SmartMobility: Innovative Mobility and Logistics

The importance of mobility and logistics has steadily increased in recent years. Today, this sector represents a significant part of economic output, but also of resource consumption. In order to achieve the ambitious environmental and climate protection goals, there is a high demand for innovative concepts.

Shared Mobility

In this area we focus on bike and car sharing. They offer considerable potential for saving fossil fuels, particularly in combination with local and long-distance public transport. In recent years, public bicycle rental systems have emerged in many cities around the world. These systems allow automatic rental and return of bicycles at a large number of stations. Modern Car-Sharing providers enable borrowing and returning at almost any parking space within a defined business area (free-floating). We concentrate on the following questions of strategic planning and dimensioning of the systems as well as operations and cooperate with a well-known German free-floating Car-Sharing provider:

  • Design of shared mobility systems: This results in numerous interesting questions that are currently coming more into the focus of research. These include, for example, the positioning and dimensioning of the stations.
  • Operational control of Shared-Mobility/E-Mobility systems: Almost all new public rental systems allow one-way rentals, i.e. the vehicle does not have to be returned to the rental location. In case of asymmetrical demand, however, this requires a regular return transport of the vehicles by the supplier, which causes a considerable part of the current operating costs. For this reason, our research is aimed at minimizing transport costs while maintaining a high level of availability.
  • Pricing of Shared Mobility/E-Mobility Systems:  Compared with the mobile communications market, for example, the tariff structure of shared mobility providers has hardly developed until now. Effective pricing is not only the key to profitability, but can also be used to manage demand operationally, as airlines have long shown. In shared mobility systems, the availability of vehicles can be increased and costly return transports by the provider reduced.


  • Rauhaus, Davina; Gönsch, Jochen; Steinhardt, Claudius: On the value of booking data for upsell decision-making in revenue management. doi:10.1007/s10696-024-09545-xCitationDetails
  • Müller, Christian: Practicable Solution Approaches for Differentiated Pricing of Vehicle Sharing Systems. In: Central European Journal of Operations Research (2024). CitationDetails
  • 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/s00291-023-00732-0Full textCitationDetails

    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, Vol 57 (2023) No 6, p. 1406-1432. doi:10.1287/trsc.2021.0524Full textCitationDetails

    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, Vol 305 (2023) No 3, p. 1194-1214. doi:10.1016/j.ejor.2022.06.058Full textCitationDetails

    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, Vol 56 (2022) No 5, p. 1111-1408. doi:10.1287/trsc.2022.1131Full textCitationDetails

    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 (Ed.): Simulation in Produktion und Logistik 2019. Wissenschaftliche Scripten, Auerbach 2019, p. 519-530. Full textCitationDetails

    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.

  • Kruk, N.; Gönsch, J.: Shared Mobility Systeme – Mathematische Ansätze für Gestaltung und Betrieb. In: WiSt – Wirtschaftswissenschaftliches Studium , Vol 46 (2017) No 6, p. 9-14. CitationDetails



Logistics is one of the oldest areas of application for operations research. Traditionally, the focus here is on increasing efficiency through route and loading optimisation in order to reduce costs and emissions.

The optimization of loading processes for auto carriers and auto trains is a crucial lever for increasing efficiency in automotive logistics. Our research focuses not only on maximizing capacity utilization but also on improving the operational loading process by creating precise loading instructions. For this purpose, we employ various methods of linear and geometric optimization. The validation of our approaches is carried out through case studies in collaboration with a renowned German automobile manufacturer.


  • Jäck, C.; Gönsch, J.: How to load your auto carrier. A hybrid packing approach for the auto-carrier loading problem. In: European Journal of Operational Research, Vol 315 (2024) No 3, p. 1167-1181. doi:10.1016/j.ejor.2024.01.001Full textCitationDetails

    The distribution of new vehicles is a critical cost factor for automotive original equipment manufacturers (OEMs). While trains are the ideal mode for overland transport, OEMs often opt for road transport via auto carriers due to flexibility reasons or unavailability of rail networks. Auto carriers are specialized trucks equipped with flexible loading platforms. Finding the optimal configuration of platforms can be a difficult task due to passenger vehicles varying in size, shape, and weight. This problem is known as the auto-carrier loading problem (ACLP). The current literature deals with the ACLP on a strategic level with the goal to maximize transport capacities. However, it neglects the resulting increase in operational complexity.

    In this paper, we present a hybrid packing approach to solve the ACLP on an operational level. Our approach considers the shapes of the vehicles as polygons and incorporates an approximation of continuous rotation by combining a geometric algorithm with a mixed integer model formulation. We aim not only to maximize loading capacities but also to provide instructions for truck drivers on how to arrange the vehicles on the truck. We conduct a proof of concept (POC) with actual auto carriers to verify the feasibility of our approach and to quantify potential benefits for our industry partner. The POC confirms that our approach reliably generates feasible and comprehensive loading instructions. Not only could the implementation of our approach reduce lead times and transportation damages, but in addition, could completely automate the manual load creation process in distribution centers.

  • Jäck, C.; Gönsch, J.; Dörmann, H.: Load Factor Optimization for the Auto-Carrier Loading Problem (ACLP). In: Transportation Science, Vol 57 (2023) No 6, p. 1696-1719. doi:10.1287/trsc.2022.0373Full textCitationDetails

    The distribution of passenger vehicles is a complex task and a high cost factor for automotive original equipment manufacturers (OEMs). On the way from the production plant to the customer, vehicles travel long distances on different carriers, such as ships, trains, and trucks. To save costs, OEMs and logistics service providers aim to maximize their loading capacities. Modern auto carriers are extremely flexible. Individual platforms can be rotated, extended, or combined to accommodate vehicles of different shapes and weights and to nest them in a way that makes the best use of the available space. In practice, finding feasible combinations is done with the help of simple heuristics or based on personal experience. In research, most papers that deal with auto carrier loading focus on route or cost optimization. Only a rough approximation of the loading subproblem is considered. In this paper, we present two different methodologies to approximate realistic load factors considering the flexibility of modern auto carriers and their height, length, and weight constraints. Based on our industry partner’s process, the vehicle distribution follows a first in, first out principle. For the first approach, we formulate the problem as a mixed integer, quadratically constrained assignment problem. The second approach considers the problem as a two-dimensional nesting problem with irregular shapes. We perform computational experiments using real-world data from a large German automaker to validate and compare both models with each other and with an approximate model adapted from the literature. The simulation results for the first approach show that, on average, for 9.37% of all auto carriers, it is possible to load an additional vehicle compared with the current industry solution. This translates to 1.36% less total costs. The performance of the nesting approach is slightly worse, but as it turns out, it is well-suited to check load combinations for feasibility.

  • Jäck, Christian: Comparing Loading Strategies for Auto Trains: Balancing Efficiency with Information Requirements. 2024. CitationDetails


Airline Schedule Planning for Low Cost Carriers (completed)

Airlines today are exposed to high pressure on costs, which will continue to rise as a result of the CO2 tax, for example. This forces them to use their capacities efficiently. The precondition for this is a flight schedule that is as attractive as possible for potential passengers, both in terms of the connections and the flight times. The design of corresponding flight schedules at the medium-term planning level is an extremely complex decision-making problem that can only be successfully tackled with the aid of quantitative methods.

The project focuses on the following two aspects:

  • How can the expected demand for a given flight schedule be adequately forecasted, taking into account the short-term effects of fleet assignments and revenue management?
  • Which subproblems can/should be considered simultaneously in an integrated optimization model - especially against the background of the special requirements of a low cost carrier - and how can these optimization problems be solved?


  • Faust, O.; Gönsch, J.; Klein, R.: Demand-oriented Integrated Scheduling for Point-to-Point Airlines. In: Transportation Science, Vol 51 (2017) No 1, p. 196-213. PDFFull textCitationDetails

    Optimizing an airline schedule usually comprises multiple planning stages. These are the choice of flights to offer (schedule design), the assignment of fleets to flight legs (fleet assignment), and the construction of rotations under consideration of maintenance constraints (aircraft maintenance routing). Moreover, the airline must assign crews to all flights (crew scheduling). Traditionally, either these scheduling stages are considered sequentially or an existing schedule is modified to cope with the arising complexity issue. More recently, some authors have developed models that integrate adjacent stages. In this paper, outcomes of a research project with airline information technology provider Lufthansa Systems are presented. We consider the case of a small to medium-sized point-to-point airline with a homogeneous fleet. Hence, fleet assignment is omitted, which offers the possibility to solve schedule design and aircraft maintenance routing simultaneously. Our approach explicitly accounts for passengers’ return flight demand and for marginal revenues declining with increasing seat capacity, hence, anticipating the effects of capacity control in revenue management systems. To solve the arising integrated mixed-integer problem, a branch-and-price approach and a column generation-based heuristic have been developed. An extensive numerical study, using data from a major European airline provided by Lufthansa Systems, shows that the presented approaches yield high-quality solutions to real-world problem instances within a reasonable time.

  • Gönsch, J.: Airline Schedule Planning — Grundlagen und aktuelle Entwicklungen. In: WiSt – Wirtschaftswissenschaftliches Studium (2010) No 39, p. 230-235. CitationDetails