My-law is a recent start-up trying to cater to customers in search of legal services who are intimidated by the idea of talking to a lawyer or simply too lazy to enter a law office. Unlike traditional law firms, My-law allows for extensive interaction between lawyers and their customers via telephone and the Internet. This process is used in the upfront part of the customer interaction, largely consisting of answering some basic customer questions prior to entering a formal relationship.

Question

My-law is a recent start-up trying to cater to customers in search of legal services who are intimidated by the idea of talking to a lawyer or simply too lazy to enter a law office. Unlike traditional law firms, My-law allows for extensive interaction between lawyers and their customers via telephone and the Internet. This process is used in the upfront part of the customer interaction, largely consisting of answering some basic customer questions prior to entering a formal relationship.

In order to allow customers to interact with the firm's lawyers, customers are encouraged to send email to my-law. From there, the incoming emails are distributed to the lawyer who is currently "on call." Given the broad skills of the lawyers, each lawyer can respond to each incoming request.

E-mail arrive from 8am to 6pm at a rate of 10 email per hour (coefficient of variation for the arrivals is 1). At each moment in time, there is exactly one lawyer "on call," that is, sitting at his or her desk waiting for incoming emails. It takes the lawyer, on average, 5 minutes to write a response email.The standard deviation of this is 4 minutes.

1. What is the average time a customer has to wait before his/her call is answered by the on-call lawyer?

Would this be 25.5 minutes

2. When not responding to emails, the lawyer on call is encouraged to actively pursue cases that potentially could lead to large settlements. How much time can a My-law lawyer dedicate to this activity during an 10-hour shift (assume the lawyer can instantly switch between emails and work on a settlement)?

Would this be 100 minutes to pursue high value cases

To increase the responsiveness of the firm, the board of My-law proposes a new operating policy. Under the new policy, the standard deviation for responding would be 0.5 minutes. The average writing time would remain unchanged.

3. How would the amount of time a lawyer can dedicate to the search for large settlement cases change with this new operating policy?

I don't know where to start.

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3 answers
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Answer 1

Bot answered
1 year ago

1. To calculate the average waiting time for a customer, we first need to find the utilization rate of the on-call lawyer.

Utilization = (average service rate / average arrival rate)
Service Rate = 1 email / 5 minutes = 1 email / (1/12 hours) = 12 emails per hour
Arrival Rate = 10 emails per hour

Utilization = Service Rate / Arrival Rate
Utilization = 12 / 10 = 1.2

The utilization rate suggests that the system is unstable; that is, the number of incoming emails is higher than the service rate. The average waiting time for the customer cannot be determined in this case.

2. The amount of time a lawyer can dedicate to pursuing high-value cases depends on the time spent on responding to emails. During a 10-hour shift, there are 600 minutes. Since the average writing time is 5 minutes, and the arrival rate is 10 emails per hour:

Total email writing time = 10 emails per hour * 5 minutes per email * 10 hours = 500 minutes

Time available for high-value cases = 600 minutes - 500 minutes = 100 minutes

3. To determine how the new policy would affect the time available for high-value cases, we must first find the new utilization rate:

New Standard Deviation = 0.5 minutes
Coefficient of Variation (CV) = Standard Deviation / Mean
New CV = 0.5 / 5 = 0.1

Utilization after the new policy = (12 * New CV^2) / (10 * Old CV^2)
Utilization = (12 * 0.1^2) / (10 * 1^2) = 0.12

Now we can calculate the average waiting time using Pollaczek-Khintchine Formula:

Average Waiting Time = (Mean Service Time * Utilization^2) / (2 * (1 - Utilization))
= (5 * (0.12^2)) / (2 * (1- 0.12)) = 0.41394 minutes

Now, we can calculate the time spent on email writing and subtract it from the total available time during the shift.
Total email writing time = (5 minutes + 0.41394 minutes) * 10 emails per hour * 10 hours = 541.394 minutes

Time available for high-value cases = 600 minutes - 541.394 minutes = 58.606 minutes

So, under the new policy, a My-law lawyer would have approximately 58.61 minutes to pursue high-value cases during a 10-hour shift.

Answer 2

Step-by-Step Bot answered
1 year ago

To determine how the amount of time a lawyer can dedicate to the search for large settlement cases would change under the new operating policy, we need to consider the impact of the change in standard deviation for responding.

Under the current policy, the standard deviation for responding is 4 minutes. This means that the actual response time can vary significantly from the average of 5 minutes. With a higher standard deviation, there may be situations where the lawyer takes longer than expected to respond to an email.

Now, let's calculate the new standard deviation for responding under the proposed policy. Given that the average writing time remains unchanged at 5 minutes and the new standard deviation is 0.5 minutes, we can use the concept of the coefficient of variation to calculate the new standard deviation.

Coefficient of variation (CV) = (Standard Deviation / Average) * 100

For the current policy:
CV = (4 minutes / 5 minutes) * 100 = 80

For the proposed policy:
CV = (0.5 minutes / 5 minutes) * 100 = 10

Now, compare the two coefficients of variation. The lower coefficient of variation indicates that the new policy would result in less variation in response times. This means that the lawyer would be able to respond to emails more consistently and predictably within the average writing time of 5 minutes.

As a result, the lawyer would have more dedicated time available to pursue large settlement cases during the 10-hour shift. With fewer unpredictable delays in responding to emails, the lawyer would be able to allocate more time towards pursuing potential high-value cases. However, without the specific data on email arrival rate or other factors, it is not possible to provide a precise estimate of the exact increase in time dedicated to settlement cases.

Answer 3

Explain Bot answered
11 months ago

To answer the third question regarding the impact of the new operating policy on the time a lawyer can dedicate to searching for large settlement cases, we need to analyze the change in the standard deviation for responding to emails.

Currently, the average writing time for a response email is 5 minutes, with a standard deviation of 4 minutes. This means that, on average, it takes the lawyer 5 minutes to write a response email, but the actual time can vary by up to 4 minutes.

Under the new operating policy, the average writing time would remain unchanged, but the standard deviation for responding to emails would decrease to 0.5 minutes. This means that the actual time taken to write a response email would vary by only up to 0.5 minutes.

To calculate the impact on the time available to search for large settlement cases, we need to consider the time it takes the lawyer to respond to each email. Currently, with a standard deviation of 4 minutes, there is a wider range of response times, which may result in longer waiting times for customers. This leaves less time for the lawyer to work on settlement cases.

With the reduced standard deviation of 0.5 minutes under the new policy, the response times will be more consistent and predictable. This means that the lawyer will spend less time waiting for emails to arrive or taking longer to write a response. As a result, the lawyer would have more uninterrupted time available to dedicate to pursuing high-value settlement cases.

Therefore, the amount of time a My-law lawyer can dedicate to the search for large settlement cases would likely increase with the new operating policy, as more time becomes available due to the reduced variability in responding to emails. However, the exact increase in time would depend on the specific details and workload of the lawyer and the firm.