Railway network dynamic pricing under discrete mixed logit demand

Hohberger, Simon ; Schön, Cornelia

Document Type: Conference presentation
Year of publication: 2019
Conference title: INFORMS Revenue Management and Pricing Section Conference
Location of the conference venue: Stanford, CA
Date of the conference: 06.-07.06.2019
Publication language: English
Institution: Business School > ABWL u. Service Operations (Schön 2014-)
Subject: 650 Management
Keywords (English): Dynamic Pricing , Revenue Management , Customer Choice , Mixed Logit
Abstract: Revenue Management is an already widespread method in the passenger rail business. In a survey that we conducted in 2018 with European rail companies we observed that leg-based approaches are still dominant in practice. However, due to the distinct network structure of railway companies, i.e., a resource is used by many different itineraries, an approach that accounts for network effects seems to offer significant additional revenue potential. In our talk, we present a choice-based network dynamic pricing model that is developed in cooperation with Deutsche Bahn Fernverkehr (DB), a leading provider for long-distance passenger transportation in Germany, with over 140 million passengers each year and several millions of pricing decisions daily. In addition to the traditional capacity constraints, the model includes railway specific constraints, such as price consistency constraints that ensure that longer itineraries are more expensive than shorter ones. Further, we use a discrete mixed multinomial logit demand model to represent the choice among different itineraries for different customer segments. A challenge that comes along with this model is that the original formulation is nonlinear, nonconvex and thus not directly solvable to global optimality. In addition, it turns out that solving the original problem formulation is very slow so that large-scale instances cannot be solved within a reasonable time limit specified by practice. While under the classical MNL model a convex representation is already well studied, the convexity does not hold under the assumption of multiple discrete customer segments. Therefore, a different approach is needed in practice that performs well with regard to solution quality and time. We present a heuristic that determines a good solution in reasonable time and show that it leads to increased revenue compared to the current approach used in practice and a classical leg-based EMSRb heuristic. To quantify the revenue improvements, we conducted an extensive simulation study that compares the three models under different scenarios (i.e., different rail network and demand cases). Furthermore, we evaluate the approaches for robustness by randomly adjusting the original choice parameters in the simulation. The results provide an insight into how inaccuracies in demand forecasting influence the performance of the approaches and give a realistic picture of the revenue potential in practice. We analyze the results in two ways: Firstly, we present statistics about the solution time and quality of large-scale networks. Secondly, we show the results in terms of revenue, i.e., compare the revenue of the new model with the two above mentioned benchmark approaches. We show that the O&D based model significantly outperforms both benchmark heuristics in terms of total revenue and that the revenue gap increases in high demand scenarios. Furthermore, even in case of incorrect choice model parameter estimates the revenue gap is still significantly positive, though smaller than in the case of correct forecasts - showing that the O&D based approach is less robust to forecasting errors.

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