Repeat the same procedure as in Question 6 using the data from the csv file “multipleitempart2.csv”. As before, submit
(i) the summary of the regressions;
(ii) the values of R2 and MAPE on the test set.
8. Assume that p i 6 = 1 and p i 5 = 1 for all i, and p 2 7 = 1, p3 7 = 1, p4 7 = 1, p5 7 = 1. Compute the values of the predicted demands d 1 7 , d2 7 , d3 7 , d4 7 , d5 7 using model (3) calibrated with the data from Question 6, when p 1 7 = 1 and when p 1 7 = 0.7 (i.e., a total of 10 different values). What can you say about the effect of promoting Brand 1?
9. Compare the estimated parameters from Questions 6 and 7. What is the difference between the 5 brands from Question 6 and the 5 brands from Question 7? Please, discuss.Optimization Formulation
10. Once the demand models are estimated from data, the next step is to formulate the optimization problem, i.e., maximizing an objective function subject to some constraints. Consider deciding promotions for 5 items throughout the next quarter (composed of 13 weeks). What types of objectives would you consider? Please discuss.
11. Very often, when formulating an optimization problem, it is convenient to use binary decision variables (variables that can take only the values 0 or 1). Denote the price of a particular SKU during week t by pt. In addition, the (normalized) price of the SKU can only take of the following four values: 1 (i.e., full price), 0.9 (10% promotion), 0.8 (20% promotion) and 0.7 (30% promotion). How can one represent such a restriction using linear constraints and binary variables? (Hint: You may use more than one constraint.)
12. As we discussed in the case study, promotions should satisfy several business rules. One such rule is to limit the frequency of promotions for a particular SKU. For example, a retailer may insist that a particular product is promoted at most 4 times during the quarter. How can you model this business rule as a linear constraint with binary variables?
13. Consider the problem of maximizing the total profit throughout the next quarter for a particular SKU (e.g., SKU88). Please, formulate the optimization problem with the constraint on the limitation of the number of promotions to be at most 4.
14. Assume that we solved the optimization problem and obtained the suggested prices for SKU88 for the next 13 weeks. The suggested prices are presented in Exhibit 5 of the case study. What can you say on this output? What tests would you conduct in order to check that the suggested prices are robust? Please discuss.
15. Consider the optimization problem for several items simultaneously. Should the promotions of the different items be at the same time, or at different times? Please discuss the various factors that may affect the answer to this question. (This question is qualitative and you are not expected to solve any optimization problem.)
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