b) My-law.com is evaluating the option of running a training program. A trained lawyer would be able to achieve a 20% reduction in the average time to respond to customer requests. Moreover, because the training program involves introducing a standardized work procedure, the standard deviation of service times will be reduced by 40% compared to before. An industry study has estimated that the cost of customer dissatisfaction from waiting for the response e-mail is $10 per hour. The training program will cost My-law.com $27,000. How long will it take My-law.com to break even? Assume 30 days per month, and My-law.com opens everyday (including weekends).
| a(avg. inter-arrival time) | p (avg. service time) | m(number of servers) | u (avg. utilization) | CVa(coef. of var.- arrival) | CVp(coef. of var.- service) |
To determine how long it will take My-law.com to break even on the investment in the training program, we need to consider several factors, including the benefits of the program and the cost of customer dissatisfaction due to delayed responses.
First, let’s break down the key information provided:
Trained lawyers will achieve a 20% reduction in the average time to respond to customer requests.
The training program will also reduce the standard deviation of service times by 40%.
The cost of customer dissatisfaction from waiting for a response is estimated at $10 per hour.
The training program will cost My-law.com $27,000.
To calculate the potential benefits of the training program, we need to understand the current situation. We’ll use some basic queuing theory concepts:
Average inter-arrival time (a) is a measure of how often customer requests arrive.
Average service time (p) is the time it takes to respond to a customer request.
Number of servers (m) represents how many trained lawyers are available to respond.
Average utilization (u) indicates the fraction of time servers are busy.
Since we don’t have specific values for a, p, or m, we’ll make some assumptions for the sake of this analysis. Let’s assume:
Average inter-arrival time (a) = 1 request per hour (this is just an example).
Average service time (p) before training = 2 hours (without training).
Average service time (p) after training = 1.6 hours (20% reduction).
Number of servers (m) = 1 (for simplicity, assuming one lawyer).
Now, we can calculate the average utilization (u) using the formula:
u = (a * p) / m
Before training: u_before = (1 request/hour * 2 hours) / 1 = 2
After training: u_after = (1 request/hour * 1.6 hours) / 1 = 1.6
Next, we need to calculate the cost of customer dissatisfaction before and after the training program. Customer dissatisfaction cost is associated with waiting for a response, and it depends on the average time a customer spends waiting.
Cost of customer dissatisfaction per hour = $10
Before training:
After training (with reduced response time):
Now, let’s calculate the difference in customer dissatisfaction cost per request before and after training:
Cost reduction per request = Cost before training – Cost after training Cost reduction per request = $10 – $8 = $2
Now, we can estimate how many customer requests My-law.com needs to handle to break even on the $27,000 training program cost:
Break-even point (in terms of requests) = Training program cost / Cost reduction per request Break-even point = $27,000 / $2 = 13,500 requests
To determine how long it will take to reach 13,500 requests, we need to know the rate at which requests are received. Let’s assume that requests arrive at a constant rate of 1 request per hour.
Time to break even = Break-even point (requests) / Arrival rate (requests per hour) Time to break even = 13,500 requests / 1 request per hour = 13,500 hours
Since there are 30 days in a month and My-law.com operates every day, including weekends, we can calculate the break-even time in months:
Time to break even (months) = 13,500 hours / (24 hours/day * 30 days/month) ≈ 5.63 months
So, it will take My-law.com approximately 5.63 months to break even on the $27,000 investment in the training program, assuming the assumptions made in this analysis hold true. Keep in mind that this is a simplified calculation, and the actual break-even time may vary depending on the specific values of a, p, and m in your real-world scenario.
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