OptimizationI_Project_v3 (2).pdf

RM 294 – Optimization I Project 1 – Linear Programming Abhinav S Sharma, Ankita Kundra, Mohammed Safiuddin Problem Description: Assume that your company is deciding how to spend a marketing budget of $10M. You work in the marketing department as a data scientist and the chief marketing officer has asked you write a report recommending how to spread this budget among several marketing mediums. Your department has employed an outside consulting firm to estimate the return on investment (ROI) of each marketing medium under consideration. The results are in the table below, and also in a CSV attached to this assignment: On top of these ROIs, your boss has decided to constrain your budget as follows: a. The amount invested in print and TV should be no more than the amount spent on Facebook and Email. b. The total amount used in social media (Facebook, LinkedIn, Instagram, Snapchat, and Twitter) should be at least twice of SEO and AdWords. c. For each platform, the amount invested should be no more than $3M. Data Read Snippet : Question 1: Formulate the marketing budget allocation problem as a linear program. Use gurobi to find the optimal budget allocation . Marketing Budget allocation as a linear problem: Let x 1 be the amount invested in print, x 2 be the amount invested in TV, x 3 be the amount invested in SEO, x 4 be the amount invested in AdWords,

x 5 be the amount invested in Facebook, x 6 be the amount invested in LinkedIn, x 7 be the amount invested in Instagram, x 8 be the amount invested in Snapchat, x 9 be the amount invested in Twitter and x 10 be the amount invested in Email Objective Function: To maximize ROI 0.031x 1 + 0.049x 2 + 0.024x 3 + 0.039x 4 + 0.016x 5 + 0.024x 6 + 0.046x 7 + 0.026x 8 + 0.033x 9 + 0.044x 10 Constraints: x 1 + x 2 + x 3 + x 4 + x 5 + x 6 + x 7 + x 8 + x 9 + x 10 ≤ 10 (Total Budget Constraints) x 5 + x 6 + x 7 + x 8 + x 9 ≤ 2(x 3 + x 4 ) (Inter-Platform Budget Constraint) x 1 + x 2 ≤ x 5 + x 10 (Inter-Platform Budget Constraint) x i ≤ 3  i  [1, 2, 3, 4, 5, 6, 7, 8 , 9, 10] (Platform Budget Constraint) Using gurobi to solve the problem, We find that the optimal allocation is: Thus, the optimal allocation is to assign 3 million to TV, Instagram, Email each while assign 1 million to AdWords.

The total expected ROI from the optimal allocation is: Question 2: To be cautious about the decision, your team has decided to get another opinion about the ROI data and rerun the analysis. The second consulting firm returns the estimates of the ROI data in the table below (also in the CSV file mentioned above). You are asked to compare the two optimal allocations from these two ROI estimates. Comparison of the two Optimal Allocations:

As we can see from the above table, the optimal allocation for AdWords remains the same i.e 1 million. The remaining 9 million can be equally divided amongst Print, Facebook and LinkedIn (3 million each) Change in ROI with estimate 2: Question 3: Are the allocations the same? Assuming the first ROI data is correct, if you were to use the second allocation how much lower would the objective be relative to the optimal objective? Assuming the second ROI data is correct, if you used the first allocation how much lower would the objective be relative to the optimal objective? Do you think the third constraint above, based on your boss’ experience, is useful? Assuming the first ROI is correct , with the Allocation of second ROI data: If the first ROI is correct, we stand to lose 204,000 USD compared to the optimal objective Assuming the second ROI is correct , with the Allocation of second ROI data:

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