Before revision:  We showed that such problems are still tractable , and can be solved efficiently as conic programs. This argument applies to optimization problems under multinomial logit models, and applies to problems under nested logit models when certain assumptionshold. These generalized problems are very common in retail and transportation industries.This paper allows practitioners to solve such problemsdirectly using commercial solvers .
After revision:  We showed that such problems are still tractable , and optimal solutions exist under certain assumptions. We also show that linear constraints in market shares (e.g. resource constraints) can be added to the optimization problems, and the tractability results still hold .