# Estimate the average customer wait before being served.

Operational management problem set

Question 1: (10 points)

Customers send emails to a help desk of an online retailer every 2 minutes. The online retailer has three employees answering emails. It takes on average 4 minutes to respond to an email. Assume that both the email inter-arrival time and the response time are exponentially distributed.

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Estimate the average customer wait before being served.
How many emails would there be, on average, waiting to be answered?
Question 2: (10 points)

Consider the order fulfillment process at a pharmacy. The pharmacy receives, on average, 100 orders per day (assume that the pharmacy is open 10 hours per day). The first step is data entry and conducting the necessary checks such as inventory availability, insurance coverage, etc. On average, this step takes one hour. 10% of all scripts are rejected after this step due to various problems. 90% of remaining scripts move through the process without encountering any problems. Including waiting and processing times, the average time for these scripts is two hours. 10% of the remaining scripts encounter problems and they spend, on average three days in the system after the initial data entry and check step.

How many scripts are there at the pharmacy on average?
Based on your answer in part a, what is the estimated total flow time for the average script entering the process?
Question 3: (10 points)

Leah’s Toys makes rubber balls. The current process is capable of producing balls that weigh on average 3.3 ounces with a standard deviation of 0.1 ounces.

Suppose that the upper and lower tolerance limits are 3.5 and 2.5 ounces. Is the process able to meet the tolerance limits 99.7% of the time?
What is the largest standard deviation that process can have and still be able to achieve Six Sigma quality levels? How would your answer change (if at all) if the process mean were 3 ounces instead of 3.3?