In classical optimization problems under discrete choice models, the decision maker can control at most one attribute for each choice . Usually, this attribute is the price of a product . However, price is not the only attribute that can impact both the product's market share and profit margin. This paperstudies a generalization of these problems, which allows multiple attributes to be controlled for each choice of product. Past research showed that we can solve the classical optimization problems efficiently , using methods like the market share reformulation. However, these methods do not apply to the generalized problems. 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 .
In classical optimization problems under discrete choice models, the decision maker control one attribute of each product . Usually, that attribute is the product's price . However, price is not the only attribute that can impact both the product's market share and profit margin. In this paper, we generalize the classical price optimization problem to allow multiple attributes to be controlled over each choice of product. Past research showed that the classical price optimization problem can be solved efficiently under many choice models , using methods such as the market share reformulation. However, these methods cannot be applied to the generalized problem. We show that the generalized problem is still tractable under the multinomial logit (MNL), the nested logit (NL) and the Markov chain (MC) choice model. Such problems can still be transformed into convex programs , 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 .
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we can solve the classical optimization problems efficiently
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problems. We showed that such problems are still tractable
problem. We show that the generalized problem is still tractable under the multinomial logit (MNL), the nested logit (NL) and the Markov chain (MC) choice model. Such problems can still be transformed into convex programs
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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
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