Real-time dynamic pricing for multiproduct models with time-dependent customer arrival rates

In this article, we study the revenue management problem of multiproduct dynamic pricing in the retail industry. Given a fixed initial inventory and assortment, the retailer monitors the inventory and sets the price to affect the behavior of customer choices over a selling season. We consider the Multinomial Logit (MNL) model of customer choice over substitutes and formulate the problem of optimal dynamic pricing as an optimal stochastic intensity control problem. We derive the optimal dynamic pricing policy for the MNL model with a time-dependent customer arrival rate. Furthermore, we propose a real-time dynamic pricing (RTDP) procedure that provides on-line optimal dynamic pricing policies based on the estimation of total customer arrivals over the entire selling season. This method is realized by a simple integral transformation by which a time-inhomogeneous model is transformed to time-homogeneous with a constant customer arrival rate. A dynamic programming based numerical algorithm is presented to compute the optimal solutions and to demonstrate the robustness of the RTDP procedure.