Vehicle sharing systems have become increasingly popular. However, one-way vehicle sharing system providers face a major challenge. The uneven distribution of vehicles across locations caused by the uneven nature of the demand patterns poses a problem, since there are accumulations of vehicles where the demand is low. This challenge can be solved with an appropriate pricing approach that creates incentives for user-based relocation by considering supply-side network effects. While the literature mostly focuses on trip-based pricing, we were inspired by the majority of car sharing providers who use origin-based minute pricing that differentiates based on the origins of rentals, such as Share Now. Therefore, we develop two different and practicable solution approaches to determine spatially and temporally differentiated origin-based minute prices that take into account supply-side network effects. The first solution approach does not differentiate between rentals and demand and calculates continuous prices for every period and location. The second solution approach determines the vehicle distribution for each period and then calculates the optimal prices for each period backwards. Extensive computational experiments show that our solution approaches anticipate supply-side network effects and thus generate a near-optimal profit in less computational time compared to more complex benchmarks from the literature. In a sensitivity analysis we additionally show that the results are robust against stochasticity of demand and that the solution approaches perform well for different price sets.

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
profit.

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.

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.

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.

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.

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.

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.

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.