Dynamically accepting and scheduling patients for home healthcare

Health Care Management Science https://doi.org/10.1007/s10729-017-9428-0 Dynamically accepting and scheduling patients for home healthcare Mustafa Demirbilek1 · Juergen Branke2 · Arne Strauss1 Received: 6 June 2017 / Accepted: 1 December 2017 © The Author(s) 2018. This article is an open access publication Abstract The importance of home healthcare is growing rapidly since populations of developed and even developing countries are getting older and the number of hospitals, retirement homes, and medical staff do not increase at the same rate. We consider the Home Healthcare Nurse Scheduling Problem where patients arrive dynamically over time and acceptance and appointment time decisions have to be made as soon as patients arrive. The objective is to maximise the average number of daily visits for a single nurse. For the sake of service continuity, patients have to be visited at the same day and time each week during their episode of care. We propose a new heuristic based on generating several scenarios which include randomly generated and actual requests in the schedule, scheduling new customers with a simple but fast heuristic, and analysing results to decide whether to accept the new patient and at which appointment day/time. We compare our approach with two greedy heuristics from the literature, and empirically demonstrate that it achieves significantly better results compared to these other two methods. Keywords Home healthcare · Optimisation · Heuristics · Simulation 1 Introduction Home Healthcare (HHC), also referred to as in-home care, social care, or domiciliary care, is becoming one of the most important components of healthcare. HHC helps hospitals and retirement homes to free capacity and decrease care delivering cost [1]. The most crucial objective of HHC is to ensure people who need medical attention and daily care to receive high-standard home services. According to patients’ needs, nurses, physicians, doctors, and operators visit patients’ homes periodically and provide services. Many elderly, people who are chronically ill, and individuals with disabilities receive HHC services [2]. In 2005, $53.4 billion were spent on 17,700 HHC service providers in the US according to The National Association for Home Care and Hospice. HHC companies employed  Juergen Branke Mustafa Demirbilek Arne Strauss 1 Warwick Business School, Coventry, UK 2 Warwick Business School, University of Warwick, Coventry, UK 200,000 nurses to service approximately 7.6 million patients in 2007 [3]. Due to some factors such as ageing population, chronic diseases, insufficient capacity of hospitals, etc., it is projected that the demand for HHC doubles by 2030 [4]. The following information shows why HHC is gaining much more importance day by day: – – – – The number of people aged 65 and over in US will be four times as many by 2040 [5]. Care of a patient in the home costs only $132 per day whilst $1889 are spent for a patient receiving care in a hospital [3]. Home-based health technologies cost $3 billion in 2007 versus $7.7 billion in 2012 [1]. The percentage of American adults who are chronically ill is more than 50% [6]. In this study, we focus on the acceptance decision of a request as well as the scheduling. In the literature, an acceptance policy is occasionally discussed in different areas such as public transportation [7] and vehicle dispatching [8]. The problem starts whenever a patient requests service. The HHC provider has to decide whether or not to accept the patient and, if accepted, assign suitable appointment days and times. Then, for each shift, all nurses start from their homes, visit scheduled patients at the agreed appointment times, serve them for the prescribed time, and M. Demirbilek et al. finally return to their homes. In this paper, only a single nurse servicing patients in a specific area is considered and any overlaps with other nurses’ regions are ignored. We leave the multi-nurse case to future research. The objective of this problem is to maximise the average number of daily visits performed by the nurse. We require that patients are serviced at the same days and times during their service horizon, which is called consistent, periodic Vehicle Routing Problem (VRP). Furthermore, the problem is dynamic, and acceptance and assignment time decisions have to be made as soon as patients arrive. Although there are some studies providing solutions to this problem by using greedy algorithms in the literature, these algorithms do not consider or only partially consider future demand. We propose a Scenario Based Approach (SBA) which simulates several scenarios, scheduling new customers with a simple but fast heuristic, and analysing results to decide whether to accept the new patient and at which appointment day\time. The basic idea is to see how many times the new request is assigned amongst all simulated requests and in which time slot it is scheduled most frequently. We examine two different variants for SBA. First, a Daily Scenario Based Approach (DSBA) constructs daily tours based on single day demand. Next, a Weekly Scenario Based Approach (WSBA) constructs weekly tours by taking into account an entire week’s requests simultaneously in each scenario. Our main contributions are the following: – – – A new acceptance and scheduling policy based on a solution methodology which anticipates future demand for the Dynamic HHC problem, Comparison of two different approaches, one depending on constructing tours for each day of the week independently and the other considering all visits of requests in the week at the same time when constructing tours for each day. Comparison of our solution method to two greedy heuristics proposed by Bennett and Erera [9]. In Section 2, we present a literature review related to home health nurse routing and scheduling problems. In Sections 3 and 4, we define the problem and present the solution approaches. In Sections 5, simulation environment, scenarios, and results are presented. Finally, we conclude our study and outline future opportunities in Section 6. 2 Literature review In this section, we go over the most relevant studies in the HHC area and Dynamic Routing Problem (DVRP) since our problem and solution methodology are directly related to the DVRP. 2.1 HHC studies HHC related models started with Begur et al. [10] in 1997, “An integrated spatial DSS for scheduling and routing home healthcare nurses”. They constructed a decision support system for a home care company to optimise their routing and rostering operation without considering time windows. We refer readers to Mutingi et al. [11] for a state-of-the-art review of the models and algorithms that have been reported in the literature between 1997 and 2013, and concentrate on some key papers from this period. Gaspero and Urli [12] focused on finding an optimal multi-day HHC schedule by employing a two-stage solution approach. First, they used constraint prog (...truncated)