A mathematical optimization model for efficient management of Nurses’ Quarters in a teaching and referral hospital in Hong Kong

Abstract

Objective

Effective use of available resources is critical in the healthcare industry. Space in the Nurses’ Quarters in an acute regional and teaching hospital in Hong Kong is under pressure and effective use of such scarce resources is warranted. We present an application of mathematical optimization to ensure rooms are optimally assigned for users, in which the least number of rooms need to be opened while entertaining the most number of user requests, while at the same time satisfying various business rules of quarter management.

Methods

Extensive consultation was embarked at the start of the project to gather requirements from quarter management and frontline users. Utilization statistics were also gathered and analyzed. A web-based booking system was designed and implemented to streamline the booking workflow for users, while a mixed integer programming model was implemented to automate the room assignment process for quarter management.

Findings

More than 70% of bookings are now booked through the automated system. Unlike the old workflow where users need to travel to the quarter for reservation of rooms, they can now access the online system using any computer workstation that is connected to the hospital intranet. This greatly simplifies the booking workflow for users and decreased the amount of no-shows. In addition, workflow wastage in the then-manual room assignment process was minimized through the use of the room assignment model. Instead of manually assigning requests to rooms each day, an optimized room assignment that takes into account new and complex business rules on room allocation is now automatically generated with a click of a button. Defects and rework that arise from the manual process were eliminated through the implementation of the mathematical model. The implementation of such a fair and transparent assignment methodology also minimized the amount of disputes and complaints from users.

Conclusion

The use of operations research methodologies is useful in enhancing workflow efficiency and resource utilization in healthcare. Through the employment of a data-driven and evidence-based methodology, buy-in from stakeholders could be obtained so that a new and enhanced workflow could be successfully implemented.

Introduction

How to efficiently and effectively utilize scarce resources has always been a focus of research in healthcare management. In most parts of the world, healthcare capacity is heavily constrained compared to the growing demand. In Hong Kong, healthcare capacity shortage stems from a variety of reasons, including but not limited to the insufficient or unmatched funding, shortage of healthcare practitioners, and the shortage of physical space. In such a densely-populated and crowded environment like Hong Kong, the efficient use of space in healthcare facilities is of particular importance.

Due to the geographically-remote nature of some hospitals in Hong Kong, staff quarters are set up in these sites for medical, nursing, and healthcare assistants so that they do not need to travel back and forth between their residence and the hospitals. These facilities are for on-call purposes for medical staff, and also serve as temporary short stay dormitory units (for 8 to 10 h) for nursing and healthcare assistant colleagues before and/or after their duty hours. These staff quarters are not only there for staff retention purposes, but also they serve a critical role in ensuring around the clock quality clinical service could be provided.

Efficient management of staff quarters is very important in ensuring precious quarters space is utilized effectively. In addition, it is vital for staff quarters to devise a convenient workflow for staff to reserve, revise, and delete their reservations. In this paper, we discuss an application of web/database programming and mathematical modeling to enhance the management of Nurses’ Quarters in Queen Mary Hospital (QMH), a tertiary/quaternary referral and teaching hospital, in Hong Kong.

QMH is one of the largest acute regional hospitals in Hong Kong with more than 1400 inpatient beds. It is located in the Pokfulam district, about 20 min of drive-time away from the Hong Kong city centre, mainly serving the acute care needs for the Central and Western District. Apart from offering secondary care for its catchment population, QMH also provides specialized services for the entire population in Hong Kong, while at the same time serving as the teaching hospital for the University of Hong Kong Li Ka Shing Faculty of Medicine.

QMH’s location is comparatively remote from residential areas, and the transportation means to and from the hospital is relatively inconvenient. Hence, it is very important for QMH to have an effectively and efficiently-run staff quarter. QMH’s doctors’ quarter is located separately with the quarter for nurses and healthcare assistants. The way that the two types of quarters are managed was also different. For the doctors’ quarters (called locally as “Housemen Quarters”), rooms are divided up among different specialties and each specialty would handle the booking and management of its own set of rooms independently. On the other hand, the quarter for nurses and healthcare assistants, called Nurses’ Quarters in QMH, is managed centrally by the hospital. This paper focuses on the Nurses’ Quarters, and details on its management and booking mechanisms are discussed thoroughly below.

The Nurses’ Quarters in QMH are located in two separate buildings, Nurses’ Quarters A (NSQA) and Nurses’ Quarters B (NSQB), in the hospital complex. Fig. 1 shows a high-level map of the QMH campus. Between these two buildings, a total of 66 rooms and 264 beds are offered for reservation. Fig. 2 illustrates the capacity and the general layout of NSQA and NSQB.

Most rooms are composed of 3–4 beds. The rooms are pre-divided by major user groups: female nursing officers, female registered nurse, female healthcare assistants, male nursing officers/registered nurses and male healthcare assistants. Three types of shifts exist for these colleagues, namely the morning shift (AM), the afternoon shift (PM), and the overnight shift (Night).

For colleagues to rest between shifts, each room’s usage was divided into the following 3 corresponding time segments (Table 1): AM-Night (AFTERNOON: 14:30–20:30), PM–AM (OVERNIGHT: 21:00–06:45), Sleeping Day (MORNING: 06:45–14:00), where the exact timings might vary slightly for nurses and healthcare assistants, due to their slightly-different duty patterns. Time periods of 14:00 to 14:30 and 20:30 to 21:00 were purposely left idle for buffering purposes. Each user is allowed to make one AFTERNOON/OVERNIGHT/MORNING booking, or an AFTERNOON + MORNING booking per day. For instance, colleagues with an AM shift following a PM shift the day before would be reserving a room for the OVERNIGHT timeslot, utilizing a room from 21:00 to 06:45. Conversely, colleagues with a Night shift could reserve an AFTERNOON room together with a MORNING room on the next day, so that he/she could stay in the quarters before and after his/her duty hours. Each room is restricted to be used as either a OVERNIGHT room or a AFTERNOON/MORNING room each day, as adequate cleansing time has to be allowed for each room (in other words, no room could be used continuously for three consecutive timeslots). All 1900 nurses and 1000 healthcare assistants in QMH are eligible to reserve the Nurses’ Quarters.

According to the prevailing workflow, nurses and healthcare assistants needed to visit the Nurses’ Quarters in person for reservation. After gathering all reservations for a given day D, staff in Nurses’ Quarters would manually assign bookings into rooms and beds on day D-2, following pre-existing business rules. These business rules included: (1) users were to be allocated to the correct room type by gender and rank, (2) rooms were to be filled up before moving on to the next room, and (3) descending room assignment priority with higher floor levels (e.g. rooms on G/F would need to be filled first, before rooms on 1/F), as users had historically preferred the convenience of staying closer to the main entrance at G/F. Special user requests also existed. For example, users might request to be placed on a specific floor, in a specific room, or even at a specific bed. In addition, some users might wish to be co-located with other users, while some may specify to not be allocated to the same room with specific colleagues. These special requests were in the subjective discretion of Nurses’ Quarters and would sometimes be honored if capacity allowed. The resulting room/bed allocations would be posted outside of the Nurses’ Quarters on day D-2, so that users with reservations could look up the allocation results anytime from D-2 and on.

This workflow posed a couple of major operational challenges for the management of the Nurses’ Quarters. First, the booking procedure was highly inconvenient for users. Not only they needed to travel to the Nurses’ Quarters in person for booking, they would also need to do the same for reservation revision or deletion. This in turn not only caused no-shows, but also encouraged users to just make same-day reservations. This was very undesirable for Nurses’ Quarters, due to the difficulty in turning away users when capacity is strained. Although this has not been a major issue in QMH, as capacity has been adequate for most of the time, two significant changes in the near future will severely impact the supply and demand of Nurses’ Quarters. Firstly, the number of nurses will rise significantly in the coming years, with the planned increase in graduates from the nursing schools in Hong Kong. Secondly, QMH will undergo a major redevelopment in the next 10 years, where part of the Nurses’ Quarters might not be available to serve as staff quarters for a significant amount of time. With such anticipated changes that will introduce severe capacity problems to QMH’s quarter services, there was a critical need to devise an effective and convenient booking mechanism for users to encourage advance bookings. A web-based electronic booking system would serve the purpose, so that users’ booking procedure is streamlined, i.e. all bookings, changes, and deletions could be made online. With such a system, users will be encouraged to make advance reservations, and be ready in advance in case they are not allocated a room/bed in the future.

The other major operational challenge was caused by the need to manually allocate users to rooms/beds. This process was highly resource-consuming: it took one Nurses’ Quarter colleague two hours each day so that a feasible bed allocation, one that satisfies all Nurses’ Quarter- and user-defined business rules, could be developed. This manual bed allocation exercise was also error-prone, as it was always difficult for Nurses’ Quarters colleagues to correctly implement the business rules described above. The rules often competed with each other by nature (e.g. room specification and rule about sequential assignment on rooms), and it was usually up to the on-duty Nurses’ Quarters colleague to determine the relatively priority of the rules, and whether all rules should be applied for all users and rooms.

More importantly, the manual process has no room for additional business rules that are more complex in nature. For example, it was very difficult to allocate users of the same ward in the same room while keeping the number of opened rooms to a minimum, despite the general support of this allocation methodology among hospital management and frontline staff. Another example is the implementation of booking priority based on place of residence, where higher priorities are given to users who live farther away from the hospital campus.

With capacity pressure mounting due to the aforementioned changes, it was necessary for Nurses’ Quarters to implement additional allocation rules to ensure that the rooms are optimally utilized. It was also important for Nurses’ Quarters to implement a fair and transparent room assignment methodology. As such, a mathematical optimization model was proposed to be set up for the room assignment. With this automated tool in hand, the resulting room assignments will satisfy all the agreed business rules, and that the room assignment will also be optimized according to the objectives laid out by quarter management.

A lot of research is available in the literature with regard to the application of assignment problems in healthcare facilities, mostly in the area of operating theater scheduling problems  [1], [2], [3], [4], patient–staff-bed assignment problems  [5], [6], [7], [8], and strategic system-level resource allocation problems  [9], [10], [11]. Additionally, there are extensive research in the literature on the room assignment problems in hotels and hostels in the area of yield management  [12], [13], [14]. However, we cannot find any related research conducted for staff quarter in healthcare facilities. In addition, literature on the design and construction of housing quarter in healthcare facilities is also scarce. The only piece of extensive literature on this topic was written by Adams, illustrating the design elements of a nurses’ residence at Royal Victoria Hospital in Montreal, Quebec, Canada  [15] from a historical architectural perspective. In this paper, we discuss how automated and optimized room assignments was implemented through an application of a mixed integer programming (MIP), and how it is integrated with a newly-designed electronic booking system to facilitate better booking workflow and enhance the overall efficiency of the quarter services in QMH.