Assignment: Linear Optimization

THE WORLD OF BUSINESS ANALYTICS Optimizing Production, Inventory, and Distribution at KelloggThe Kellogg Company (http://www.Kellogs.com) is the largest cereal producer in the world and a leading producer of convenience foods. In 1999, Kellogg’s world-wide sales totaled nearly $7 billion. Kellogg operates 5 plants in the United States and Canada and has 7 core distribution centers and roughly 15 co-packers that contract to produce or pack some of Kellogg’s products. In the cereal business alone, Kellogg must coordinate the production of 80 products while inventorying and distributing more than 600 stock keeping units (SKUs) with roughly 90 pro-duction lines and 180 packaging lines. Optimizing this many decision variables is obviously a daunting challenge.Since 1990, Kellogg has been using a large-scale, multiperiod linear program, called the Kellogg Planning System (KPS), to guide production and distribution decisions. Most large companies like Kellogg employ some sort of enterprise re-source planning (ERP). Kellogg’s ERP system is a largely custom, home-grown product, and KPS is a custom-developed tool to complement the ERP system.An operational-level version of KPS is used at a weekly level of detail to help de-termine where products are produced and how finished products and in-processproducts are shipped between plants and distribution centers. A tactical-level ver-sion of KPS is used at a monthly level of detail to help establish plant budgets and make capacity and consolidation decisions. Kellogg attributes annual savings of $40–$45 million to the use of the KPS system.Source: Brown, G., J. Keegan, B. Vigus, and K. Wood. “The Kellogg Company Optimizes Production, Inventory, and Distribution.” Interfaces, vol. 35, no. 6, 2001.

4.Refer to question 14 at the end of Chapter 2. Implement a spreadsheet model for this problem and solve it using Solver.

5.Refer to question 16 at the end of Chapter 2. Implement a spreadsheet model for this problem and solve it using Solver.

7.Refer to question 21 at the end of Chapter 2. Implement a spreadsheet model for this problem and solve it using Solver.

14. Bearland Manufacturing produces 4 different types of wood paneling. Each type of paneling is made by gluing and pressing together a different mixture of pine and oak chips. The following table summarizes the required amount of gluing, pressing, and mixture of wood chips required to produce a pallet of 50 units of each type of paneling:

Resources Required per Pallet of Paneling Type

Paneling Type Tahoe Paciﬁc Savannah Aspen

Glue (quarts) 50 50 100 50

Pressing (hours) 50 150 100 50

Pine chips (pounds) 500 400 300 200

Oak chips (pounds) 500 750 250 500

Assume the company has 6,000 quarts of glue; 7,500 hours of pressing capacity; 30,000 pounds of pine chips; and 62,500 pounds of oak chips available in the next production cycle. Further assume that each pallet of Tahoe, Pacific, Savannah, andAspen panels can be sold for profits of $450, $1,150, $800, and $400, respectively.9781337512954, Spreadsheet Modeling & Decision Analysis, Seventh edition. Ragsdale – © Cengage Learning. All rights reserved. No distribution allowed without express authorization. Distributed by Grand Canyon University.

Finally, for marketing purposes, the company wants to produce at least 4 pallets of each type of paneling.

A. Formulate an LP model for this problem.

b. Create a spreadsheet mode for this problem, and solve it using Solver.

c. What is the optimal solution?

The Sentry Lock Corporation manufactures a popular commercial security lock at plants in Macon, Louisville, Detroit, and Phoenix. The per unit cost of production at each plant is $35.50, $37.50, $39.00, and $36.25, respectively, while the annual pro-duction capacity at each plant is 18,000, 15,000, 25,000, and 20,000, respectively. Sen-try’s locks are sold to retailers through wholesale distributors in seven cities across the United States. The unit cost of shipping from each plant to each distributor is summarized in the following table along with the forecasted demand from each distributor for the coming year.

**Unit Shipping Cost to Distributor in**

Plants

Tacoma

San Diego

Dallas

Denver

St. Louis

Tampa

Baltimore

Macon

$2.50

$2.75

$1.75

$2.00

$2.10

$1.80

$1.65

Louisville

$1.85

$1.90

$1.50

$1.60

$1.00

$1.90

$1.85

Detroit

$2.30

$2.25

$1.85

$1.25

$1.50

$2.25

$2.00

Phoenix

$1.90

$0.90

$1.60

$1.75

$2.00

$2.50

$2.65

Demand

8,500

14,500

13,500

12,600

18,000

15,000

9,000

Sentry wants to determine the least expensive way of manufacturing and shipping locks from its plants to the distributors. Because the total demand from distributors exceeds the total production capacity for all the plants, Sentry realizes it will not be able to satisfy all the demand for its product but wants to make sure each distributor will have the opportunity to fill at least 80% of the orders received

a. Create a spreadsheet model for this problem and solve it.

b. What is the optimal solution?

The purpose of this assignment is to employ linear optimization techniques, interpret results, and determine optimal solutions for business problems.

Complete Chapter 3 Problems 4, 5, 7, 14, and 34 from the textbook, using the student data files provided in the Course Materials, as directed.

Submit the Excel outputs required for each problem. Note that Excel files are to include all Solver settings, functions, and formulas used to generate the problem solutions.

Submit a narrative to discuss the optimal solution for each problem as a Word document.

In addition, write a 250-word executive summary related to Problem 34. Summarize for management the least expensive way Sentry can manufacture and ship locks from the plants to the distributors to optimize organizational performance and effectiveness. Justify your explanation based on the linear optimization model.

Submit your executive summary and associated Microsoft Excel files to the instructor.

APA style is not required, but solid academic writing is expected.

This assignment uses a rubric. Please review the rubric prior to beginning the assignment to become familiar with the expectations for successful completion.

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**Linear Optimization – Part 1 **

**1**

** Unsatisfactory**

** 0.00% **

**2**

** Less than Satisfactory**

** 74.00% **

**3**

** Satisfactory**

** 79.00% **

**4**

** Good**

** 87.00% **

**5**

** Excellent**

** 100.00% **

**100.0 %Content**

**20.0 %** **Excel Outputs **

Excel outputs are not included.

Excel outputs are incomplete or incorrect.

Excel outputs are included with some errors in accuracy.

Excel outputs are included and mostly accurate.

Excel outputs are all complete and correct.

**20.0 %** **Solver Settings, Functions, and Formulas **

Solver settings, functions, and formulas are not included.

Solver settings, functions, and formulas are incomplete or incorrect.

Solver settings, functions, and formulas are included but lack accuracy.

Solver settings, functions, and formulas are included and mostly accurate.

Solver settings, functions, and formulas are complete and accurate.

**20.0 %** **Linear Optimization Techniques**

Problem answers reflecting the use of linear optimization techniques to formulate optimal solutions are not included.

Problem answers reflecting the use of linear optimization techniques to formulate optimal solutions are incomplete or incorrect.

Problem answers reflecting the use of linear optimization techniques to formulate optimal solutions are included and partially correct.

Problem answers reflecting the use of linear optimization techniques to formulate optimal solutions are included and mostly correct.

Problem answers reflecting the use of linear optimization techniques to formulate optimal solutions are complete and correct.

**30.0 %** **Executive Summary **

Executive summary, including discussion and justification of the least expensive solution for manufacturing and shipping locks to optimize organizational performance, is not included.

Executive summary, including discussion and justification of the least expensive solution for manufacturing and shipping locks to optimize organizational performance, is incomplete or incorrect.

Executive summary, including discussion and justification of the least expensive solution for manufacturing and shipping locks to optimize organizational performance, is included but lacks relevant details.

Executive summary, including discussion and justification of the least expensive solution for manufacturing and shipping locks to optimize organizational performance, is complete and includes relevant details.

Executive summary, including discussion and justification of the least expensive solution for manufacturing and shipping locks to optimize organizational performance, is expertly crafted and includes extensive relevant details.

**10.0 %** **Mechanics of Writing (includes spelling, punctuation, grammar, language use)**

Surface errors are pervasive enough that they impede communication of meaning. Inappropriate word choice or sentence construction is used.

Frequent and repetitive mechanical errors distract the reader. Inconsistencies in language choice (register) or word choice are present. Sentence structure is correct but not varied.

Some mechanical errors or typos are present, but they are not overly distracting to the reader. Correct and varied sentence structure and audience-appropriate language are employed.

Prose is largely free of mechanical errors, although a few may be present. The writer uses a variety of effective sentence structures and figures of speech.

Writer is clearly in command of standard, written, academic English.

**100 %** **Total Weightage**

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