hw3 - IE426 Problem Set #3 Prof Jeff Linderoth IE 426...

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IE426 Problem Set #3 Prof Jeﬀ Linderoth IE 426 – Problem Set #3 Due Date: October 31, 2006. 4:30PM. 1 Selling Swoosh Shoes – 35 Points Swoosh Shoes, Inc. has established goals for the market share it wants two new products to capture in their respective markets. Speciﬁcally, Swoosh management wants Product 1 to capture 25% of its market and Product 2 to capture 20% of its market. Three advertising campaigns are being planned to achieve to try and achieve these market shares. The ﬁrst is targeted directly on the ﬁrst product. The second targets the second product, and the third is intended to enhance the general reputation of the company and its products. Letting x 1 , x 2 , and x 3 be the amount of money (in millions of dollars) allocated to each campaign, management estimates that the resulting market shares can be expressed (in percentages) as Market Share for Product 1: 0 . 5 x 1 + 0 . 2 x 3 (1) Market Share for Product 2: 0 . 3 x 2 + 0 . 2 x 3 . (2) A total of \$55M is available for the three advertising campaigns, but management wants at least \$10M devoted to the third campaign. 1.1 Problem Formulate a linear program that will determine the proper allocation of money to advertising campaigns. 1.2 Problem Build your model from Problem 1.1 in the Mosel modeling language and solve it. What is the result of solving the instance? 1.3 Problem Change your Problem 1.2 to a linear program that will come as close as possible to meeting market share for Product 2 while satisfying all others constraints. Solve this instance. What is the result? 1.1 Goal Programming Approaches Swoosh Management has ranked the advertising campaign goals/criteria in the following order of importance. Goal I. Satisfy budget of \$55M. Goal II. Meet 20% market share for Product 2. Problem 1 Page 1

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IE426 Problem Set #3 Prof Jeﬀ Linderoth Goal III. Invest \$10M in advertising campaign 3. Goal IV. Meet 25% market share for product 1. We will present Swoosh Management with three different solutions that accomplish these goals to varying degrees. Please show your work for all instances. 1.4 Problem Solve this instance using a weighted goal-programming approach. (You can decide the weights, but they should be consistent with Swoosh’s management objectives). 1.5 Problem Solve this instance in a hierarchical fashion, where the ﬁrst goal is “inﬁnitely” more impor- tant than the second goal, and so on. 1.6 Problem Solve a hierarchical version of this problem, where goals 2 and 3 are within 1% of their optimal values from the solution to the previous level’s hierarchy. 1.2 Extra Credit 1.7 Problem Keeping the \$55M budget constraint and the \$10M investment in ad campaign three con- straint, let f ( α ) be the maximum obtainable market share for Product 2 if the market share of product 1 is required to be α . Plot f ( α ) .
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This note was uploaded on 02/29/2008 for the course IE 426 taught by Professor Linderoth during the Spring '08 term at Lehigh University .

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hw3 - IE426 Problem Set #3 Prof Jeff Linderoth IE 426...

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