Maximizing the efficiency of use of nurses under uncertain surgery durations: A case study
Introduction
The operating room scheduling problem has been the focus of increasing attention from operations researchers and management scientists during the last decades (Cardoen et al., 2010, Guerriero and Guido, 2011, May et al., 2011). However, the growth in this research area is mainly motivated by cost containment with respect to facilities such as operating rooms (ORs) and ward beds, and little effort is made to improve the efficiency and welfare of nursing staff. Nurses are among the most critical human resources in delivering surgical services. Because salaries of nurses account for nearly 37% of OR suite costs (National Health Services Survey in China, 2012), it is important for OR suites to minimize overtime and idle time of nurses. Moreover, scheduling of nurses plays a decisive role in ensuring on-time starts of surgeries, which is strongly related to the service quality perceived by patients as well as medical staff (Denton, Viapiano, & Vogl, 2007).
In this paper, we focus on the nurse scheduling problem of assigning a set of nurses to surgeries scheduled on each workday, functioning in scrub and circulating roles. The nurse scheduling problem can be complicated because of the competing performance measures involved regarding multiple stakeholders (i.e., patients, surgeons, nurses). First, nurses should be used as efficiently as possible. The efficiency of use of nurses is maximized by minimizing both nurse overtime and idle time. Overtime stresses nurses and thus decreases the quality of care, while idleness causes waste (Maenhout and Vanhoucke, 2010, Welton, 2006). Second, due to significant uncertainty in surgery durations, scheduling of nurses highly affects on-time surgery starts. For example, consider a situation when a nurse is assigned to two non-overlapping surgeries in two ORs. If the former surgery finishes later than scheduled, the latter surgery could be delayed only because of the absence of the nurse. On-time surgery starts are important in practice since late starts increase the likelihood of overtime which results in higher direct surgery costs, patient and surgeon fatigue (Denton et al., 2010, Marcon et al., 2003). Given uncertain surgery durations, there is a trade-off between nurse efficiency and on-time surgery start performance: assigning nurses to surgeries in different ORs provides more flexibility for nurse scheduling and thus allows more efficient use of nurses. However, this may result in poor on-time surgery start performance as illustrated by the example above (see Section 2.1 for a graphic illustration of the trade-off).
To the best of our knowledge, most previous studies on OR scheduling only consider the aggregated capacity of nurses, and neglect the detailed scheduling of nurses for a workday (in which nurses are assigned to surgeries), which is a fundamental element of OR scheduling in practice. Consequently, OR suite performance measures such as nurse efficiency, on-time surgery start performance and especially their inherent trade-off has not been addressed. Sier, Tobin, and McGurk (1997) propose a simulated annealing approach to find feasible OR schedules according to predefined constraints, which consider availability of nurses and surgeons. Guinet and Chaabane (2003) propose an assignment model with nurse capacity constraint for assigning surgeries to ORs over a planning horizon. Jebali, Hadj Alouane, and Ladet (2006) also study the problem of assigning surgeries to ORs with the objective of improving OR utilization. The availabilities of nurses are considered. Pham and Klinkert (2008) treat the OR scheduling problem as a multi-mode job shop problem. A mode is defined as a possible choice of resource set that considers both personnel as well as facilities. Roland, Di Martinelly, Riane, and Pochet (2010) apply the resource constrained project scheduling model to formulate the OR scheduling problem. Several constraints regarding human resources’ availabilities and preferences are included in their model. Fei, Meskens, and Chu (2010) formulate the surgery assignment problem as a set partitioning problem, taking into account the maximal working hours of nursing staff. Marques, Captivo, and Vaz Pato (2011) develop an integer linear programming model for scheduling surgeries on a weekly time horizon with the objective of maximizing OR utilization. Nurses’ regular working hours are considered in the model.
The extreme importance of optimal use of nurses has been emphasized by several researchers. Beliën and Demeulemeester (2008) formulate the nurse rostering problem using a branch and price approach combined with different surgery workload patterns. He, Dexter, Macario, and Zenios (2012) propose a newsvendor framework to determine the optimal nurse staffing levels for an OR suite with different information sets: no information, information on surgery number, and information on surgery number and type. Altamirano et al. (2012) propose a particle swarm optimization algorithm to determine the shifts assignment of nurses (i.e., Day shift, Emergency day shift, Emergency night shift) at a French public hospital. Unfortunately, these studies fall into the category of tactical nurse rostering problem at medium term (1 or 2 weeks), in which collective agreement requirements such as legal regulations, personnel policies are the major concerns (Cheang, Li, Lim, & Rodrigues, 2003). In contrast, the nurse scheduling problem concerned in this paper lies at an operational level at short term (one workday), whose distinctive feature is the trade-off between nurse efficiency and on-time surgery start performance given uncertain surgery durations.
The goal of this paper is to develop a methodology for nurse scheduling under uncertain surgery durations. The primary contributions of this paper include: (1) a mixed integer programming model that explores the trade-off between the two competing performance criteria (i.e., nurse efficiency, on-time surgery start performance) with respect to nurses, patients and surgeons; (2) an explicit probability modeling of uncertain surgery durations that can be used for mastering on-time surgery start performance. Our work is based on a real world case study of an OR suite that frequently receives complaints about unbalanced nurses’ workload and poor on-time surgery start performance. By applying the present MIP model to the OR suite, significantly improved nurse efficiency can be achieved with good on-time surgery start performance. We also investigate the applicability of the MIP model in various problem settings.
The rest of the paper is organized as follows. In Section 2, we first illustrate the trade-off between nurse efficiency and on-time surgery start performance. Then we propose the probability modeling of uncertainty in surgery durations and the MIP formulation of nurse scheduling. Section 3 presents the case study of applying the MIP model to the OR suite of interest. The results of the case study are discussed in Section 4, followed by the conclusion in Section 5.
Section snippets
Trade-off between performance criteria
Due to significant uncertainty in surgery durations, nurse scheduling in practice is complicated by the trade-off between the performance criteria regarding nurses, patients and surgeons. In this paper, we focus on nurse efficiency in terms of overtime and idle time of nurses and on-time surgery start performance. The two performance measures are in conflict that can be illustrated by the following example: Consider a simple illustrative surgery schedule, which have 6 surgeries allocated in 2
Case study
The goal of the MIP model for nurse scheduling is to help increase nurse efficiency in terms of overtime and idle time, while mastering the risk of delay of surgeries. Thus, four performance criteria of the MIP model are considered: (1) overtime and idle time of nurses; (2) expected number of surgery delays; (3) expected surgery delay time; (4) number of nurses used.
Given a nurse schedule obtained by solving the MIP model, criteria (1) and (4) can be obtained directly, and criteria (2) and (3)
Nurse scheduling in the OR suite of interest
The nurse scheduling practice of the OR suite of interest is to staff each open OR with a number of nurses throughout the regularly scheduled workday (i.e., 8 h). This policy ensures on-time starts of surgeries (see Section 2.1), but results in significant overtime and idle time of nurses. During the period (between 1 August 2011 and 31 July 2012), 21.4 ± 4.1 (mean ± SD) nurses are used on each workday, and there are 3.3 ± 1.2 overtime and 7.3 ± 2.1 idle time (in h) of nurses per workday.
This
Conclusion
This paper tackles the nurse scheduling problem of assigning a set of nurses to surgeries scheduled on each workday in an OR suite, which plays a decisive role in using nurses efficiently while ensuring on-time starts of surgeries. Due to significant uncertainty in surgery durations, this problem is complicated by the competing performance criteria regarding different stakeholders (patients, surgeons, nurses). We first illustrate the trade-off between nurse efficiency (in terms of overtime and
References (31)
- et al.
A branch-and-price approach for integrating nurse and surgery scheduling
European Journal of Operational Research
(2008) - et al.
Operating room planning and scheduling: A literature review
European Journal of Operational Research
(2010) - et al.
Nurse rostering problems: A bibliographic survey
European Journal of Operational Research
(2003) - et al.
A planning and scheduling problem for an operating theatre using an open scheduling strategy
Computers & Industrial Engineering
(2010) - et al.
Operating theatre planning
International Journal of Production Economics
(2003) - et al.
Robust surgery loading
European Journal of Operational Research
(2008) - et al.
Operating rooms scheduling
International Journal of Production Economics
(2006) - et al.
The operating theatre planning by the follow-up of the risk of no realization
International Journal of Production Economics
(2003) - et al.
Surgical case scheduling as a generalized job shop scheduling problem
European Journal of Operational Research
(2008) - et al.
Scheduling an operating theatre under human resource constraints
Computers & Industrial Engineering
(2010)
Anesthesiology nurse scheduling using particle swarm optimization
International Journal of Computational Intelligence Systems
Optimal allocation of surgery blocks to operating rooms under uncertainty
Operations Research
Optimization of surgery sequencing and scheduling decisions under uncertainty
Health Care Management Science
Automatic updating of times remaining in surgical cases using Bayesian analysis of historical case duration data and “Instant Messaging” updates from anesthesia providers
Anesthesia & Analgesia
Which algorithm for scheduling add-on elective cases maximizes operating room utilization? Use of bin packing algorithms and fuzzy constraints in operating room management
Anesthesiology
Cited by (11)
A bi-objective integrated approach to building surgical teams and nurse schedule rosters to maximise surgical team affinities and minimise nurses' idle time
2017, International Journal of Production EconomicsCitation Excerpt :Whereas the first provides a pool of many solutions from which to choose, the second yields a smaller number of solutions that are closer to the decision-maker's preferences. Guo et al. (2014a) investigated the link between the uncertainty of surgery duration and OR nurses' idle time and overtime. In contrast to Mobasher et al. (2011), they modelled the daily assignment of nurses to surgical operations as a mixed-integer programming (MIP) problem and applied it to different surgery duration parameters.
A two-stage method to determine the allocation and scheduling of medical staff in uncertain environments
2016, Computers and Industrial EngineeringCitation Excerpt :Third, hospital managers should determine which medical staff member is going to work which shift(s). This is a staff scheduling issue (Defraeye & Van Nieuwenhuyse, 2016; Guo, Wu, Li, & Rong, 2014; Legrain, Bouarab, & Lahrichi, 2015; Van den Bergh, Beliën, De Bruecker, Demeulemeester, & De Boeck, 2013). For the hospital staff policy and staff allocation issues, most hospitals make their staff assignments to each department either when creating a new department or when considering reallocations.
Scheduling operating rooms with consideration of all resources, post anesthesia beds and emergency surgeries
2016, Computers and Industrial EngineeringNurse Rostering via Mixed-Integer Programming
2023, Advances in Transdisciplinary EngineeringQuantifying and enforcing robustness in staff rostering
2021, Journal of Scheduling