Dynamic Pricing and Capacity Optimization in Railways

Abstract

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 throughout the sales horizon. Consequently, the joint optimization of prices and capacity assumes genuine importance. (ii) Capacity can only be added in discrete "chunks", i.e., coaches. (iii) Passengers with unreserved tickets can travel in any of the multiple trains available during the day. Further, passengers in unreserved coaches are allowed to travel by standing, thus giving rise to the need to manage congestion. Motivated by our work with a major railway company in Japan, we analyze the problem of jointly optimizing pricing and capacity – this problem is a more-general version of the canonical multiproduct dynamic-pricing problem. Methodology/Results: Our analysis yields four asymptotically optimal policies. From the viewpoint of the pricing decisions, our policies can be classified into two types – static and dynamic. With respect to the timing of the capacity decisions, our policies are again of two types – fixed capacity and flexible capacity. We establish the convergence rates of these policies: when demand and supply are scaled by a factor $\kappa$, the optimality gaps of the static policies scale proportional to $\sqrt{\kappa}$, and those of the dynamic policies scale proportional to $\log\kappa$. We numerically illustrate the attractive performance of our policies on a test-suite of instances based on real-world operations of the high-speed “Shinkansen” trains in Japan, and develop associated insights. Managerial implications: Our work provides railway administrators with simple and effective policies for pricing, capacity, and congestion management. Our policies cater to different contingencies that decision-makers may face in practice: the need for static or dynamic prices, and for fixed or flexible capacity.

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