Optimizing dynamic pricing problem under multinomial demand models using a convex nonlinear programming approach

The addressed problem considers a market model where a firm produces and sells a single product over a finite horizon divided into different periods. The firm aims to set the price of each period such that the total profit is maximized, while also satisfying constraints on available production capacity and price bounds. The market demand for each period is represented by the multinomial logit (MNL) model. This problem has been previously tackled in the literature, where it was formulated as a non-convex nonlinear programming (NLP) model. The solution approach involved the integration of neural networks and evolutionary algorithms. In this paper, the initial non-convex (NLP) model is transformed into a convex one based on properties of the MNL model. This new formulation enables the resolution of the addressed problem in an optimal way. A large experimental study is carried out to evaluate the solution quality and computational times of the two models. The obtained results show the effectiveness of the convex formulation compared to the non-convex one.