Final Exam

In each issue of Wharton Magazine, we’ll test your knowledge with a question straight from an actual Wharton exam, crafted by one of the School’s esteemed faculty members. Submit the correct answer and you’ll be entered into our drawing for a fabulous prize—tuition-free attendance at a Wharton Executive Education program.

This Final Exam challenge comes from Noah Gans, the Joel S. Ehrenkranz Family Professor of Operations and Information Management. Good luck!

The Basics:

The U.S. Board of Immigration Appeals in Philadelphia has a backlog of almost 5,000 cases waiting to be processed. Each of five attorneys is assigned cases as they arrive. Figure 1 shows the number of cases assigned per month to each attorney (x-axis), as well as the average number of cases in each attorney’s backlog (y-axis).

The Question:

Assume that the arrival rate of cases to the board is fairly constant over time and that the success rate of appeals is the same across attorneys. Based on the data shown in Figure 1, if you had an immigration appeal pending before the court and wanted to minimize the expected delay before the case is heard, to which of the five attorneys would you hope it would be assigned? Why?

The Answer:

We can use the data from Figure 1 and Little’s Law (L = l·W, or I = R·T) to calculate each attorney’s average delay:

 

Attorney

1

2

3

4

5

l = average rate at which cases assigned

110

115

120

130

140

L = average backlog

990

920

1020

949

980

W = L /l = average delay

9

8

8.5

7.3

7

 

Based on these data, Attorney 5 has the shortest average time per case.  You would want Attorney 5.

Noah Gans thanks Professor Avishai Mandelbaum of the Technion, whose work motivated the exam question.

The Winner:

Winner of the fall issue Final Exam challenge: John L. Jackson, W’78


  • Aldo Buono C70

    It is too late to submit my answer, so I will do it here. 

    You want your case to be assigned to the attorney who has the highest average case resolution rate.  How do you figure that??

    (Number of cases assigned per month X 12) Minus (Average number of cases in each attorney’s backlog) Equals (Average Resolution Rate)

    Average Resolution  Rate

    Attorney 1 = 330
    Attorney 2 = 460
    Attorney 3 = 420
    Attorney 4 = 611
    Attorney 5 = 700

    Answer: Attorney 5, with a resolution rate more than double Attorney 1 even though Attorney 1 receives the least number of cases per month. 

    Submitted by: Aldo Buono, C70

  • Matthew Brodsky

    For future reference, the best way to submit a response for Final Exam is by email, at: 
    finalexam@whartonmagazine.com

  • Anonymous, w87

    This analysis presumes that each attorney’s cases get resolved at a rate on average equal to the rate at which new cases are assigned, thus keeping the ‘backlog’ roughly constant over time.  However, the more telling aspect of determining which attorney would move through their backlog the fastest would hinge on each attorney’s rate of resolving their cases.  If attorney 1 resolved 200 cases per month, while attorney 5 only resolved 100 cases per month, on average, it would stand to reason that attorney 1 would get to a new case a lot faster than attorney 5, despite the fact that attorney 1 has the highest ‘average delay’ based on the incoming case rate only, as shown in the chart.  However, it is the ‘net resolution rate’ that is most critical, or the rate at which the backlog is being addressed, that will determine how much time it takes for a new case to be heard.  This analysis assumes a constant backlog, or a resolution rate equal to the new case rate, which ignores an important variable of how quickly each attorney works through their cases.  The backlogs shown here are a snapshot in time, but knowing whether each attorney’s backlog is growing or shrinking, and at what rate, would make a big difference in determining the answer to the question.

  • w95 again

    Where did Aldo come up with multiplying the number of assigned cases by 12.  I realize that there are 12 months in a year, but I did not read anything in the question that directly or indirectly addresses this time period assumption.   

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