Problem definition: Revenue management in railways distinguishes itself from that in traditional sectors such as airline, hotel, and fashion retail, in several important ways: (i) Capacity is substantially more flexible, in the sense that changes to the capacity of a train can often be made...

We study fixed-dimensional stochastic dynamic programs in a discrete setting over a finite horizon. Under the primary assumption that the cost-to-go functions are discrete L♮-convex, we propose a pseudo-polynomial time approximation scheme that solves this problem to within an arbitrary...