By Kristina A. Krail

Resolving complex resource allocation quandaries-such as configuring the nursing department with the right number/mix of staff to meet variable patient demand-requires a robust, mathematically rigorous approach known as operations research, a systems engineering tool.

At a Glance

Background: Following the lead of other industries, progressive healthcare organizations are enlisting the help of systems engineers and operations researchers to pinpoint solutions to complex and costly problems, using mathematical and computer-based approaches.

Results: In this case study, a medical-surgical division reduces annual nursing labor costs by $583,297, or 14.7 percent, using operations research approaches. (See also a related article.)

Action steps:  

  • Identify a complex problem, such as staffing/scheduling, patient flow, or regional planning.
  • Determine how to partner with operation researchers, systems engineers, academics, or engineering students on the problem.

For decades, hospitals have struggled to figure out how to have a proper number of human resources available and deployed to appropriately care for patients. Today, hospital revenue architecture allows for only minuscule margins at best, and the professional nurse shortage necessitates the most efficient use of every single registered nurse (RN).

There are quality implications as well: There is ample evidence that adequate nurse staffing and balanced workloads are central to achieving good patient outcomes (Unruh, L., "Nurse Staffing and Patient, Nurse and Financial Outcomes," American Journal of Nursing, January 2008, vol. 108, no. 1, pp 62-72).

Over the years, there have been incremental improvements in nurse staffing strategies, such as the introduction of alternative shifts, creative delivery models, and the modest use of per diems. But despite the application of automated scheduling and/or acuity systems, which allow nursing departments to know how many staff are required at a given moment, there are no systems to help nurse leaders set up the right staffing configurations-in the first place-to ensure that those people are available when and where they are needed.

To get staffing right on a planning level (budgeting, staff distribution, recruitment requirements) as well as on a tactical level (daily staffing and deployment), health care needs to look to other industries-manufacturing, transportation, the military-that have solved resource allocation problems using the applied science of operations research.

What Exactly Is Operations Research?

Operations research is the systematic use of analytical and quantitative methodology to assess the overall implications of various alternative courses of action. The term is something of a misnomer, for operations research is more of a planning than an operational tool and provides practical, rather than theoretical, output for solving real problems.

As shown in the exhibit below, operations research uses a similar problem-solving approach as the Plan-Do-Check-Act process improvement approach. However, operations researchers use sophisticated, computer-based mathematical models to arrive at solutions. Operations researchers use model building and mathematical manipulation (e.g., linear and nonlinear programming, queuing theory, and gaming theory) to clarify the various options available, estimate the expected outcome of each, and evaluate these in terms of the goals identified-often goals that address the allocation of scarce resources and risk-benefit trade-offs.


Improving Nurse Staffing

"If you really want to figure out how many nurses you need based on patient demand, you have to use operations research-everything else would just be guessing," according to Eugene Litvak, PhD, professor of operations management, Health Policy Institute, Boston University.

Operations research can help hospitals deal proactively with variation in the staffing equation-both on the demand side (number of patients and acuity) and on the supply side (the right amount of staff of the right category)-and reduce the need to secure, reassess, and deploy nursing personnel on a daily basis.

How exactly might a hospital's nurse staffing process change using operations research approaches? As shown in the exhibit below, the staffing process is improved through predictive modeling and the sophisticated analytics of operations research.


Annual resource requirements are calculated in an exacting way and translated into individual unit position rosters, or optimized position controls, that tell nursing and finance leaders how many fixed FTEs and variable FTEs (i.e., agency, overtime, and float pool) are needed to be available for specified times on specified days on specified units. The beauty of having the right composition of positions assigned to each unit is that daily schedules simply fall into place.

Operations Research in Action

The following example uses data associated with a real 87-bed three-unit, medical-surgical division. Although the division was budgeted at an annual 74 percent occupancy, the average daily census varied significantly between the units and fluctuated by day and season. While the average caregiver hours/patient day standard was 6.0 to 6.2 hours per patient day (HPPD), workload levels also varied significantly due to the organization's inability to respond in a timely way to all the demand variation.

To mathematically solve this problem, nursing and finance gathered key data that represented the hospital's multiple objectives, thousands of variables, and numerous constraints, including:

  • Census information by shift and unit
  • Hours worked and paid for each individual employee
  • Personnel policy requirements
  • Staffing standards

Analysts then built and modeled unit-based plans in the form of optimized rosters or position control documents. These plans established:

  • The right mix of full-timers, part-timers, and extra hours (i.e., agency overtime and float pool hours)
  • The right mix of RNs, licensed practical nurses (LPNs), and certified nursing assistants (CNAs)
  • The right distribution across shifts
  • The right number of staff
  • The rotation to weekends and certain days of the week

Unit-assigned staff formed the core work group for each cost center and constituted a base schedule that would meet that particular unit's patient needs the majority of the time. However, a large part of the reconfiguration solution was a calculated shift to additional variable labor categories, in the form of appropriately sized/composed RN and nursing assistant float pools, as well as appropriately sized agency and overtime budgets.

As shown in the two exhibits below, the medical-surgical division was able to save more than $500,000 a year by reducing fixed labor costs while increasing variable labor costs.



Determining the Right Configurations

It may come as no surprise to experienced finance and nursing leaders that creating an appropriately sized and composed fixed and variable labor supply allows hospitals to respond efficiently to a variable patient demand. However, the trick is in properly configuring this labor supply. Operations research-via sophisticated mathematical calculations and analytics-can best answer who, when, where, and how much-down to the fraction of each FTE.

Kristina Krail, RN, MPH, NEA-BC, FACHE, is an independent healthcare consultant in nursing labor resource management (

Publication Date: Thursday, June 17, 2010