Marianist Hospital of Dayton (MHD)

Background.  As you know, your small group was established several years ago to support the management team of Marianist Hospital of Dayton.  The group has been used for numerous special projects and ad-hoc problem solving and data gathering efforts.  It is an honor for young, ‘up and coming’ professionals to be assigned to this group; the experience gives them broad exposure to hospital management issues and to key executives.  The management team sometimes refer to you as their issue analysis team.  However, the official name of your organization is the AIG Team (your motto is Analysis leads to Insights leads to Good decisions).

The Issue.  Mary Dana, the President of Marianist Hospital of Dayton, has been thinking about hospital staffing.  She was a manager not too many years ago and knows that the emergency department (ED) managers have a difficult job in scheduling full time and part time staff (nurses) to meet the variable patient demand that occurs over the operating hours: 24 hours each day.  She knows first hand that it is impossible to exactly match the patient demand because of three factors: (i) The hospital cannot schedule its staff for either unreasonably short or long work periods, (ii) There are significant hour by hour variations in patients arriving, and (iii)There is also random variation from one day/ week to another in patient demand for a particular hour.  Some managers tend to overstaff resulting in significant parts of most days with idle and demotivated staff and extra operating costs.  Other managers tend to under staff leading to at times harried employees and, in some cases, angry patients (maybe lost customers)

The President’s Request.  President Dana has requested that your group conduct a study of the ED nurse-scheduling problem.  She says that her hope is that you are able to recommend an approach that ED managers can use to help them develop their daily nurse schedules.  By ‘approach,’ she says she means a step-by-step, data-based procedure or a specific set of rules or perhaps specific mathematical relationships that managers can use.  She has indicated that, perhaps, your approach can be implemented with software (such as Excel that all our managers have access to) and that an ED manager would be able to easily input data and obtain a recommended schedule.  [Such a system is sometimes called a Decision Support System.]  You are asked to use some recent typical data that have been gathered from our ED to demonstrate any approach you develop.

Goal Statement.  President Dana has identified the tentative statement of the goal for your project as follows:  to develop a way for our ED managers to be able to construct low cost nurse schedules that meet our patient-driven nurse requirements in a manner that conforms to our hospital personnel policies.

Patient Demand.  The hospital has gathered data from eight months of recent operation of our ED.  The data are available to you on our web site.  The data are from days that the managers think are very similar (Tuesday through Thursday) and are organized based on the 24 hours of ED operation each day.  Data values are the numbers of patients arriving at the ED each hour for some medical problem.  The data for each hour have been sorted from low to high. Use these data to “demonstrate” a one-day nurse schedule using the approach you develop.

Patient Service Level.  We set our minimum nurse requirement for each hour focused on two measures of patient demand:  the estimated average demand for an hour and an estimated high value of demand that may occur at times.  (1) For the average patient demand, our target for a minimum level of patient service is one nurse for every five patients.  (2) For high patient demand that occurs sometimes, we know that if the patient/nurse ratio gets above eight patients for each nurse for an hour, our ED operations become difficult.  We want to limit this occurrence such that its likelihood is only about 5% — for each hour.  Another way to state this requirement is that we want an 8:1 patient to nurse staffing ratio for the estimated 95th percentile of patients each hour.  Note that we round to whole numbers of required nurses per hour when doing this calculation, i.e. round up or down to the nearest integer number of nurses.  We look at both criteria – # of nurses to achieve 5:1 for the average (# rounded, up or down) and # of nurses to achieve 8:1 for the 95%tile (this # also rounded) and, if different, we choose the higher value to set each hour’s minimum nurse requirement.


Desired Study Output.  With the data set provided, if you can develop and demonstrate an effective approach to nurse scheduling one typical day, then hopefully we can use your approach to support scheduling every day.  The ED manager would (1) gather hourly data on their actual or estimated patient demand, (2) use your scheduling aid to set a nurse schedule for each day or groups of similar days, and (3) regularly reassess demand and use the scheduling aid to adjust nurse staffing.  Note, for this demonstration, just show one day’s schedule and don’t worry about the interface from one day to another.  We’ll do that after your study.


Personnel Policies, Costs, and a Possible Change.  The President told your group that you must gather all the specific hospital personnel policies that apply and said that these will not change in the near term.  The list of personnel policies is one of the first pieces of information gathered and is found in Table 1.  This table includes at the bottom one policy change possibility that is being considered. You also obtained the current average staff costs as shown in Table 2.

Analysis Charge.  In summary, your task is to study this scheduling problem and prepare a business memo for President Dana and for the operations manager. The due date is … (date and time of the 5th week live session).  Use the analysis memo format that MHD uses for reporting on analysis projects.  Your memo plus supplements should be complete: these documents will constitute the record of our work on this issue for the future.  Make sure you answer the following business questions:

  • Are there insights from the recent ED patient arrival data?
    1. Are there some good ways to show the ED patient demand we just gathered that might provide insights for the assignment of nurses to our shifts for days like these?
    2. What insights would you offer?
  • Is there an effective approach for our ED nurse scheduling problem?
    1. If yes, explain it and describe how it might work with our ED manager?
    2. If yes, demonstrate what an ED one-day schedule would look like for a T, W, or TH (if the operational data recently collected continues to be representative of these days) and what is the overall nurse staffing cost for the day? Show using our MHD ED Nurse Schedule Template. Note, just show one day & ignore interfaces between days.

[As seen in this template, we use a graphical approach to view schedules with 24 work hours on the horizontal axis and horizontal bars above the axis showing each shift of FT nurses (with numbers assigned) and the 3- and 4-hour work shifts for the PT nurses (with numbers assigned.)  Below the horizontal axis, we also always show the PT/FT ratio for each hour & for the whole day.  The contact person can show you this schedule template.]

  • Would the change to current personnel policies that is been identified (Table 1) lead to significantly improved scheduling for days like those associated with the sample data?
    1. Use your “tool” to demonstrate a nurse schedule for the possible change.
    2. Include discussion of the pros and cons—from your team’s perspective—of such a change to the hospital personnel policies.
    3. Show the results of your analysis on this question in one or more comparative tables.
  • Are there any additional insights or recommendations from your analysis?

Your Contact Person.  As you develop your approach, keep in close contact with Jim Dunne one of the hospital’s experienced managers (has been an ED manager).

[Note that I have seen before that President Dana can be very impatient with wasted efforts.  I know that last year one group had a bad experience.  In one of the group’s early studies, the group thought they had some great ideas and results.  Unfortunately, they were “off the mark” in terms of what the key managers had asked them to address.  Some people almost lost their jobs over that incident.  You do not want to develop a study that misses or misunderstands any of the key issues or questions here.  Your job is to provide your best answers to the president’s questions.  Use your contact person!]

The President said as she left the meeting, “Have the analysis team contact Jim at any time since they may need clarifications and further discussion about this problem and their project work.” 


  1. Part Time (PT) Proportions.  Since part time nurses are generally not as well trained or current (especially with administrative procedures) as full timers, for any day, the part time nurse hours are limited to a maximum of 33% of the day’s total nurse hours.  Another way to state this is that a day’s PT/FT ratio (in hours) must be equal to or less than 0.5. In addition to the whole day, we also apply this ratio requirement to each of what we believe are the six most critical hours:  the two hours between 11 a.m. and 1 p.m. and the four hours between 8 p.m. and midnight. [This requirement may be expressed in the form of a linear inequality as follows:  PT – 0.5*FT <= zero.]
  2. Full Time (FT) Employees & Shifts.  Full time employees work for 7 hours (with a 1 hour dinner break) and thus there are eight hours between the start and end time.  A full timer’s productive (paid) time is 35 hours per week.  There are three full time shifts: FT1 starting at 6 a.m., FT2 starting at 2 p.m., and FT3 starting at 10 p.m.  Our policy is that we have at least three FT nurses assigned to each of the first two shifts and at least one FT nurse assigned to the third FT shift.  All full time nurses take a scheduled meal break after 4 hours of their shift.
  3. Part Time Hours.  Part timers work for either 3 or 4 hours a day and are not scheduled a meal break.
  4. PT Shift Start Times.  There are eight possible starts for 3-hour PT shifts with the first beginning at midnight and six possible starts for 4-hour PT shifts with the first beginning also at midnight.
  5. *Possible Change to Policies.  MHD has been thinking about our current policies that, if altered, may allow more efficient nurse scheduling.  This change under consideration includes the following three elements: (1) Revise the FT shift start times to be more consistent with patient demand patterns (make the FT shift start times 8AM, 4PM, and midnight). (2) Stagger FT meal hours (rather than all meals taken at the same time) to reduce the negative impact of the absence of all of a shift’s FT nurses during the same hour.  For each FT shift, there would be three meal times – after 3 hours, after 4 hours, and after 5 hours. Note that, in effect, we are establishing two more FT shifts for each shift start time – a total of 9 FT shifts.  We would keep the FT minimums for each of the three shift start times.  (3) Alter the PT/FT ratio requirements:  maintain the “ratio <= 0.5” for the whole day and the four hours from 8 p.m. to midnight but remove the requirement for the two hours between 11 a.m. and 1 p.m.

    Make your order right away

    Confidentiality and privacy guaranteed

    satisfaction guaranteed