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Operations Research for Health Care

Robust combined operating room planning and personnel scheduling under uncertainty

Abstract

Providing timely access to costly surgical services in a manner that balances needs of multiple stakeholders (patients, staff, administrators) is made even more challenging by inherent uncertainty. Decisions about clinician scheduling, shift preferences, operating room planning, and patient assignment also often are decentralized or made separately. We develop a robust optimization model that combines staffing and scheduling decisions to minimize the impact of foreseeable variation in surgery durations, staff availability, and urgent or emergency arrivals. Model performance is tested with data from a major academic medical center, resulting in improved service level (% patients served), overtime, utilization, and shift preferences. Although robustness to staffing, duration, and urgent or emergency uncertainty increases operating costs by 6% on average, overtime is reduced by 68% while utilization decreases by only 6%. The number of necessary schedule adjustments on the day of surgery also is reduced by 13% on average in the robust model compared to the nominal model.

Introduction

Hospital expenses are affected significantly by the cost of operating rooms (ORs), accounting for approximately 30% of the United State's $2.7 trillion healthcare costs in 2011 [1]. ORs are highly complex systems comprised of scarce personnel and physical resources, various specialties, planned and unplanned operations, and time limitations for room turnover. Timely care for acute patients is a growing problem throughout the U.S. due to increased volumes of moderate to complex care patients and a shortage of surgeons [2]. If required resources for a scheduled procedure are unavailable, often due to coordination challenges of multiple staff and system variability (e.g. case durations), procedures either are delayed or canceled. This is very costly with estimates of OR time ranging from $22 to 133 per minute [3].

This paper addresses two important needs: (1) coordinating decision-making of key operating room staffing, scheduling, and resource allocation decisions and (2) doing so in a manner that is robust to uncertain case durations and changes in surgeon availability and case mix realizations. Effective long-term planning and ongoing scheduling of operating room resources both are critical so that all needs are sufficiently met. Planning refers to assigning OR time to surgical departments, a process that typically occurs on an annual or quarterly basis. Scheduling is the process of then assigning clinicians to specific shifts or blocks, which typically is done roughly four weeks prior to surgery and determines assignments for four to six week horizons. One to five days in advance, patients then are scheduled to specific rooms at certain times. ORs typically use either block or open scheduling processes. In the former, large blocks of time (e.g. half of a day) are reserved for a specific surgeon or practice, whereas in the latter multiple surgeons may book cases in any room at any open time, resulting in more flexibility but also greater complexity. Hence we consider block scheduling from here on out.

These problems are complex even when key data are assumed known and constant (e.g. patient volume, staff availability, and skill set). However, uncertainty in clinician availability across multiple disciplines makes it difficult to ensure that elective, urgent, and emergency patients can be accommodated. In addition, clinicians may experience excessive patient volume or be dissatisfied with assigned shifts, both of which increase individual workload and result in unsafe patient conditions and medical errors stemming from exhaustion and depression [4], [5]. Shift preference, legal, and fiscal needs also have to be met. Deviations in case durations, variable clinician and equipment availability, and delayed case starts all cause uncertainty in day-to-day OR environments. Late starts increase patient wait times, staff overtime, and may imbalance resource availability by time of day. OR schedules nonetheless need to be able to work reasonably well if cases are canceled or switched with others. Lastly, the number of patients needing each given specialty typically is not known in advance, especially for urgent and emergency patients.

Each professional discipline (e.g. surgeons, nurses, surgical technicians, and anesthetists) typically generates schedules separately for a specific time frame and relies on expert opinion and past data to hedge against surgery delays, overtime, and cancellations. However, this decentralized decision making often leads to sub-optimal resource allocations (e.g. nurse shift preferences cannot be accommodated because surgeon blocks predetermine when cases of a certain specialty are performed). Schedules with minimal overtime for every discipline cannot be ensured when block, surgeon, and nurse schedules are generated sequentially or separately.

We introduce a centralized robust optimization model that provides decision support for a wide range of resource allocations to OR planning and personnel scheduling under uncertainty. A key focus of our proposed model is to design personnel schedules that remain feasible even when deviations from planned schedules occur. Additionally, scheduling all aspects simultaneously ensures that the optimal solution offers the desired trade-off among stakeholders desires and that patient needs are met. The primary foci and contributions of this research thus are threefold:

1.

Combining the planning and scheduling problems across operating rooms, clinical personnel, and assignment of patients,

2.

Using robust optimization to incorporate uncertainty and changes in procedure durations, surgeon availability, and case mix, and

3.

Emphasizing clinician preferences and skill sets to allocate resources optimally.

We use these results to generate schedules that reduce patient wait times and increase access with only minimal cost trade-offs. In the next section we describe the problem context in greater detail and summarize relevant literature. Section 3 introduces a nominal optimization model (that excludes uncertainties), describes its robust adaptation to account for deviations from planned schedules, and compares their results. Section 4 identifies parameters for a case study in a large hospital OR and explores performance under different conditions. Sections 5 Discussion, 6 Conclusion conclude with general implications, limitations, insights, and future possible work.

Section snippets

Problem description and related work

The central problem addressed in this paper is the combined scheduling of multiple clinical disciplines under uncertainty. In addition, we consider the planning and assignment of patients to rooms and blocks because of their integral role in affecting personnel schedules. The objective is to generate schedules over a planning horizon that maximize the needs of all disciplines, while decreasing delays and operating costs. More specifically, the problem is to reduce patient wait time, minimize

Methodology

This section presents the model notation, a nominal mixed integer linear program (MILP) of the OR planning and scheduling problem, the corresponding robust formulation, and a comparison of model performance. The model includes the primary decision variables and scheduling rules. Blocks and shifts are scheduled taking clinician preferences into account, with elective patients scheduled to blocks according to specialty and the latest date that their surgery can occur. Urgent or emergent patients

Case study: Maine medical center

We tested the above model using data from Maine Medical Center (MMC) in Portland, ME, an academic medical center serving northern New England with 637 licensed beds, 27 ORs, and 18 surgical specialties. Input data used to parameterize the model are summarized in Table 6. A total of 143 surgeons currently operate on the main campus, 35% of whom perform 80% of all cases. The nurse and surgical technician rosters each consist of more than 70 individuals. Not all rooms contain the equipment

Discussion

Choosing a centralized approach to scheduling all operating room professional disciplines reduces the chance that the needs or preferences of one are unmet while also ensuring patients are scheduled in a timely manner. With increasing pressure from payers to consolidate services, moreover, some health systems will move towards one or two larger OR suites with 30 + rooms as opposed to several smaller-sized suites across their system. Schedules thus increasingly may need to be solved for

Conclusion

This paper developed a combined personnel planning and scheduling robust optimization model that produces high quality schedules even when several sources of uncertainty exist, in our case in surgery durations, personnel availability, and case volumes. Results also illustrate the value of centralized decision-making over the more traditional creation of personnel schedules within each professional discipline. Building on previous work that predominantly focused on single-discipline schedules or

Credit authorship contribution statement

Dominic J. Breuer: Conceptualization, Methodology, Software, Validation, Formal analysis, Writing - original draft, Visualization. Nadia Lahrichi: Conceptualization, Writing - review & edit-ing, Project administration. David E. Clark: Conceptualization, Data curation, Clinical expertise and insights, Writing - review & editing. James C. Benneyan: Supervision, Funding acquisition, Writing - review & editing, Visualization.

Acknowledgments

The authors thank Jordan Peck, PhD and Mohit Shukla, MS from Maine Health's Center for Performance Improvement and Diana Turi, MHA, Jonathan Bradstreet, CRNA, Christine Sheetz, RN and Susan Holloran, RN from Maine Medical Center's operating room team. This research was partially supported by a National Science Foundation (NSF), USA grant (IIP-10341990) although any views expressed herein are those of the authors and not necessarily the NSF.

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