Dr. Christian Müller

Wissenschaftlicher Mitarbeiter

Dr. Christian Müller

LC 011a
+49 203 37-94313
Nach Vereinbarung
Universität Duisburg-Essen
Mercartor School of Management
Lehrstuhl für Betriebswirtschaftslehre, insbesondere Service Operations
Lotharstraße 65
47057 Duisburg


seit 04/2017:

Wissenschaftlicher Mitarbeiter am Lehrstuhl für Betriebswirtschaftslehre, insb. Service Operations


  • Müller, C.: Practicable Solution Approaches for Differentiated Pricing of Vehicle Sharing Systems, 2024. BIB DownloadDetails
  • Müller, C.; Gönsch, J.; Albrecht, L.; Staskiewicz, M.: Dynamic Pricing for Car Sharing Systems Reduces CO2 Emissions, 2024. BIB DownloadDetails
  • Müller, C.; Gönsch, J.; Albrecht, L.; Staskiewicz, M.: Optimizing Citrus Production by considering Food Waste, 2024. BIB DownloadDetails
  • Müller, C.; Gönsch, J.; Soppert, M.; Steinhardt, C.: Dynamic Pricing for Shared Mobility Systems Based on Idle Time Data. In: OR Spectrum (2023). doi:10.1007/s00291-023-00732-0VolltextBIB DownloadDetails

    In most major cities today, various shared mobility systems such as car or bike sharing
    exist. Maintaining these systems is challenging, and, thus, public and private
    providers strive to improve operational performance. An important metric which is
    regularly recorded and monitored in practice for this purpose is idle time, i.e., the
    time a vehicle stands unused between two rentals. Usually, it is available for different
    temporal and spatial granularities. At the same time, dynamic pricing has been
    shown to be an efficient means for increasing operational performance in shared
    mobility systems, but data necessary for traditional dynamic pricing approaches,
    like unconstrained demand, is much less available in practice. Thus, dynamic pricing
    based on idle time data appears promising and first ideas have been proposed.
    However, the existing approaches are based either on simple business rules or on
    myopic optimization. In this work, we develop a novel dynamic pricing approach
    that determines prices by online optimization and thereby anticipates future profits
    through the integration of idle time data. The core idea is quantifying the remaining
    profitable time by using idle times. With regard to application in practice, the
    developed approach is generic in the sense that different types of readily available
    historical idle time data can be seamlessly integrated, meaning data of different
    spatio-temporal granularities. In an extensive numerical study, we demonstrate that
    the operational performance increases with higher granularity and that the approach
    with the highest one outperforms current pricing practice by up to 11% in terms of

  • Müller, C.; Gönsch, J.; Soppert, M.; Steinhardt, C.: Customer-Centric Dynamic Pricing for Free-Floating Vehicle Sharing Systems. In: Transportation Science, Jg. 57 (2023) Nr. 6, S. 1406-1432. doi:10.1287/trsc.2021.0524VolltextBIB DownloadDetails

    Free-floating shared mobility systems offer customers the flexibility to pick up and drop off vehicles at any location within the business area and, thus, have become the most popular type of shared mobility system. However, this flexibility has the drawback that vehicles tend to accumulate at locations with low demand. To counter these imbalances, pricing has proven to be an effective and cost-efficient means. The fact that customers use mobile applications, combined with the fact that providers know the exact location of each vehicle in real-time, provides new opportunities for dynamic pricing.

    In this context, we develop a pricing approach for the dynamic online problem of a provider who determines profit-maximizing prices whenever a customer opens the provider’s mobile application to rent a vehicle. Our pricing approach has three distinguishing features: First, it is customer-centric, i.e., it considers the customer’s location as well as disaggregated choice behavior to precisely capture the effect of price and walking distance to the available vehicles on the customer’s propensity to choose a vehicle. Second, our pricing approach is origin-based, i.e., prices are differentiated by location and time of rental start, which reflects the real-world situation where the rental destination is usually unknown. Third, our approach is anticipative and uses a stochastic dynamic program to anticipate the effect of current decisions on future vehicle locations, rentals, and profits. As solution method, we propose a non-parametric value function approximation, which offers several advantages for the application, e.g., historical data can readily be used and main parameters can be pre-computed such that the online pricing problem becomes tractable. Extensive numerical studies, including a case study based on Share Now data, demonstrate that our approach increases profits by up to 13% compared to existing approaches from the literature and other benchmarks.

  • Soppert, M.; Steinhardt, C.; Müller, C.; Gönsch, J.; Bhogale, P.: Matching Functions for Free-Floating Shared Mobility System Optimization to Capture Maximum Walking Distances. In: European Journal of Operational Research, Jg. 305 (2023) Nr. 3, S. 1194-1214. doi:10.1016/j.ejor.2022.06.058VolltextBIB DownloadDetails

    Shared mobility systems have become a frequently used inner-city mobility option. In particular, free-floating shared mobility systems are experiencing strong growth compared to station-based systems. For both, many approaches have been proposed to optimize operations, e.g., through pricing and vehicle relocation. To date, however, optimization models for free-floating shared mobility systems have simply adopted key assumptions from station-based models. This refers, in particular, to the models’ part that formalizes how rentals realize depending on available vehicles and arriving customers, i.e., how supply and demand match. However, this adoption results in simplifications that do not adequately account for the unique characteristics of free-floating systems, leading to overestimated rentals, suboptimal decisions, and lost profits.

    In this paper, we address the issue of accurate optimization model formulation for free-floating systems. Thereby, we build on the state-of-the-art concept of considering a spatial discretization of the operating area into zones. We formally derive two novel analytical matching functions specifically suited for free-floating system optimization, incorporating additional parameters besides supply and demand, such as customers’ maximum walking distance and zone sizes. We investigate their properties, like their linearizability and integrability into existing optimization models. Our computational study shows that the two functions’ accuracy can be up to 20 times higher than the existing approach. In addition, in a pricing case study based on data of Share Now, Europe’s largest free-floating car sharing provider, we demonstrate that more profitable pricing decisions are made. Most importantly, our work enables the adaptation of station-based optimization models to free-floating systems.

  • Soppert, M.; Steinhardt, C.; Müller, C.; Gönsch, J.: Differentiated Pricing of Shared Mobility Systems Considering Network Effects. In: Transportation Science, Jg. 56 (2022) Nr. 5, S. 1111-1408. doi:10.1287/trsc.2022.1131VolltextBIB DownloadDetails

    Over the last decades, shared mobility systems have become an integral part of inner-city mobility. Modern systems allow one-way rentals, i.e. customers can drop off the vehicle at a different location to where they began their trip. A prominent example is car sharing. Indeed, this work was motivated by the insight we gained in collaborating closely with Europe's largest car sharing provider, Share Now. In car sharing, as well as in shared mobility systems in general, pricing optimization has turned out to be a promising means of increasing profit while challenged by limited vehicle supply and asymmetric demand across time and space. Thus, in practice, providers increasingly use minute pricing that is differentiated according to where a rental originates, i.e., considering its location and the time of day. In research, however, such approaches have not been considered yet. In this paper, we therefore introduce the corresponding origin-based differentiated, profit-maximizing pricing problem for shared mobility systems. The problem is to determine spatially and temporally differentiated minute prices, taking network effects on the supply side as well as several practice relevant aspects into account. Based on a deterministic network flow model, we formulate the problem as a mixed-integer linear program and prove that it is NP-hard. For its solution, we propose a temporal decomposition approach based on approximate dynamic programming. The approach integrates a value function approximation to incorporate future profits and account for network effects. Extensive computational experiments demonstrate the benefits of capturing such effects in pricing generally, as well as showing our value function approximation's ability to anticipate them precisely. Further, in a case study based on Share Now data from Florence in Italy, we observe profit increases of around 9% compared to constant uniform minute prices, which are still the de facto industry standard.

  • Christian Müller, Jochen Gönsch: Simulation zur Evaluation der Optimierung eines Bikesharing-Systems. In: Matthias Putz, Andreas Schlegel (Hrsg.): Simulation in Produktion und Logistik 2019. Wissenschaftliche Scripten, Auerbach 2019, S. 519-530. VolltextBIB DownloadDetails

    Bike sharing has been introduced in many cities, often by municipalities and is nowadays an established alternative for other short-distance transport systems. However, in cities with high elevations, the usual bike-sharing systems face a severe problem. Resulting from an imbalance of demand, the number of bikes at stations at elevated locations decreases during the day, while it increases at stations at lower locations. This situation poses a challenge for the relocation process because high numbers of bicycles have to be transported to the stations at elevated locations in order to achieve a suitable starting point for the next period. With the usage of e-bike sharing-systems, this problem can be circumvented because e-bikes facilitate the mobility in elevated and steep terrains. This paper considers an e-bike sharing-system with removable batteries. In the first step, a deterministic Mixed-Integer Linear Program (MILP) calculates the optimal route for trucks and the optimal initial distribution of bikes. In the second step, a stochastic simulation should evaluate these results.


  • Müller, Christian: Customer-centric dynamic pricing for freefloating car sharing, OR Bern 2021, 01.09.2021, Bern. Details
  • Müller, Christian: Dynamic Pricing in Shared Mobility Systems, EURO Athen 2021, 13.07.2021, online. Details
  • Müller, Christian: Customer-centric dynamic pricing for freefloating carsharing, Pricing Workshop, 10.05.2021, online. Details
  • Christian Müller, Matthias Soppert: Pricing for Shared Mobility Systems, Intensiv-Workshop Operations Research 2019, 08.10.2019, Würzburg. Details
  • Müller, Christian: Simulation zur Evaluation der Optimierung eines Bikesharing-Systems, 18. ASIM Fachtagung: Simulation in Produktion und Logistik, 19.09.2019, Chemnitz. Details
  • Müller, Christian: Price list optimization for freefloating carsharing, Operations Research Conference 2019, 05.09.2019, Dresden. Details
  • Christian Müller, Matthias Soppert: Price list optimization for car-sharing, 4. Pricing Workshop, 05.12.2018, Obergurgl. Details
  • Müller, Christian: Optimization of an e-bike-sharing-system with dynamic relocation, Operations Research Conference 2018, 12.09.2018, Brüssel. Details
  • Müller, Christian: Shared Mobility: E-Bike-Sharing, BKM Doctoral Workshop, 24.07.2018, Kingston Business School, London. Details
  • Müller, Christian: Shared Mobility: E-Bike-Sharing, 28. Quantitative BWL, 14.03.2018, Odenwald. Details
  • Müller, Christian: Shared Mobility: E-Bike-Sharing, Intensiv-Workshop Operations Research 2017, 04.10.2017, Würzburg. Details