A dynamic programming framework for optimal delivery time slot pricing

We study the dynamic programming approach to revenue management in context of attended home delivery. draw on results from theory for Markov decision problems show that underlying Bellman operator has a unique fixed point. then provide closed-form expression resulting point and it admits natural interpretation. Moreover, we also – under certain technical assumptions value function, which discrete domain continuous codomain, extension, is finite-valued, concave function its state variables, at every time step. Furthermore, derive monotonicity prices with respect number orders placed our setting. These open road achieving scalable implementations proposed formulation, as allows making informed choices basis functions an approximate context. illustrate findings low-dimensional industry-sized numerical example using real-world data, approximately optimal pricing policy based theoretical results.