ASW Publishing, Inc. a small publisher of college textbooks,must make a decision regarding which books to publish next year. The books under consideration are listed in the following table, along with the projected three-year sales expected from each book:

Book Subject Type of Book Projected Sales($)

Business Calculus New 20000

Finite Mathematics Revision 30000

General Statistics New 15000

Mathematical Statistics New 10000

Business Statistics Revision 25000

Finance New 18000

Financial Accounting New 25000

Managerial Accounting Revision 50000

English Literature New 20000

German New 30000

 

The books listed as revisions are texts that ASW already has under contract; these books are being considered for publication as new editions. The books that are listed as new have been reviewed by the company, but contracts have not yet been signed.

Three individuals in the company can be assigned to to these projects, all of whom have varying amounts of time available; John has 60 days available, and Susan and Monica both have 40 days available. The days required by each person to complete each project are shown in the following table. For instance, if the business calculus book is published, it will require 30 days of John's time and 40 days of Susan's time. An "X" indicates that the person will not be used on the project. Note that at least two staff members will be assigned to each project except the finance book.

 

ASW will not publish more than two statistics books or more than one accounting book in a single year. In addition, management decided that one of the mathematics books (business calculus or finite math) must be published, but not both.

Book Subject John Susan Monica

Business Calculus 30 40 X

Finite Mathematics 16 24 X

General Statistics 24 X 20

Mathematical Statistics 20 X 24

Business Statistics 10 X 16

Finance X X 14

Financial Accounting X 24 26

Managerial Accounting X 28 30

English Literature 40 34 30

German X 50 36

 

I need a report for the managing editor of ASW that describes your findings and recommendations regarding the best publication strategy for the next year. In carrying out your analysis, assume that the fixed costs and the sales revenue per unit are approximately equal for all books: management is interested primarily in maximizing the total unit sales volume.

I need a maximization integer linear model with constraints included.

 

The managing editor also asked that you include recommendations regarding the following possible changes:

If it would be advantageous to do so, Susan can be moved off another project to allow her to work 12 more days.

If it would be advantageous to do so, Monica can also be made available for another 10 days.

If one or more of the revisions could be postponed for another year, should they be? Clearly the company will risk losing market share by postponing a revision.

Management Report

TO:                  ASW Publishing, Inc. Management

FROM:            Your Name

DATE:             Current Date

SUBJECT:      Publication Strategy Analysis and Recommendations

Section of Report

Statement of the Business Problem.. 4

Other requirements. 4

Constraints Applied on Strategy. 4

Assumptions in analysis. 4

Decision Variables. 5

Analysis, Results and Recommendations. 6

Appendices. 10

Statement of the Business Problem

1. If it would be advantageous to do so, Susan can be moved off another project to allow her to work 12 more days.
2. If it would be advantageous to do so, Monica can also be made available for another 10 days.
3. If one more of the revisions could be postponed for another year, should they be? Clearly the company will risk losing market share by postponing a revision.

Other requirements

1. Development of publication strategy that maximizes total units sales volume
2. Meeting the labour-day constraints of John, Susan and Monica

Constraints Applied on Strategy

1. No more than 2 statistics books in a single year,
2. No more than one accounting text in a single year
3. Publish one mathematics texts but not both.

Assumptions in analysis

Fixed costs and the sales revenue per unit are approximately equal for all books

Decision Variables

Here are the 0/1 decision variables.

Step-by-step explanation

1. Variable with value 0 implies corresponding book will not be published
2. Variable with value 1 implies corresponding book is to be published

Analysis, Results and Recommendations

Requirement Case One:

If it would be advantageous to do so, Susan can be moved off another project to allow her to work 12 more days.

Optimal Solution for this Requirement is provided as follows:

Constraints Applied: Please check Appendix A for constraints

Decisions For book publication

Object Function value: 73.000

Findings:

1. Publish the finite mathematics, business statistics and finance texts for expected sales of 73,000.
2. John has slack of 34 days, Susan 16 days and Monica 10 days.

Analysis and Recommendations:

Expected Sales are less. Thus this strategy is not advantageous

Result: This publication Strategy is not recommended

Requirement Case 2:

If it would be advantageous to do so, Monica can also be made available for another 10 days

Optimal Solution for this Requirement is provided as follows:

Constraints Applied: Please check Appendix B for constraints

Decisions For book publication

Object Function value: 80.000

Findings:

1. Publish just two texts: finite mathematics and managerial accounting for expected sales of 80,000.
2. Monica has now 10 days available as required.
3. Better use of Susan but not of John.

Analysis and Recommendations:

Sales are more, but John is not used, therefore, this strategy is not advantageous.

Result: This publication Strategy is not recommended.

Optimal Solution to increase sales and make better use of all resources

Optimal Solution for this Requirement is provided as follows:

Constraints Applied: Please check Appendix C for constraints

Decisions For book publication

Object Function value: 105.000

Findings:

1. Publish finite mathematics, business statistics and managerial accounting for expected sales of 105,000 books.
2. Monica has now moved to another project.
3. Better use of John.

Analysis and Recommendations:

Sales are more 105,000 books. Monica and Susan are now moved to other projects

Result: This publication Strategy is recommended.

Recommendations for Requirement Case 3:

1. It is noted that none of the solutions include new books - only revisions.
2. Therefore, it is not recommended to postpone any revision for next year.
3. It might be prudent policy to add a constraint such as at least one book in the publication schedule should be a new text in order to grow a new business.

Appendices

APPENDIX A:

Maximum Publications possible:

Please see the attached file for the complete solution