Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A common problem faced in economics is to decide the pricing of products of a company, since poorly chosen prices might lead to low profit. One important model for this is the unit-demand envy-free pricing problem, in which one considers that every consumer buys an item that maximizes his own profit, and the goal is to find a pricing of the items that maximizes the expected profit of the seller. This is a practical and interesting problem which is, unfortunately, not in  APX unless P=NP.  present two new MIP formulations for this problem and experimentally compare them to previous ones from the literature.  describe three models to generate different random instances for general unit-demand auctions, that  designed for the computational experiments. Each model has a nice economic interpretation. Our results show that one of our MIP formulations can sometimes lead to better results than the previous ones from the literature.  also consider a variant of the network pricing problem in which one has to price toll arcs in a highway, and prove that it is as hard to approximate as the envy-free pricing problem.
['Cristina G. Fernandes', 'Carlos Eduardo Ferreira', 'Álvaro Junio Pereira Franco', 'Rafael C. S. Schouery']
I am writing a research paper on a idea The envy-free pricing problem, unit-demand markets and connections with the network pricing problem
[{"from": "human", "value": "I am writing a research paper on a idea The envy-free pricing problem, unit-demand markets and connections with the network pricing problem"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A common problem faced in economics is to decide the pricing of products of a company, since poorly chosen prices might lead to low profit. One important model for this is the unit-demand envy-free pricing problem, in which one considers that every consumer buys an item that maximizes his own profit, and the goal is to find a pricing of the items that maximizes the expected profit of the seller. This is a practical and interesting problem which is, unfortunately, not in\u00a0 APX unless P=NP.  present two new MIP formulations for this problem and experimentally compare them to previous ones from the literature.  describe three models to generate different random instances for general unit-demand auctions, that  designed for the computational experiments. Each model has a nice economic interpretation. Our results show that one of our MIP formulations can sometimes lead to better results than the previous ones from the literature.  also consider a variant of the network pricing problem in which one has to price toll arcs in a highway, and prove that it is as hard to approximate as the envy-free pricing problem."}]