Assignment task:
We Solve Problems (WSP) receive a wide variety of customer emails. Messages range from requests for technical support from existing customers to general inquires about products from potential customers. WSP's policy is to reply to all emails within 24 hours of receipt. WSP has two contact centers processing emails. The first is on the east coast (NY) and is open from 8:00AM to 4:00PM (all times are Eastern Standard Times). It can process 45 emails per hour. The second facility is on the west coast (LA) and opens at noon (EST) and can process 30 emails per hour. It also operates for an eight-hour shift. The two contact centers pull emails from the same server in a first come, first served fashion. Work unfinished by the east coast facility is completed by the west coast center. On an average day, emails arrive at a rate of 35 per hour from 8:00AM until 6:00PM (EST). At all other times, emails arrive at a rate of 15 per hour.
i. On a grid like the one below (you may scan a hand drawn graph), draw an inventory buildup sketch showing the number of emails waiting to be answered on a typical day of operations (not the very first day!) Note that time zero on the grid below is midnight eastern time, so hour 13 is 1:00PM EST etc.
ii WSP plans to close one facility and increase the staffing at the remaining facility so that it can handle 70 emails per hour during the same original 8 operating hours.
a) Using the new single facility plan, will WSP still be able to answer all emails arriving within a 24-hour period?
b) What is the longest time that a customer will have to wait for a reply under the old and new systems?
c) Does it matter which center is closed? Which would you close and why?
d) Would you switch to the new system with your closing recommendation in c)? or stay with the old system. Explain your reasoning
For the next question you do not need to perform any calculations; give a qualitative answer!
e) How do your answers to a) and c) change if emails arrive not at a constant rate but at a rate that is Normally distributed at N(35,15) and N(15,5) i.e. with the same means as before but with a standard deviation.