Chemotherapy appointment scheduling is a challenging problem due to the uncertainty in pre-medication and infusion durations. In this paper, we formulate a two-stage stochastic mixed integer programming model for the chemotherapy appointment scheduling problem under limited availability and number of nurses and infusion chairs. The objective is to minimize the expected weighted sum of nurse overtime, chair idle time, and patient waiting time. The computational burden to solve real-life instances of this problem to optimality is significantly high, even in the deterministic case. To overcome this burden, we incorporate valid bounds and symmetry breaking constraints. Progressive hedging algorithm is implemented in order to solve the improved formulation heuristically. We enhance the algorithm through a penalty update method, cycle detection and variable fixing mechanisms, and a linear approximation of the objective function. Using numerical experiments based on real data from a major oncology hospital, we compare our solution approach with several scheduling heuristics from the relevant literature, generate managerial insights related to the impact of the number of nurses and chairs on appointment schedules, and estimate the value of stochastic solution to assess the significance of considering uncertainty.
Disease management programs have emerged as a cost-effective approach to treat chronic diseases. Appointment adherence is critical to the success of such programs; missed appointment are costly, resulting in reduced resource utilization and worsening of patients' health states. The time of an appointment is one of the factors that impacts adherence. We investigate the benefits, in terms of improved adherence, of incorporating patients' time-of-day preferences during appointment schedule creation and, thus, ultimately, on population health outcomes. Through an extensive computational study, we …
In a recently published article, Liu (2016) used M/M/1/K and M/D/1/K queuing models to determine the optimal window for patient appointment scheduling considering clinic environ- mental factors such as panel size, provider service rate, and delay-dependent no-show probability. In this note, we show that the application of one of the no-show functions was incorrect. The required corrections are proposed.
Diagnostic clinics are among healthcare facilities that suffer from long waiting times which can cause medical issues and lead to increases in patient no-shows. Reducing waiting times without significant capital investments is a challenging task. We tackle this challenge by proposing a new appointment scheduling policy for such clinics that does not require significant investments. The clinic in our study serves outpatients, inpatients, and emergency patients. Emergency patients must be seen on arrival, and inpatients must be given next day appointments. Outpatients, however, can be given late…
We study a single-server appointment scheduling problem with a fixed sequence of appointments, for which we must determine the arrival time for each appointment. We specifically examine two stochastic models. In the first model, we assume that all appointees show up at the scheduled arrival times yet their service durations are random. In the second model, we assume that appointees have random no-show behaviors and their service durations are random given that they show up at the appointments. In both models, we assume that the probability distribution of the uncertain parameters is unknown bu…
An important challenge confronting healthcare is the effective management of access to primary care. Robust appointment scheduling policies/templates can help strike an effective balance between the lead-time to an appointment (a.k.a. indirect waiting time, measuring the difference between a patient's desired and actual appointment dates) and waiting times at the clinic on the day of the appointment (a.k.a. direct waiting time). We propose methods for identifying effective appointment scheduling templates using a two-stage stochastic mixed-integer linear program model. The model embeds simulat…
This study is concerned with the determination of optimal appointment times for a sequence of jobs with uncertain duration. We investigate the data-driven Appointment Scheduling Problem (ASP) when one has $n$ observations of $p$ features (covariates) related to the jobs as well as historical data. We formulate ASP as an Integrated Estimation and Optimization problem using a task-based loss function. We justify the use of contexts by showing that not including the them yields to inconsistent decisions, which translates to sub-optimal appointments. We validate our approach through two numerical …
We study a routing and appointment scheduling problem with uncertain service and travel times arising from home service practice. Specifically, given a set of customers within a service region that an operator needs to serve, we seek to find the operator's route and time schedule. The quality of routing and scheduling decisions is a function of the total operational cost, consisting of customers' waiting time, and the operator's travel time, idle time, and overtime. We propose and rigorously analyze a stochastic programming model and two distributionally robust optimization (DRO) models to sol…
Consider a set of jobs with independent random service times to be scheduled on a single machine. The jobs can be surgeries in an operating room, patients' appointments in outpatient clinics, etc. The challenge is to determine the optimal sequence and appointment times of jobs to minimize some function of the server idle time and service start-time delay. We introduce a generalized objective function of delay and idle time, and consider $l_1$-type and $l_2$-type cost functions as special cases of interest. Determining an index-based policy for the optimal sequence in which to schedule jobs has…
In the Home Service Assignment, Routing, and Appointment scheduling (H-SARA) problem, a set of homogeneous service teams must visit a set of customers. The home service provider needs to decide how many teams to hire (i.e., sizing problem), how to assign service teams to customers (i.e., assignment problem), how to route service teams (i.e., vehicle routing problem),and how to schedule the appointment times for the customers (i.e., appointment scheduling problem) such that the total cost is minimized. To tackle the H-SARA problem, we propose an efficient solution method that comprises two stag…
We consider the problem of scheduling appointments for a finite customer population to a service facility with customer no-shows, to minimize the sum of customer waiting time and server overtime costs. Since appointments need to be scheduled ahead of time we refer to this problem as an optimization problem rather than a dynamic control one. We study this optimization problem in fluid and diffusion scales and identify asymptotically optimal schedules in both scales. In fluid scale, we show that it is optimal to schedule appointments so that the system is in critical load; thus heavy-traffic con…
We study web and mobile applications that are used to schedule advance service, from medical appointments to restaurant reservations. We model them as online weighted bipartite matching problems with non-stationary arrivals. We propose new algorithms with performance guarantees for this class of problems. Specifically, we show that the expected performance of our algorithms is bounded below by $1-\sqrt{\frac{2}π}\frac{1}{\sqrt{k}}+O(\frac{1}{k})$ times that of an optimal offline algorithm, which knows all future information upfront, where $k$ is the minimum capacity of a resource. This is the …
Patient transportation systems are instrumental in lowering access barriers in primary care by taking patients to their GPs. As part of this setting, each transportation request of a chronic or walk-in patient consists of an outbound trip to the GP and an inbound trip back home. The economic sustainability of patient transportation systems mainly depends on their utilization and how well transportation requests can be bundled through ride sharing. To ease the latter, we consider a flexible scheduling of chronic patients in which only a certain range for an appointment is fixed a priori while t…
A classical problem in appointment scheduling, with applications in health care, concerns the determination of the patients' arrival times that minimize a cost function that is a weighted sum of mean waiting times and mean idle times. One aspect of this problem is the sequencing problem, which focuses on ordering the patients. We assess the performance of the smallest-variance-first (SVF) rule, which sequences patients in order of increasing variance of their service durations. While it was known that SVF is not always optimal, it has been widely observed that it performs well in practice and …
We formulate and solve the H-SARA Problem, a Vehicle Routing and Appointment Scheduling Problem motivated by home services management. We assume that travel times, service durations, and customer cancellations are stochastic. We use a two-stage process that first generates teams and routes using a VRP Solver with optional extensions and then uses an MC Scheduler that determines expected arrival times by teams at customers. We further introduce two different models of cancellation and their associated impacts on routing and scheduling. Finally, we introduce the Route Fracture Metaheuristic that…
Parallel processing is a principle which enables simultaneous implementation of anesthesia induction and operating room (OR) turnover with the aim of improving OR utilization. In this article, we study the problem of scheduling surgeries for multiple ORs and induction rooms (IR) that function based on the parallel processing principle under uncertainty. We propose a two-stage stochastic mixed-integer programming model considering the uncertainty in induction, surgery and turnover durations. We sequence patients and set appointment times for surgeries in the first stage and assign patients to I…
