Problem A: (20 points) An online store receives orders throughout the day, but the order fulfillment process each day starts at 11:00am and ends until all the orders received in the last 24 hours (i.e. from 11:00am of the previous day to 11:00am of the current day) are fulfilled. The orders that arrive after 11:00am on a day will be fulfilled on the next day. There are three steps required to fulfill a customer order. The first step is to process the order from the order pool that keeps all the orders that have arrived in the last 24 hours. The second step is to pack the order and the last step is to ship the order. Orders go through these steps one by one. The manager wants to analyze the fulfillment process and has provided the process flow diagram shown below. The capacity of each step is shown in the process flow diagram. The storage buffers between consecutive steps are sufficiently large such that there is no blocking at any time.

Assume that there are a total of 3000 orders in the order pool at 11:00am on a specific day. The store needs to fulfill all these orders on this day. (a) How long will the order processing operations have to work on this day? How long will the order packing operations have to work on this day?

How long will the order shipping operations have to work on this day? What is the maximum number of orders waiting to be packed (i.e. at storage #1) at any moment?

What is the maximum number of orders waiting to be shipped (i.e. at storage #2) at any moment? (b) On average, how long does an order have to wait at storage #1? Similarly, on average, how long does an order have to wait at storage #2?