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Assignment: Linear Optimization. Just For For Prof Dan

Assignment: Linear Optimization. Just For For Prof Dan

Assignment: Linear Optimization. Just For For Prof Dan

Assignment: Linear Optimization

THE WORLD OF BUSINESS ANALYTICS Optimizing Production, Inventory, and Distribution at KelloggThe Kellogg Company ( 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


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