Approximation Methods for Pricing Problems Under the Nested Logit Model with Price Bounds

the expected revenue we obtain given that nest i is selected is Ri(wi) = P j∈N wij (κij−ηij logwij) P j∈N wij , where M = {1, . . . ,m}, N = {1, . . . , n} and γi ∈ [0, 1] measures product dissimilarity within nests. Due to a one-to-one relationship, control of the preference weights equates to control of the prices κij−ηij logwij , where 1/ηij represents product price sensitivity and κij/ηij represents product quality. We wish to maximize the total expected revenue subject to lower and upper bound constraints, i.e.