What we can learn about scheduling from the airline and package-delivery industries

Your drive to work begins as usual—with your thoughts racing. You think about the patients you’ve been caring for, the last-minute instructions you’ll give to help prepare a patient for discharge, creative interventions to ease the intractable pain of another patient on your unit.

Underlying your thoughts is a sense of dread: For yet another busy shift, will your unit lack the nursing resources it needs? Will yet another day start with a frantic call from the charge nurse to the staffing office seeking additional nurses to meet unit demands?

Traditional approaches for addressing the challenges of clinical staffing and scheduling aren’t always effective in today’s complex healthcare environment. Many staffing offices are chaotic, budgets frequently are overrun, and staffing levels too often fail to match demands. More state legislatures are mandating specific nurse staffing levels, and many nurses are dissatisfied with their work schedules.

Mathematical formulations typically used to create hospital personnel budgets and staffing patterns originated in a more stable healthcare era when lengths of stay were counted in days, not hours. But budgeting staff based on an average daily census (often measured at midnight) doesn’t reflect the fast pace of admissions and discharges throughout the day. These days, a busy medical-surgical unit may turn over 50% to 60% of its census on a typical day shift. How can managers create schedules and accurately configure staffing in this climate?

New technologies developed over the past few years aim to promote more effective scheduling and staffing. Computerized schedules, which began as rudimentary spreadsheet tools, have evolved into sophisticated, algorithmically driven applications that allow staff to self-schedule from home, view and offer availability for extra shifts, and modify staffing requirements based on a continual census feed. These automated tools offer significant benefits: Managers spend less time scheduling and searching for resources; staff competencies and credentials are documented in a central location and can be used to drive the schedule; and, just as important, staff can participate in the process.

Understanding optimization modeling

So why do scheduling problems still plague the healthcare industry, when many other industries with complex scheduling needs have figured out how to manage them? Consider, for instance, the airline industry, which is able to coordinate flights, maintenance and other crews, and equipment staging across multiple time zones and weather conditions—in a manner that maximizes revenue. Another example is the package-delivery industry, which must schedule trucks, routes, and pickup times to service customers.

These industries use logistics science and a form of mathematical modeling called optimization to solve their scheduling problems. Logistics refers to management of the flow of goods, information, and other resources (including people) between the point of origin and the point of consumption in a way that meets all parties’ requirements. Two different types of logistics exist. One optimizes the steady flow of materials through a network of transport links and storage nodes. The other coordinates a sequence of resources, such as staffing and scheduling clinical resources.

How optimization modeling works

To mathematically represent a staffing-related business situation, the optimization model should include:

  • business objectives, such as minimizing staffing costs, maximizing staff preferences, and ensuring adequate coverage
  • decision variables, for instance, skill mix, demand fluctuation, and cost differences
  • business constraints, including staff availability and work rules. (See Key qualitative indicators for configuring the workforce by clicking the PDF icon above.)

Step 1: Creating a mathematical model

In optimization modeling, the real-world problem is defined as a set of mathematical equations. All inputs, qualitative requirements, assumptions, constraints, and the objective of the outcome (solution) must be defined. Say, for example, a unit manager wants to create an optimal schedule for a given period.

  • Inputs include the number of nurses required per shift (demand), all available nurses (supply), and nurses’ credentials, vacations, weekend rotations, weekday preferences.
  • The qualitative requirement is to meet the demand. In the model, this requirement can be represented mathematically and becomes part of the optimal solution.
  • Constraints may include the need to schedule every nurse to his or her required full-time equivalency level, the assurance that nurses aren’t scheduled on their off days, and the need to meet various work rules (such as the maximum number of consecutive days a nurse can be scheduled).
  • The objective is to minimize the number of holes in the schedule and maximize nurse preferences. (See Scheduling optimization model by clicking the PDF icon above.)

Step 2: Solving the model

To solve the model created in step 1, staffing and scheduling personnel use advanced optimization algorithms to produce optimal business objectives with stated outcomes, given the identified constraints. In this case, the objective is a schedule that provides the best coverage at the lowest cost while meeting all work rules and staff nurses’ preferences.

Step 3: Interpreting the solution

The nurse leader interprets the solution provided by the optimization algorithm. Once the mathematical model is created, alternate scenarios can be created easily by changing a constraint (such as the maximum number of days a nurse can be scheduled) or a business objective.

From a zero-sum game to win-win

Optimization moves decision-making from a “what-if” to a “what’s-best” solution. An example of an optimal solution is producing a cost-effective (lowest-cost) schedule while simultaneously ensuring the best unit coverage by the right nurse with the right credentials.

For human capital-resource planning, leaders tend to think about likely solutions in zero-sum terms. In other words, a solution that meets financial goals might mean sacrificing staff satisfaction, whereas achieving staff satisfaction might mean forfeiting financial targets. But optimization modeling can create a win-win solution even for complex problems. Although it requires leaders to reconceptualize the planning and deployment process as a logistics problem, it allows them to use innovative solutions that other industries have relied on for years to revolutionize processes and improve business results.

More precise modeling of staffing to actual demand helps healthcare organizations meet staffing and scheduling challenges. These organizations have seen improvements—for instance, having resources available when required, reducing staffing costs, and significantly decreasing float time for nurses. Optimization modeling also cuts in half the amount of time spent on the scheduling process.

Although optimization modeling tools and techniques haven’t been widely used in health care, they’re not beyond our reach. Nurse leaders are skilled at modeling the processes of care, such as patient throughput, discharge, medication administration, and patient identification. Such modeling is a requisite step for identifying and quantifying the constraints and variables in any optimization problem.

Selected references

Fitzpatrick TA, Brooks BA. The nurse leader as logistician: optimizing human capital. J Nurs Adm. 2010;40(2):69-74.

Storfjell JL. Fitzpatrick TA. Financial management. In: Huber DL, ed. Leadership and Nursing Care Management. St. Louis, MO: Saunders; 2013: 665-84.

Therese A. Fitzpatrick is an assistant professor in the Department of Health Systems Science at the College of Nursing at the University of Illinois-Chicago.

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