OPERATION MANAGEMENT
OPERATION MANAGEMENT
2nd Edition
ISBN: 9781260242423
Author: CACHON
Publisher: MCG
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Book Icon
Chapter 13, Problem 1PA

Dan McClure owns a thriving independent bookstore in artsy New Hope, Pennsylvania. He must decide how many copies to order of a new book, Power and Self-Destruction, an exposé on a famous politician’s lurid affairs. Interest in the book will be intense at first and then fizzle quickly as attention turns to other celebrities. The book’s retail price is $20, and the wholesale price is $12. The publisher will buy back the retailer’s leftover copies at a full refund, but McClure Books incurs $4 in shipping and handling costs for each book returned to the publisher. Dan believes his demand forecast can be represented by a normal distribution with a mean of 200 and a standard deviation of 80.

  1. a. Dan will consider this book to be a blockbuster for him if it sells more than 400 units. What is the probability that Power and Self-Destruction will be a blockbuster? [LO13-1]
  2. b. Dan considers a book a “dog” if it sells less than 50 percent of his mean forecast. What is the probability this exposé is a “dog”? [LO13-1]
  3. c. What is the probability that demand for this book will be within 20 percent of the mean forecast? [LO13-1]
  4. d. What order quantity maximizes Dan’s expected profit? [LO13-1]
  5. e. If Dan orders the quantity needed to achieve a 95 percent in-stock probability, what is the probability that some customer won’t be able to purchase a copy of the book? [LO13-2]
  6. f. Suppose Dan orders 300 copies of the book. What is Dan’s expected leftover inventory? [LO13-2]
  7. g. Suppose Dan orders 300 copies of the book. What are Dan’s expected sales? [LO13-2]
  8. h. Suppose Dan orders 300 copies of the book. What is Dan’s expected profit? [LO13-2]
  9. i. How many books should Dan order if he wants to achieve a 95 percent in-stock probability? [LO13-3]

a)

Expert Solution
Check Mark
Summary Introduction

To determine: The probability that the book will be a blockbuster.

Explanation of Solution

Given information:

Retail price (RP)             = $20

Wholesale price (WP)         = $12

Shipping and handling cost (SC)     = $4

Mean (M)                 = 200

Standard deviation (SD)         = 80

Target sales (T)             = 400 units

Calculation of Z – value:

Z=T-MSD=400-20080=20080=2.5

Using the Excel =NORMSDIST (2.5) function, the probability value is 0.99379.

Calculation of probability of being a blockbuster:

Probability=1-F=1-0.99379=0.00621

The probability that the book will be a blockbuster is 0.0062.

b)

Expert Solution
Check Mark
Summary Introduction

To determine: The probability that the book will be a dog.

Explanation of Solution

Given information:

Retail price (RP)             = $20

Wholesale price (WP)         = $12

Shipping and handling cost (SC)     = $4

Mean (M)                 = 200

Standard deviation (SD)         = 80

Target sales (T)             = 50% of mean

  = 100 units

Calculation of Z – value:

Z=T-MSD=100-20080=-10080=-1.25

Using the Excel =NORMSDIST (-1.25) function, the probability value is 0.10565.

The probability that the book will be a dog is 0.1057.

c)

Expert Solution
Check Mark
Summary Introduction

To determine: The probability that the demand of the book will be within 20% of the mean forecast.

Explanation of Solution

Given information:

Retail price (RP)             = $20

Wholesale price (WP)         = $12

Shipping and handling cost (SC)     = $4

Mean (M)                 = 200

Standard deviation (SD)         = 80

Expected demand             = within 20% of the mean forecast

Calculation of probability:

The expected demand value is said to be within 20% of the mean forecast. It means, the demand will be 20 % less or 20% more than the mean.

When sales is 20% less:

Z=(M-(M×20100))-MSD=(200-(200×20100))-20080=160-20080=-0.5

When sales is 20% more:

Z=(M+(M×20100))-MSD=(200+(200×20100))-20080=240-20080=0.5

Using the Excel =NORMSDIST (-0.50) function, the probability value is 0.30854.

Using the Excel =NORMSDIST (0.50) function, the probability value is 0.69146.

The two probabilities are subtracted to identify the demand probability as shown below:

Probability=0.69146-0.30854=0.38292

The probability that the demand of the book will be within 20% of the mean forecast is 0.3830.

d)

Expert Solution
Check Mark
Summary Introduction

To determine: The order quantity that maximizes the profit.

Explanation of Solution

Given information:

Retail price (RP)             = $20

Wholesale price (WP)         = $12

Shipping and handling cost (SC)     = $4

Mean (M)                 = 200

Standard deviation (SD)         = 80

Calculation of critical ratio:

Critical ratio=RP-WP(RP-WP)+SC=20-12(20-12)+SC=88+4=812=0.6667

Using the Excel =NORMSINV (0.6667) function, the value of Z using the round up rule is 0.5.

Calculation of order quantity that maximizes the expected profit:

Order quantity=M+(Z×SD)=200+(0.5×80)=200+40=240 units

The order quantity that maximizes the profit is 240 units.

e)

Expert Solution
Check Mark
Summary Introduction

To determine: The probability that some customers won’t be able to purchase a copy of the book.

Explanation of Solution

Given information:

In-stock probability = 95%

Calculation of probability of some customers not able to purchase the book:

The in-stock probability is 95% which means 95% percent of customers are able to purchase the book. Therefore, the probability that the customers will not be able to purchase the book will be:

Probability=100-In-stock probability=100-95%=5%

The probability that some customers won’t be able to purchase a copy of the book is 5%.

f)

Expert Solution
Check Mark
Summary Introduction

To determine: The expected leftover inventory.

Explanation of Solution

Given information:

Retail price (RP)             = $20

Wholesale price (WP)         = $12

Shipping and handling cost (SC)     = $4

Mean (M)                 = 200

Standard deviation (SD)         = 80

Target sales (T)             = 300 units

Calculation of Z – value:

Z=T-MSD=300-20080=10080=1.25

From the standard normal distribution table, using the roundup rule, the value of expected inventory distribution (I) for a Z-value of 1.3 is 1.3455.

Calculation of expected leftover inventory:

Expected leftover inventory=SD×I=80×1.3455=107.64

The expected leftover inventory is 107.64 units.

g)

Expert Solution
Check Mark
Summary Introduction

To determine: The expected sales.

Explanation of Solution

Given information:

Retail price (RP)             = $20

Wholesale price (WP)         = $12

Shipping and handling cost (SC)     = $4

Mean (M)                 = 200

Standard deviation (SD)         = 80

Target sales (T)             = 300 units

Calculation of expected sales:

Expected sales=Target sales-Expected leftover inventory=300-107.64=192.36

The expected sales is 192.36 units.

h)

Expert Solution
Check Mark
Summary Introduction

To determine: The expected profit.

Explanation of Solution

Given information:

Retail price (RP)             = $20

Wholesale price (WP)         = $12

Shipping and handling cost (SC)     = $4

Mean (M)                 = 200

Standard deviation (SD)         = 80

Target sales (T)             = 300 units

Calculation of expected profit:

Expected profit=(RP×Expected sales)+[(RP-WP)×Leftover inventory]-(WP×T)=(20×192.36)+[(20-12)×107.64]-(12×300)=3,847.2+861.12-3,600=$1,108.32

The expected profit is $108.32.

i)

Expert Solution
Check Mark
Summary Introduction

To determine: The number of books that must be ordered to achieve an in-stock probability of 95%.

Explanation of Solution

Given information:

Retail price (RP)             = $20

Wholesale price (WP)         = $12

Shipping and handling cost (SC)     = $4

Mean (M)                 = 200

Standard deviation (SD)         = 80

Target sales (T)             = 300 units

Calculation of order quantity:

The in-stock probability of 95% and the roundup rule corresponds to z- value of 1.70 from the standard distribution table.

Order quantity=M+(Z×SD)=200+(1.7×80)=200+136=336 units

The number of books that must be ordered to achieve an in-stock probability of 95% is $336 books.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Summarize chapters 1 through 8 of the book "food and beverage cost control"
Can you guys help me with this? Thank you! Here's the question: Compared to the CONSTRAINT model, how has the network changed? How do you plan to add contingency to your network? Please answer this thoroughly Here's the what-if scenario: Assume that the LA warehouse becomes temporarily or even indefinitely disabled since facing a large-scale labor disruption. Re-optimize the network considering this new constraint. Here's the scenario comparison analysis:  Scenario Constraint Scenario vs What-if Scenario Summary The Constraint Scenario exhibits a higher total cost of $7,424,575.45 compared to the What-if Scenario's total cost of $6,611,905.60, signifying a difference of approximately $812,669.85, which indicates a more expensive operation in the Constraint Scenario. The average service time is slightly higher in the Constraint Scenario (0.72 days vs. 0.70 days), suggesting that the What-if Scenario provides a marginally quicker service. Moreover, the average end-to-end service time…
Can you guys help me with this? Thank you! Here's the question: Compared to the CONSTRAINT model, how has the network changed? How do you plan to add contingency to your network? Please answer this throughly Here's the what-if scenario: Assume that Dallas plant has lost power. It cannot serve the DCs anymore and has to remain locked indefinitely. Re-optimize the network considering this new constraint. Here's the scenario comparison analysis:  Scenario Constraint Scenario vs What-if Scenario Summary In comparing the Constraint Scenario to the What-if Scenario, a few key differences highlight the efficiencies evident in the supply chain. Firstly, the total cost in the Constraint Scenario is lower at $7,424,575.45, while the What-if Scenario incurs a total cost of $7,486,369.12, resulting in a cost delta of $61,793.67. Additionally, although both scenarios exhibit the same average service time of 0.72 days, the What-if Scenario has a more favorable average end-to-end service time of 2.41…

Additional Business Textbook Solutions

Find more solutions based on key concepts
Knowledge Booster
Background pattern image
Operations Management
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, operations-management and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Marketing
Marketing
ISBN:9780357033791
Author:Pride, William M
Publisher:South Western Educational Publishing
Text book image
Practical Management Science
Operations Management
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:Cengage,
Text book image
MARKETING 2018
Marketing
ISBN:9780357033753
Author:Pride
Publisher:CENGAGE L
Text book image
Foundations of Business (MindTap Course List)
Marketing
ISBN:9781337386920
Author:William M. Pride, Robert J. Hughes, Jack R. Kapoor
Publisher:Cengage Learning
Text book image
Foundations of Business - Standalone book (MindTa...
Marketing
ISBN:9781285193946
Author:William M. Pride, Robert J. Hughes, Jack R. Kapoor
Publisher:Cengage Learning
Inventory Management | Concepts, Examples and Solved Problems; Author: Dr. Bharatendra Rai;https://www.youtube.com/watch?v=2n9NLZTIlz8;License: Standard YouTube License, CC-BY