy heuristic was also developed to obtain solutions much more quickly. Out of practical considerations, it was necessary to develop appointment templates with time slots at fixed intervals, which are not available from the WS solution. The first to be derived was the expected value (EV) template that is used to find the expected value of the EV solution (EEV). This solution provides an upper bound on the objective function value of the two‐stage stochastic program. The average gap between the EEV and WS solutions was 18%. Results from extensive computational testing are presented for the EV template and for our adaptation of three other templates found in the literature. Depending on the relative importance of the two objective function metrics, the results demonstrate the trade‐off that exists between them. For the templates investigated, the “closing time” ranged from an average of 235 to 275 minutes for a 300‐minute session, while the corresponding “total patient time in clinic” ranged from 80 to 71 minutes.

A stochastic programming approach for chemotherapy appointment scheduling

“…Note that in our case the patients are assigned to multiple resources simultaneously in the premedication step. Continuous appointment times make our SP model structure different from that of Hur et al (2020) as well.…”

“…In the literature of outpatient scheduling, the articles that consider multiple resources in the model are the most relevant ones to our study (Alvarez‐Oh, Balasubramanian, Koker, & Muriel, 2018; Batun, Denton, Huschka, & Schaefer, 2011; Hur, Bard, & Morrice, 2020; Klassen & Yoogalingam, 2019; Leeftink, Vliegen, & Hans, 2019; Perez, Ntaimo, Malave, Bailey, & McCormack, 2013; Riise, Mannino, & Lamorgese, 2016). Below, we provide an in‐depth comparison between our study and the studies that formulate two‐stage stochastic programming model.…”

“…Hur et al (2020) scheduled patients of a multidisciplinary outpatient clinic using SP formulation. They assigned patients to multiple providers to be seen during their visit at a back pain integrated practice unit.…”

Using Simulation Optimization to Solve Patient Appointment Scheduling and Examination Room Assignment Problems for Patients Undergoing Ultrasound Examination

“…The patient appointment scheduling problem involves variables such as number of physicians and examination rooms (single or multiple rooms), type of patients (single or multiple types), patient visit-time distribution (constant or random arrival time), and patient examination-time intervals (fixed and variable time interval) and considers whether a patient arrives on time or not [ 14 , 21 ], and whether a patient is absent [ 14 , 22 , 23 , 24 ]. Methods such as system simulation [ 15 , 25 ], simulation optimization [ 1 , 17 , 26 , 27 , 28 ], heuristic or meta-heuristic algorithms [ 6 , 16 , 23 , 29 ], and mathematical programming [ 5 , 19 , 30 ] are employed to solve the patient appointment scheduling problems. This study reviews the literature associated with these problems.…”

“…In studies regarding patient appointment scheduling, the type of patients diagnosed typically consists of a single type [ 15 , 16 ], such as otorhinolaryngology or ophthalmology, and the patient visit time is assumed to be a single probability distribution [ 6 , 17 , 18 , 19 , 20 ]. Additionally, patients in this study were subjected to external examinations by radiologists; if internal examinations were required, specialists other than radiologists would take care of the patients.…”