Part II –Problem Solving (70%) [Note: For Problems 3, 4, and 5, you are supposed
ID: 457405 • Letter: P
Question
Part II –Problem Solving (70%)
[Note: For Problems 3, 4, and 5, you are supposed to show necessary analysis and justify your answers. Problem 6 consists of some multiple-choice questions for which you do not need to show your work.]
Problem 3: (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.
(8 points) 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) (4 points) 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?
(this problem is continued on next page)
(c) (8 points) Now suppose that storage #2 has a limited capacity and can only hold 600 orders whereas storage #1 still has unlimited capacity. When storage #2 is full, the order packing step has to slow down to the same processing rate as the order shipping step. When will storage #2 be full? 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? On average, how long does an order that arrives at storage #2 during the time this storage is full have to wait at this storage?
Part II –Problem Solving (70%)
[Note: For Problems 3, 4, and 5, you are supposed to show necessary analysis and justify your answers. Problem 6 consists of some multiple-choice questions for which you do not need to show your work.]
Problem 3: (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.
(8 points) 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) (4 points) 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?
(this problem is continued on next page)
(c) (8 points) Now suppose that storage #2 has a limited capacity and can only hold 600 orders whereas storage #1 still has unlimited capacity. When storage #2 is full, the order packing step has to slow down to the same processing rate as the order shipping step. When will storage #2 be full? 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? On average, how long does an order that arrives at storage #2 during the time this storage is full have to wait at this storage?
Order rde pool Pack grder 500 orders Ship rde order 400 orders pe hour 300 orders pe hour pe hourExplanation / Answer
a)
b)
c)
How long will the order processing operations have to work on this day? Ans. : = 3000 orders /400 orders perhour 7.5 hours How long will the order packing operations have to work on this day? Since the capacity of order processing is leass than the order packing hence, order packing will have to work as many hours as order processing is working, as it will receive only 400 orders/hour even if it has a capacity to pack 500 orders/hour Ans.: 7.5 hours How long will the order shipping operations have to work on this day? Since the caapcity of order shipping is 300 orders/hour, it will work for 3000/300 hours Ans.: 10 hours What is the maximum number of orders waiting to be packed (i.e. at storage #1) at any moment? Ans. : Zero Orders Since, the capacity of Packing is higher than processing, there wont be any orders waiting for packing What is the maximum number of orders waiting to be shipped (i.e. at storage #2) at any moment? Orders are being packed at 400 orders/hour (as the actual capacity of packing is reduced as it is getting only 400 orders/hour from processing), and are being shipped at 300 orders/hour hours Orders packed Orders Shipped No. of orders at storage # 2 1 400 300 100 2 400 300 200 3 400 300 300 4 400 300 400 5 400 300 500 6 400 300 600 7 400 300 700 8 200 300 600 9 0 300 300 10 0 300 0 3000 3000 (200 orders are packed in 8 th hour,as packing was completed in 7.5 hours) Ans.: 700 orders