Vehicle Relocation in One-Way Carsharing: A Review

Abstract

Carsharing has become increasingly popular in recent years as a sustainable transportation solution, offering individuals access to shared vehicles on a short-term basis. One-way carsharing, in particular, presents unique challenges due to its flexible nature, allowing users to pick up and drop off vehicles at different locations within a designated service area. This flexibility increases the service ridership but comes at the expense of vehicle imbalance among the stations, as some stations may have excess vehicles while other stations have vehicle shortages. Therefore, carsharing companies need to decide on strategies to ensure a balanced distribution of vehicles among the stations. This is essential as unbalanced vehicle distribution can lead to an unavailability of vehicles when needed or, conversely, result in an increased number of unnecessary rebalancing trips, thereby exacerbating traffic congestion and environmental pollution. Such issues can potentially undermine the overall contribution of carsharing to urban sustainability. To this end, this paper reviews the vehicle imbalance problem that arises in this field and the solution algorithms that solve them.

1. Introduction

Carsharing services (CSSs) have gained more attention and interest from both industry and academia. Numerous car rental agencies started to provide one-way CSsS in addition to conventional rental services. Global Market Trends estimated that the CSS market size exceeded 2 billion USD in 2020, and the annual growth rate is expected to grow by over 24% by 2026.

Carsharing is an attractive mobility option due to its various advantages. Carsharing is a cost-effective mobility option as users only pay for the time and distance they use the car for, eliminating expenses associated with vehicle ownership like insurance and maintenance [1]. Refraining from owning a car would require individuals to limit their travels to essential trips, resulting in a reduction in the overall number of vehicles on the roads, leading to lower carbon emissions and congestion [2]. It was shown by [3] that carsharing can decrease CO₂ emissions by between 3% and 18%. Moreover, it can complement public transit systems, providing first- and last-mile connectivity and therefore promoting sustainable urban mobility [2,4,5].

There are two business models in which carsharing operates, either free-floating or station-based [6]. In free-floating systems, vehicles are distributed among service areas, and commuters can check their availability using their mobile phones [6]. In station-based systems, however, commuters can pick up or drop off a vehicle from a designated carsharing station. For a review of the operations and management of free-floating carsharing systems, readers can refer to the work of [7]. In particular, the authors have reviewed the optimization models for service region design and fleet balancing in detail. The focus of this paper is on station-based carsharing.

There are two types of station-based carsharing: one-way and two-way. The latter mandates users to pick up and return the car to the same location. In contrast, the former offers a more flexible and convenient option as commuters can pick up and return the vehicle from different stations. Figure 1 shows the key difference in operating two-way and one-way carsharing. However, the flexibility associated with operating a one-way CSS is associated with an operational challenge of vehicle balancing among the network’s stations, as some stations may have excess vehicles while others may have a shortage of vehicles throughout the day. Vehicle unavailability at certain stations can cause demand losses and poor service levels. Therefore, operating one-way station-based carsharing faces a huge operational challenge of vehicle balancing. Two commonly used strategies were explored to achieve system balance in practice in the literature: demand management and vehicle relocation strategies.

Demand management, on the one hand, can be achieved either through trip selection or through dynamic trip pricing. The former allows the carsharing operator to choose profitable trips from a total demand, i.e., the operator does not necessarily need to fulfill all the commuting requests [8]. Dynamic pricing imposes high rental rates for trips that increase imbalances and lower fares for trips that improve the system’s balance, as in the work of [9]. However, commuters’ acceptance of discounted trips to balance the system is not guaranteed. Vehicle relocation strategies, on the other hand, mandate vehicle movement between stations to achieve vehicle balance, and they can be user-based (UB) or operator-based (OB) relocation.

UB relocation is usually carried out through customer incentivization, where commuters are incentivized to change the pickup or delivery station or the vehicle access time. This way, the customer may choose a less-favorable location to reduce the balancing problem. Carsharing operators yet need to find the optimal destination for a commuter to drop off the vehicle, the optimal incentive value, and the prediction of the commuter’s willingness to accept the incentivized trip [10]. The authors in [11] showed that substantial profit can be realized when commuters are incentivized to be more flexible in their choice of pickup and delivery locations.

OB relocation, on the other hand, necessitates the operator to relocate the vehicles, which has been studied by [12,13]. Operators either utilize part-time staff [14] or full-time staff [15,16] to perform the vehicle relocations. A trade-off between the staff and fleet sizes is among the key tactical decisions to be made by the operator. For example, hiring a relatively large fleet and distributing it among stations would lower the need for vehicle relocation and, therefore, the number of relocation staff hired. Several operational decisions should be made when operating an OB relocation, such as staff and vehicle routing and scheduling to ensure vehicle availability.

Let us consider the following example to distinguish between UB and OB relocation. In Figure 2a, the original commuter’s route using a shared vehicle is from $S_1$ to $S_2$. However, since $S_2$ has an excess of vehicles while $S_3$ has a shortage of vehicles, the carsharing operator offers an incentivized trip (i.e., a lower commuting price) if the commuter slightly alters their route to drive the shared vehicle from $S_1$ to $S_3$, drop the vehicle there, and then use a different commuting mode (such as Uber or bicycle) to move to the final destination. If the commuter accepts the alternative routes, the shared vehicle is placed at a station that has a shortage of vehicles $S_3$ instead of increasing the number of vehicles at $S_2$, which has an excess of vehicles. In Figure 2b, in order to relocate a vehicle to $S_3$ (which has a shortage of vehicles), a relocation employee is hired to move from $S_3$, either by public transportation or bike, to $S_2$ (which has an excess of vehicles). Then, the operator drives the shared vehicle to $S_3$, where it can be used.

As described above, trip pricing to control the demand does not guarantee system balance. Moreover, UB relocation is usually for short-distance relocations as it causes the users to alter their origin or destination slightly. Therefore, it cannot guarantee a balanced system, even if all commuters accept the incentives for vehicle relocations. Therefore, carsharing operators must accompany pricing strategies or UB relocations with OB relocations to guarantee system balance. Therefore, we focus in this study on OB vehicle relocation formulations.

This paper aims to review the operational research issues arising in operating-station-based one-way carsharing and the proposed solution approaches to address them. The aim is to provide scholars and carsharing operators with an overview of how to relocate vehicles effectively to ensure vehicle availability and, therefore, increase carsharing ridership over private car ownership [17] on one hand. On the other hand, finding optimal routes and optimal vehicle assignment to relocation staff can decrease the total miles driven and, hence, lower the emissions generated. We review the vehicle balancing problem that arises in operating one-way carsharing. Although this is an operational problem, there exists a connection between these challenges and strategic as well as tactical considerations. Therefore, we review studies that address strategic, tactical, and operational aspects, particularly those related to optimizing the OB relocation of vehicles. In particular, we review vehicle rebalancing, resource dimensioning and allocation, trip pricing, and station decisions. For each topic, we present an overview of the problem and describe selected solution approaches that we think are important. We further extend the review to include how the three-level decisions can impact commuters’ travel behavior and acceptance of the carsharing service. In other words, we review studies that simultaneously considered the operator’s decisions and the commuters’ convenience when planning the operation on one-way CSSs.

In this review, we answer the following research questions for a carsharing operator who aims to operate a one-way carsharing system or for a researcher who aims to optimize carsharing operations: (1) How can vehicle balancing operations that are needed to ensure vehicle availability within the network stations be optimized? (2) How can the associated decisions regarding the staff and fleet sizes be optimized, and what are their optimal locations? (3) How can the trip pricing be optimized while considering vehicle relocation? Finally, (4) How should carsharing stations’ location and their capacity be optimized to maximize the benefits of carsharing?

The works of [18,19] inspire this research. The authors in [18] surveyed the operational research issues in shared mobility in general. The authors successively reviewed the strategic, tactical, and operational decisions from the operations research point of view and reviewed methods that solve these problems. Meanwhile, [19] have addressed the service operation issues of one-way carsharing systems, theoretically, from various aspects and scopes. However, our work is different in terms of focusing on and analyzing the mathematical formulations and the solution algorithms that arise during the operation of one-way carsharing. Moreover, this is still an active field, and several research dimensions have emerged since.

2. Vehicle Rebalancing

OB vehicle relocation can be either predictive or non-predictive [20]. Predictive rebalancing is when the operator utilizes the historical trip transactions or complete vehicle reservation information to plan the relocation proactively. Non-predictive relocation, or immediate relocation, refers to the immediate fulfillment of the relocation demand [21].

The predictive rebalancing approach is performed in two steps: relocation needs determination and relocation plan execution as in the work of [20]. In the former, the operator estimates the commuter’s vehicle’s pickup and drop off at the network’s stations, then vehicle inventory at these stations is estimated, and, finally, relocation needs are computed. In the latter, the network flow model is optimized, where the operator first determines the upper and lower vehicle threshold at stations. Then, an optimal relocation plan is performed so that the difference between the estimated inventory level and the thresholds is minimized.

The authors in [22] also studied predictive relocation, where the authors used the Markovian model to approximate the stations’ future states, and then the rebalancing strategy was optimized accordingly. We are unaware of the existence of another optimization-based proactive relocation modeling approach. Non-predictive relocation can be either static or dynamic [18,20].

Static rebalancing refers to the case where vehicles’ movement is only performed by relocation staff while no commuters’ demands influence the relocation. This is commonly observed when performing overnight relocation with no commuter vehicle demand. This type of relocation is relatively easier to solve due to lower uncertainty. While overnight relocation helps redistribute vehicles after a day’s use, it may not effectively address the fluctuations in demand and usage patterns that occur throughout the day. Overnight relocation was studied by [14]. An integer programming model to solve the overnight vehicle rebalancing problem was proposed. The authors considered the hiring of temporary workers to redistribute vehicles. The model aims to minimize the total rebalancing costs while fulfilling the commuters’ demands by developing relocators’ employment plans and schedules. Workers were allowed to move only using the shared vehicles that could be shared with other temporary workers. To minimize movement costs, return restriction constraints were incorporated into the model, ensuring that the last movement of each relocator would be back to their original location. This way, participating relocators would not be required to bear the cost of participating in the relocations operation. The authors proposed an iterative optimization approach to solve large-scale relocation problems. It was shown that using a time-based salary reduces about 49% of working hours and about 34% of relocation costs.

Similar to the work in [14], The authors of [23] work have considered vehicle movement only by relocation staff. The authors presented a stochastic, mixed-integer program (MIP) to create a least-cost vehicle relocation plan while the stations’ demand is satisfied with a probability of at least p. The model assesses each station’s short-term planning period, the fleet size, and available parking spaces. If there is a shortage of vehicles, then vehicle movement is needed from a neighbor station. If the parking space at a station exceeds a threshold, then vehicle movement to a neighbor station is carried out to satisfy the demand with a certain probability. Two distinct algorithms were introduced for efficiently solving stochastic programs in which randomness affects only the constraints’ right-hand side. These algorithms are based on the concept of p-efficient points.

More formally, each station i is characterized by a capacity $C_i$ and initial vehicle number $V_i$. Moreover, there is a demand for vehicles and for parking spaces denoted by a random variable of known distributions ${\zeta }_i^v$ and ${\zeta }_i^s$, respectively. The demand must be fulfilled with a probability of at least p. The relocation costs between stations i and j are denoted by $a_{ij}$, and there is an additional penalty cost for each relocated vehicle $\delta$. Binary decision variables $x_{ij}$ indicate whether a vehicle is relocated from i to j. An integer decision variable $y_{ij}$ presents the number of vehicles relocated from i to j. The mathematical model is formulated as the following:

$$\begin{array}{}\mathrm{(1)}& \hfill \min \sum _{i,j\in N}^{}(a_{ij}{x}_{ij}+\delta y_{ij})\hfill \mathrm{(2)}& \mathrm{s}.\mathrm{t}.P_r\left(\begin{array}{c}{V}_i+\sum _{j=1}^n(y_{ji}-y_{ij})+{\zeta }_i^s\ge {\zeta }_i^v,i\in N\hfill \\ C_i-V_i+\sum _{j=1}^n(y_{ij}-y_{ji})+{\zeta }_i^s\ge {\zeta }_i^v,i\in N\hfill \end{array}\right)\ge p\hfill \mathrm{(3)}& \sum _{j\in N}{y}_{ij}\le V_i\hfill & \hfill \forall i\in N\mathrm{(4)}& \sum _{j\in N}{y}_{ji}\le C_i-V_i\hfill & \hfill \forall i\in N\mathrm{(5)}& y_{ij}\le M{x}_{ij}\hfill & \hfill \forall i,j\in N\mathrm{(6)}& y_{ij}\ge 0\mathrm{and}\mathrm{integer},x_{ij}\in \{0,1\}\hfill & \hfill \forall i,j\in N\end{array}$$

The objective (1) is to minimize the relocation costs. Constraints (2) ensure that the demand (for both the vehicles and parking spaces) is satisfied with a probability of at least p. Constraints (3) ensure that the total number of relocated vehicles out of a station cannot exceed its initial inventory $V_i$, while Constraints (4) ensure that the number of relocated vehicles to a station i cannot exceed its capacity. Constraints (5) are proposed to link x and y, where M is a large number.

The authors conducted thorough computational experiments using actual data obtained from the Singapore carsharing system. The system consisted of 14 stations, a combined capacity of 202 spaces, and a fleet of 94 vehicles. They conducted simulation studies and found that the suggested solution strategies were effective and reliable. Furthermore, they analyzed the trade-offs between relocation costs and the service level provided. The authors assumed an unrealistic assumption of relocation staff availability for relocation operations. Modeling the relocators’ routes and schedules is vital in ensuring vehicle availability and system profitability.

Another stream of research formulated the static relocation problem as a set of relocation pickup and delivery requests, i.e., requests to move a vehicle out of a station to prevent it from running out of parking lots and requests to deliver vehicles to a station to prevent it from running out of vehicles, respectively. We review two research works on this topic.

Determining the set of pickup and delivery requests of shared vehicles and finding the optimal relocators’ routes to serve these requests to maximize the operator’s profit was solved by [24]. The authors formulated a set-packing model to solve the problem and developed a branch-and-cut-and-price algorithm. Specifically, the developed algorithm is a branch-and-bound algorithm in which a column generation method is first applied in the branch-and-bound branch, followed by the linearization of the problem using a relaxation method.

The authors determined only the routes of the relocation staff to serve the pickup and delivery requests separately. The authors in [25], on the other hand, optimally found the routes and schedules of the relocation staff to maximize the number of served requests by considering pickup and delivery pairs. The authors proved the efficiency of their model in terms of running time and solution quality compared with treating the pickup and delivery requests separately. The authors considered staff route familiarity, which is measured as the ratio of time reduction in a familiar staff’s relocation time to the unfamiliar staff’s relocation time. For example, higher road familiarity leads to a lower relocation time and distance, especially in complex road conditions where the unfamiliar staff will find it difficult to reach the destination even with the powerful navigation function of Google Maps.

Dynamic vehicle relocations refer to the case where commuters can also move the shared vehicles during the OB relocations. The authors in [26] proposed two formulations for operating and non-operating hours. The former model optimizes the operator’s profit by solving an exact model for relocation operations that determines, at the beginning of the day and for each vehicle, the optimal initial location. The overnight relocation model can achieve this initial vehicle distribution. The authors formulated the problem as a time–space network and defined the following arcs:

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$A_c$ denotes customer requests on arc $a=(i_t,j_{t^{\prime }})$. Each time a commuter request is transversed by this arc, there is a negative variation in vehicle energy, i.e., $c_a<0$, and a positive profit, i.e., $p_a>0$.

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$A_w$ is the waiting arc for either vehicles or relocation staff at a station i, $a=(i_t,i_{t^{\prime }})$. Each waiting arc is associated with a positive energy variation, $c_a>0$, and a zero profit, i.e., $p_a=0$.

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$A_r$ is the vehicle relocation arc by at least one relocator, $a=(i_t,j_{t^{\prime }})$. Each relocation arc is associated with a negative energy variation, i.e., $c_a<0$, and a negative profit, i.e., $p_a<0$.

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$A_t$, the transfer arc $a=(i_t,j_{t^{\prime }})$, represents the relocator’s movement when they do not move by vehicle or wait at a station. Each transfer arc is correlated with zero energy consumption, $c_a=0$, and zero generated profit, $p_a=0$.

The authors defined two sets of binary decision variables related to the vehicle, $x_a^h$, $a\in A_r\cup A_w\cup A_c$ and relocators $y_a^q$, $a\in A_r\cup A_w\cup A_t$, taking a value of 1 when the vehicle and relocator travel on arc $a=(i_t,j_{t^{\prime }})$, respectively. Moreover, the authors defined decision variables related to the vehicle battery charge, $z_t^h$, donating vehicle h charge at time t.

$$\begin{array}{}\mathrm{(7)}& \max \sum _{h\in H}^{}\sum _{a\in A_c\cup A_r}^{}{p}_a{x}_a^h\hfill \mathrm{(8)}& \sum _{h\in H}{x}_a^h⩽d_{a}a\in A_c\hfill \mathrm{(9)}& \sum _{h\in H}\sum _{a=(i_t,i_{t+1})\in A_w}{x}_a^h\le C_{i}i\in S,0\le t<T_{max}\hfill \mathrm{(10)}& \sum _{h\in H}\sum _{a\in \left({\delta }^{+}\left(i_0\right)\right)\cap (A_c\cup A_w\cup A_r)}{x}_a^h\le C_{i}i\in S\hfill \end{array}$$

$$\begin{array}{}\mathrm{(11)}& \sum _{i\in S}\sum _{a\in \left({\delta }^{+}\left(i_0\right)\right)\cap (A_c\cup A_w\cup A_r)}{x}_a^h=1h\in H\hfill \mathrm{(12)}& \sum _{a\in \left({\delta }^{+}\left(i_0\right)\right)\cap (A_c\cup A_w\cup A_r)}{x}_a^h=\sum _{a\left({\delta }^{-}\left(i_0\right)\right)\cap (A_c\cup A_w\cup A_r)}{x}_a^{h}h\in H,i\in S,1<t<T_{max}\hfill \mathrm{(13)}& \sum _{i\in S}\sum _{a\in \left({\delta }^{+}\left(i_0\right)\right)\cap (A_c\cup A_w\cup A_r)}{y}_a^q=1q\in Q\hfill \mathrm{(14)}& \sum _{a\in \left({\delta }^{+}\left(i_0\right)\right)\cap (A_c\cup A_w\cup A_r)}{y}_a^q=\sum _{a\left({\delta }^{-}\left(i_0\right)\right)\cap (A_c\cup A_w\cup A_r)}{y}_a^{q}h\in H,i\in S,1<t<T_{max}\hfill \mathrm{(15)}& (\mathit{x},\mathit{y})\in B1<t<T_{max}\hfill \mathrm{(16)}& \sum _{h\in H}{x}_a^h⩽\sum _{q\in Q}{y}_a^{q}a\in A_r\hfill \mathrm{(17)}& \sum _{q\in Q}{y}_a^q⩽B\sum _{h\in H}{x}_a^{h}a\in A_{}r\hfill \mathrm{(18)}& x_a^h\in \{0,1\}h\in H,a\in A_c\cup A_w\cup A_r\hfill \mathrm{(19)}& y_a^q\in \{0,1\}q\in Q,a\in A_r\cup A_t\cup A_w\hfill \end{array}$$

The objective (7) is to maximize the profit, which is a function of the revenue associated with the fulfilled customers’ requests minus the vehicle relocation costs. Constraints (8) guarantee that the customer demand, $d_a$, is not exceeded. The stations’ capacity constraints at any time t > 0 and at instant t = 0 are guaranteed in Constraints (9) and (10), respectively. Constraints (11) ensure the vehicle’s departure from one station at the beginning of time 0, while flow conservation at the network nodes is in Constraints (12). The same conditions for the relocators are ensured in Constraints (13) and (14). Constraints (15) impose the feasibility of the assigned trips regarding the battery charge. Matching vehicles and relocators on the relocation arcs are imposed in Constraints (16) and (17). Constraints (16) ensure that the number of vehicles traveling on a relocation arc a ∈ Ar is not greater than the number of relocation staff, and Constraints (17) impose a limitation on the number of relocators who can travel on a vehicle. Constraints (18) and (19) present the decision variables domain.

The above formulation describes the relocation for the operating hours by determining the optimal initial location for each vehicle on the network. To meet the optimal initial locations of the vehicles, the authors extended the model to the staff’s operations during non-operating hours. An additional variable is $R_i$, which presents the number of requested vehicles at station i at the start of the next planning period. The system configuration at the end of the day determines the initial vehicle position and initial battery charge $o_h$, $z_h^0$. The same network is operated but with the removal of the commuter requests during non-operating hours. Therefore, the overnight model for vehicle relocation is as follows:

$$\begin{array}{}\mathrm{(20)}& \max Z\hfill \mathrm{(21)}& \mathrm{s}.\mathrm{t}.Z\le z_h^{T_{max}}\hfill & \hfill \forall h\in H\mathrm{(22)}& \sum _{\alpha \in \left({\delta }^{+}\left(o_h\right)\right)\cap (A_w\cup A_r)}{x}_a^h=1\hfill & \hfill \forall h\in H\mathrm{(23)}& \sum _{\alpha \in \left({\delta }^{-}\left(i_{T_{max}}\right)\right)\cap (A_w\cup A_r)}{x}_a^h=R_i\hfill & \hfill \forall h\in H,i\in S\end{array}$$

The objective (20) is to maximize the charge level for all vehicles at the end of the day, $z_h^{T_{max}}$, which is defined in (21). Constraints (22) ensure the vehicle’s departure from its initial location, while Constraints (23) ensure the required vehicle distribution.

Finding the optimal solution for the presented model is impractical. Therefore, the authors proposed two model-based heuristics for addressing the relocation problem in the context of large-scale instances during operational hours. First, the authors proposed the removal of or reduction in the relocation density. This method ensures that the problem remains feasible as the relocators can still move in the waiting arcs. The impact of relocation arc reduction on the optimal solution obtained depends on the number of relocation arcs removed. Another approach proposed is the rolling horizon approach, where the authors split the planning period into $\rho$ sub-periods, and the rebalancing arcs associated with the following period after the first sub-period are disabled. The resultant model is then optimally solved, with the initial period’s value being set, and this process is repeated for the subsequent sub-periods.

The two models for the daily relocation and the overnight staff schedules give the readers a comprehensive optimization tool for managing shared vehicles with battery constraints.

3. Resource Dimensioning and Allocation

Vehicle relocation, which is necessary to ensure vehicle availability, constitutes a major cost, including the cost of vehicles and the costs of hiring relocation staff. In other words, investment in a huge fleet size may require hiring a smaller number of relocation personnel. Therefore, there is a trade-off between the resource size, their schedules, and the level of service offered [15].

Most of the previously mentioned research works assumed that vehicles could be relocated between stations regardless of the availability of staff to perform the relocation tasks. Resource dimensioning refers to the problem of determining the ideal number of vehicles and relocation staff to be hired in a working day to fulfill the relocation demand. Resource allocation refers to determining the optimal allocation of the resources at the network’s stations and the staff’s assignments to various relocation tasks. Determining the optimal number and allocation of resources is crucial in determining the profitability of a carsharing system. We reviewed five papers related to this topic; each distinctively formulated the problem.

The authors of [27] were the first to incorporate staff balancing in modeling vehicle relocation in carsharing. The authors proposed a three-phase decision support system that combines optimization, trend analysis, and simulation to identify parameters that yield near-optimal results for vehicle relocation operations. Staff rebalancing was considered at the optimization phase of the three-phase approach. The relocators’ movements were modelled by binary decision variables indicating the relocators’ activities at each time t, i.e., whether a relocator relocates a vehicle between two stations, achieving rebalance between stations; is waiting at a station; or is maintaining a vehicle at a station. Although the model details the relocators’ activities, it becomes computationally challenging for large-scale problems. Moreover, the authors have not considered the optimal staff and vehicle level to minimize the overall costs.

The influence of the user’s spatial and temporal flexibility regarding vehicle pickup and drop off on the system profitability and vehicle utilization was also studied by [15]. In particular, the authors in [15] proposed a framework to decide vehicle relocation, relocation staff movements, and the decision of accepting or rejecting SV commuting requests. The authors of [28] have proposed a dynamic decision support system to maximize carsharing profit by solving the vehicle relocation problem. The authors optimized the relocation operations and determined the ideal fleet size. An interesting feature of their model is the testing of the impact of increasing the reservation time, which is the interval between a vehicle request and pickup, on the optimal number of the fleet size. It was shown that increasing the reservation time from 0 to 30 min can result in a substantial reduction of approximately 86% in the fleet size. However, the authors did not consider staff balancing or availability in their model.

Later, the authors of [29] solved the vehicle relocation and staff balancing problem while optimizing the staff and fleet sizes to minimize the overall relocation costs. The authors formulated the problem using two integrated multi-traveling salesman formulations: one presents vehicle relocation, and the other presents staff balancing. The following questions regarding the vehicle relocation and staff balancing were answered by solving the model: (1) Given a set of user reservations, what should be the ideal fleet and staff size to fulfill all these requests? (2) How should the vehicles be relocated between the stations? (3) What should be the relocator’s assignment to different relocation tasks? Since the model cannot solve instances involving 40 users within an acceptable time, the authors proposed a decomposition-based heuristic that divides the relocation model into a master problem (MP) and a sub-problem (SP). The MP focuses on solving vehicle relocation problems without considering staff rebalancing. On the other hand, the SP utilizes the relocation solutions obtained from the MP to address the staff rebalancing problem. After the execution of each MP and the SP iteration, a set of additional constraints called “Relocation Restrictions” are identified and incorporated into the MP for subsequent iterations. The results indicate that fleet size is more sensitive to demand than staff size. Additionally, there is an inverse relationship between staff size and vehicle cost. The main drawback of this formulation is that it assumes an optimized resource allocation at the beginning of the planning period. Moreover, the model focused on fulfilling the commuter’s request without measuring the waiting time for order fulfillment, which is a key service for users’ choice of shared mobility [30].

It is noteworthy to mention that the authors of [26] mentioned in Section 2 considered staff balancing when deploying the relocation plan. Similar to their work, the authors in [31] formulated the vehicle relocation problem and staff balancing using a time–space network. However, the authors included determining the optimal vehicle and staff sizes and allocations to satisfy user demands with minimum overall costs. The model was formulated as a multi-vehicle routing problem with complex coupling constraints, which proved difficult to address using existing solvers. Therefore, the authors devised a tailored solution approach based on Lagrangian relaxation embedded with forward dynamic programming and branch-and-bound. This custom approach allowed for a more efficient and precise resolution of the model.

4. Trip Pricing

The previously mentioned studies rely entirely on relocation staff to achieve system balance by considering a fixed rental rate between stations throughout the day. Some other research streams focused on trip pricing solely to achieve vehicle balance within the network’s stations, as in the work of [32]. Though never proven, the theory is that carsharing systems could yield higher profits by managing the demand through pricing. In other words, significantly low rental prices will attract more commuters to the service and, therefore, increase the operator’s revenue. However, this may not necessarily increase the profit as it may increase the relocation expenses due to the increased decentralization of vehicles throughout the network.

The authors in [33] work have optimized the vehicle fleet size and trip pricing while considering the vehicle relocation and staff assignment to maximize the overall profit. Based on the work of [12], in which the authors optimized the vehicle relocations between stations, the authors in [9] introduced new decision variables to account for price variations between pairs of zones and periods of the day. More formally, considering a predefined set of carsharing stations at which the set of origin-destination demands is known in advance, the problem aims to find newly optimized prices between station groups throughout a typical working day such that the profit is maximized while fulfilling the demand. A summary of research works that studied operational and tactical decisions are summarized in

Table 1. Tactical and operational decisions in modeling one-way carsharing.

Reference	Tactical Decisions		Operational Decisions			Additional Decisions	Profit	Application	Main Outcomes
	(1)	(2)	(3)	(4)	(5)
[34]	✗	✗	✓	✗	✗	Fleet allocation	Max profit	Historical operational data from Beijing and Guangzhou No. of stations: 30, average No. of trips: 11.16	The proposed relocation plan achieved overall profit improvement compared to state-of-the-art relocation plan.
[26]	✗	✗	✓	✓	✗	Battery charge	Max profit	Realistic instances from Honda Motor CS initiative in Singapore No. of stations = 14 No. of trips (50,125) No of vehicles: 20 No. of relocators: 2	The proposed relocation strategies allow a balance between the no. of vehicles and trip requests, which led to higher profits achieved.
[33]	✓	✓	✓	✓	✗	Staff assignment to vehicles Trip pricing	Max profit	A case study based on CS operator in Singapore	Evaluated the impact of demand, demand uncertainty, SV costs, and relocator costs on the performance of a carsharing system.
[35]	✗	✗	✓	✓	✗	Dynamic trip pricing	Max profit	A case study from Chengdu No. of stations = 35, variable no. of trips accepted based on dynamic pricing	Analyzed the impact of operation strategies, nonlinear charging profiles, and road congestion for CS. High no. of vehicles in a zone would result in a reduction in relocation requests and no. of relocators needed in that zone
[14]	✓	✓	✓	✓	✗	Vehicle and staff initial allocation	Min relocation costs	CS in Chengdu (i.e., EVCARD)	Employing time-based relocators reduces working hours by 49% and the relocation costs by 33.8.%
[25]	✗	✗	✓	✓	✗	✗	Max no. of served relocation requests	Go fun in Wuhan (56 stations in 4 different regions)	Proactive relocation that utilizes reservation information has a positive performance compared to state-of-the-art relocation policy.
[24]	✗	✗	✓	✓	✗	Staff routes and schedules	Max profit	Random generated instances	Formulates relocation problem into a set-packing model, designs a branch-and-price-and-cut algorithm to exactly solve the problem.
[36]	✓	✓	✓	✓	✓	State of charge of a vehicle at a specified time Vehicle and staff inventory at a specified time at a certain station Vehicle assignment to a trip	Max profit	GoFun platform in Beijing, China Network with 87 stations. Min and max no. of requests are (1577, 4908)	Network size, request arrival rates, and operational efficiency have significant impacts on the operator’s profit and service level.
[22]	✓	✓	✓	✓	✓	Vehicle and staff initial allocation	Max no. of accepted requests	A case study from Grenoble (27 stations and 80 vehicles)	Utilizing historical data leads to a higher no. of served demands.
[23]	✗	✗	✓	✗	✗	Parking space inventory Vehicle inventory		Intelligent Community Vehicle System (ICVS) operated by Honda Motor Company in Singapore (14 stations, and 94 vehicles)	Formulating CS problem as stochastic MIP and proposed two solution techniques, one based on enumeration and the other on cone generation.
[27]	✗	✗	✓	✓	✓	No. of rejected demands No. of rejected vehicle returns	Min relocation costs	ICVS in Singapore. 1236 trips in a month	The no. of relocators suggested by the proposed framework reduces the staff costs by 50% and the zero-vehicle time by up to 13%.
[28]	✓	✗	✓	✗	✗	Vehicle availability time	Min relocation costs	Autoshare in Toronto 209 parking locations (50 to 200) trip requests per day	Increasing the time between the request and picking up from 0 to 30 min can decrease the fleet size by 86%
[29]	✓	✓	✓	✓	✗	✗	Min costs	Car2Go in Toronto 200 parking spaces	Fleet size is more sensitive to demand than staff size. Fleet and staff sizes and relocation and staff balancing time are sensitive to the vehicle costs.
[31]	✓	✓	✓	✓	✗	Fleet initial allocation Staff initial allocation Battery volume at time steps	Min investment and operational costs	CS from Seattle 26 parking spaces	Proposed a solution approach based on the Lagrangian relaxation to solve vehicle relocation and staff balancing drew managerial insights on the impact of the vehicle battery on the system performance.
[37]	✗	✗	✓	✗	✓	Find a profitable trip chain	Max profit	Randomly generated instances A case from CS from Singapore	Managerial insights on the impact of costs of vehicles, relocation, electricity, and charging on the system’s performance.
[15]	✓	✓	✓	✓	✓	No. of vehicles being charged Trip selection	Multi-objective: max no. of trips served, min relocation costs	VENAP Auto Bleue in Nice, France Various random aggregate demands	Demand forecast and optimizing initial resource locations lead to elevated resource utilization.
[16]	✓	✗	✓	✓	✗	✗	Min weighted difference between the estimated and real travel time	Auto Bleue from Nice France 60 stations	Analyze the effect of location and departure time flexibility & the discount rate on the system’s performance.
[38]	✓	✗	✓	✗	✗	Fleet initial allocation Trip pricing	Bilevel model: upper level: max. operator’s profit; lower level: min commuters’ traveling cost	Case study from Rotterdam, The Netherlands 39 stations at the center of the zones 50 vehicles at each zone	Out of four scenarios of vehicle relocation, pricing, and a combination of relocation and pricing, the latter showed to be the most profitable.
[39]	✗	✗	✓	✓	✗	Staff routes and schedules for vehicle relocation	Max profit	Randomly generated instances Average pickup requests range between (15, 47) Average delivery requests range between (14, 49)	Developed a hybrid adaptive large neighborhood search and tabu search algorithm to solve the problem. Computational experiments proved the competitiveness of the algorithm in solution performance and time.

Note: (1) fleet size, (2) staff size, (3) vehicle relocation, (4) staff balancing, (5) trip selection.

.

In Table 1, we indicate, in the first column, the cited reference. Columns 2–6 include whether the cited reference covers the decisions regarding fleet size, staff size, vehicle relocation, staff balancing, and trip selection, respectively. Column 7 covers the additional decisions that are optimized and are not included in Columns 2–6, such as trip selection decisions. In Column 8, we mention the model’s objective function. The case study or the application settings under which the model is applied and tested are summarized in Column 9. We also include in Column 9, when available, the problem settings in terms of the number of stations, zones, fleet or staff size, and the number of trips considered. Finally, the main research outcomes are summarized in Column 10.

5. Carsharing-Station-Related Decisions

The success of carsharing systems relies significantly on vehicle availability through vehicle relocation. However, commuters’ ability to access the carsharing service within an acceptable walking distance is imperative. Moreover, the number of stations that can be operated is subject to constraints posed by budget limitations and available land space. Therefore, station-related decisions should be considered when optimizing carsharing operations. Neglecting the close interaction between different decision-making levels may result in sub-optimal system design and operation [13,40].

Numerous researchers have delved into station-related decisions, exploring aspects such as the number of stations to be installed, their locations, and their size. Station size, in this context, encompasses considerations such as the allocation of car parking spaces or the installation of charging stations. Addressing these decisions becomes crucial for optimizing the system’s performance.

Therefore, this section highlights a series of papers that explicitly delve into station-related decisions and their correlation with vehicle relocation strategies.

The station location and vehicle relocation problem was solved by [8]. More formally, the authors proposed mixed-integer linear programming (MILP) under three trip selection schemes to optimally determine the station location for a given carsharing demand to maximize the operator’s profit. This was the first work that considered the trip selection, which gives the operator more flexibility in managing the supply–demand imbalance issue. The authors showed the importance of the trip selection strategy (i.e., selecting profitable trips out of total demand) in determining carsharing profitability. They showed that fulfilling all commuters’ requests would be unprofitable even under high-pricing trips as it mandates the operator to deploy more vehicles. The authors, however, only considered overnight relocation while neglecting staff balancing, as the main focus of the study was on the selection of depot location.

The authors in [8] have considered the optimization of stations’ locations and vehicle relocations while considering a deterministic shared vehicle demand. However, strategies designed for deterministic demand might not be able to capture the demand fluctuations and, therefore, be a less-optimal option [41]. In particular, demand uncertainty, along with its variation over time, can increase the difficulty of vehicle balancing, which could lead to an unnecessary increase in fleet and staff sizes, station capacity, and, hence, vehicle underutilization or demand loss [41].

Therefore, when dealing with uncertain demand, there are two primary modeling approaches: robust optimization and stochastic optimization. Robust optimization aims to control risk by focusing on minimizing the maximum potential negative impact. It strives to develop strategies that can withstand the worst-case scenario or scenarios within safe limits. On the other hand, stochastic optimization works with known demand distributions. These distributions are often estimated by sampling various scenarios. The approach then selects the solution with the best-expected outcome, such as maximizing expected profit or minimizing expected operational costs. This is typically formulated using a two-stage or multi-stage stochastic program [41]. It was shown by [42] that optimizing the strategic and operational decisions when considering uncertain demand can improve the carsharing profit by 20.49% compared with optimizing the decisions based on deterministic demand. Therefore, we review in the following paragraphs the relevant research works that considered demand uncertainty when optimizing the carsharing station’s related decisions.

While the authors in the previous work did not consider the station location, ref. [41] presented a two-stage stochastic program aimed at optimizing carsharing profitability. The number of parking spaces, vehicles, and staff are determined in stage one; stage two assesses the profitability of the stage one decisions and determines the vehicle relocation and vehicle assignment in response to various demand realizations. To address the complexities arising from the interactions among variables across these two stages, the authors introduced a novel concept termed service reliability (SR). The SR-based modeling approach separates the long-term strategic planning and the short-term operational decisions into two distinct problems. These problems are connected through SR. In other words, the first-stage decisions are optimized for a specific SR. Then, in the second stage, operational decisions are made considering the actual stochastic demand to maximize overall profit and mitigate the negative impacts of fluctuating and uncertain demand.

It was shown that the SR-based two-stage model has the potential to assist one-way carsharing service providers in achieving higher profitability.

The authors in [43] work have jointly optimized the charging station location, fleet size, allocation, and relocation operations. An accelerating solution based on Lagrangian relaxation was proposed to deal with the complexity of the problem. The authors have neglected the difference in the energy demand for different trips and assumed the operation of a homogeneous fleet. This is an important distinction, as rental fare and energy consumption for a two-seat vehicle should be less than for a four-seat vehicle. After performing a series of sensitivity analyses, it was found that the total number of vehicles deployed is dominated by demand, and the number of charging stations is not very sensitive to penalty and relocation costs. However, the scale of the problem is still challenging.

The authors in [44] presented a MINLP to optimize the stations’ capacity and location along with vehicle relocation to maximize the daily profit. The authors established a correlation between the location variables and the likelihood of a user’s travel choice. To address this, they developed a specialized gradient algorithm.

An interesting approach involves integrating optimization and simulation modeling to explore the integration of strategic planning and operational decisions. In the work in [40], the authors optimized the allocation of parking spaces and how vehicles should be distributed initially to specific zones while considering the relocation activities to minimize the overall expenses. The operational planning problem incorporates demand uncertainty. The model is formulated as the following:

$$\begin{array}{}\mathrm{(24)}& \hfill \min & C_i\sum _{i\in N}^{}{x}_i+w\ast v+R(x,v)+Q(x,v)\hfill \mathrm{(25)}& \hfill \mathrm{s}.\mathrm{t}.& g(x,v)\le \alpha \hfill \mathrm{(26)}& \hfill & x_i\ge v_i,\forall i\in N\hfill \mathrm{(27)}& \hfill & \sum _{i=1}^N{v}_i=v\hfill \mathrm{(28)}& \hfill & x_i,v_i\in Z+\hfill \end{array}$$

where $C_i$, is the cost of renting a parking space in zone i; x is a vector with a dimension that presents the number of zones, and its value presents the number of parking spaces at each zone. w is the vehicle’s daily depreciation costs; v presents the system’s total number of vehicles; while $v_i$ presents the number of vehicles initially placed in zone i. Vehicle balancing costs are presented by $R(x,v)$; $Q(x,v)$ presents the additional parking costs incurred when a commuter does not find an available parking space; $g(x,v)$ is the commuter loss rate due to vehicle unavailability at the time of rental; and $\alpha$ is the maximum customer rate loss that can be tolerated.

The objective (24) is to minimize the overall costs, which include the parking rental costs, vehicle depreciation costs, and relocation costs. Constraint (25) is the main constraint not to exceed a demand loss rate $\alpha$, while Constraints (26)–(28) define the search space.

To facilitate the computation, the model is relaxed by incorporating the violation of Constraint (25) in the objective function as a penalty cost $\mu$. The updated objective function is shown in (29).

$$\begin{array}{cc}\hfill & \min f(x,v)=C_i\sum _{i\in N}^{}{x}_i+w\ast v+R(x,v)+Q(x,v)+\mu \ast {(g(x,v)-\alpha )}^2\hfill \end{array}$$

(29)

Due to the computational complexity of solving the relocation operation, which must respond to real-time demand changes, a discrete event simulator is adopted. In other words, a discrete event simulator is created to approximate the values $f(x,v)$, $R(x,v)$, $Q(x,v)$, and $g(x,v)$ for a given x and y as shown in (30), (31), (32), and (33), respectively.

More formally, for a given set of decision variables, parameters, and simulation iterations, k, the simulator generates the necessary set of sample points that encompass the rebalancing costs, $r_k$; additional parking costs, $q_k$; and customer loss rate, $g_k$, for each demand scenario. ${\gamma }_{ij}$ is the rebalancing costs from zone i to j, $r_{ij}$ is the number of rebalanced vehicles from zone i to j, $p_i$ is the parking costs at zone i, $s_{it}$ is the number of vehicles at zone i at time t, and $d_{ijt}$ is the vehicle pickup demand between zone i and j at time t.

$$\begin{array}{}\mathrm{(30)}& f(x,v)\sim C_i\sum _{i\in N}^{}{x}_i+w\ast v+\widehat{R}(x,v)+\widehat{Q}(x,v)+\mu \ast {(\widehat{g}(x,v)-\alpha )}^2\hfill \mathrm{(31)}& \widehat{R}(x,v)=\frac{\sum r_k}{K},r_k=\sum _{t\in T}\sum _{j\in N,i\ne j}^{}\sum _{i\in N}^{}{\gamma }_{ij}\ast r_{ijt}\hfill \mathrm{(32)}& \widehat{Q}(x,v)=\frac{\sum q_k}{K},q_k=\sum _{t\in T}\sum _{i\in N}{p}_i\ast max(s_{it}-x_i,0)\hfill \mathrm{(33)}& \widehat{g}(x,v)=\frac{\sum g_k}{K},g_k=\frac{{\sum }_{t\in T}{\sum }_{i\in N}max({\sum }_{j\in N,\ne i}{d}_{ijt}-s_{it},0)}{{\sum }_{t\in T}{\sum }_{j\in N,\ne i}{\sum }_{i\in N}{d}_{ijt}}\hfill \end{array}$$

The simulator calculates the rebalancing decisions between zones by applying an integer programming model at the start of every hour. The objective is to minimize the rebalancing costs (34) while guaranteeing that each zone can meet the specific loss rate for the following hour. The model is formulated as the following:

$$\begin{array}{}\mathrm{(34)}& \min \sum _{j\in N,\ne i}^{}\sum _{i\in N}^{}{r}_{ijt}{\gamma }_{ij}\hfill \mathrm{(35)}& L_{it}\le s_{it}-\sum _{j\in N,\ne i}^{}{r}_{ijt}+\sum _{j\in N,\ne i}^{}{r}_{jit}\le U_{it}\hfill \mathrm{(36)}& \sum _{j\in N,\ne i}^{}{r}_{ijt}\le s_{it}\hfill \mathrm{(37)}& r\in Z+\hfill \end{array}$$

To explicitly consider the stochastic nature of the demand, the model calculates the lower ($L_{it}$) and upper bound ($U_{it}$) of vehicle stock at each zone to meet the required service rate on vehicle pickups and returns, respectively. This is guaranteed in Constraints (35). The lower limit of the vehicle stocks is assumed when there are only vehicle returns, i.e., no commuter is requesting a vehicle pickup for the next hour. The upper limit of vehicle stocks is assumed to be the station’s capacity. Constraints (36) ensure that the number of relocated vehicles out of a station is not greater than the number of existing vehicles. Constraints (37) specify the domain of the decision variables.

The performance of various system configurations is assessed. The results demonstrate that the optimal solutions when no rebalancing operations are considered lead to a significantly higher number of parking spaces to be rented and more vehicles to be purchased, which does not improve the demand loss rate. Moreover, rebalancing is highly needed in the case of high demand fluctuations and high demand imbalance.

Recently, the authors of [45] have proposed a holistic, collaborative mathematical formulation that encloses the three decision levels. The authors optimized the strategic planning decisions involving the number, location, and parking capacities of stations. They also optimized the tactical planning decisions related to fleet size and initial vehicle distribution while considering all-day vehicle relocation and dynamic trip selection at the operational level. The trip selection decision mandates the operator to choose profitable and balanced trips, enhancing the self-balance ability.

Their model suggests that operators are advised to prioritize medium–long-distance travel within a travel time range of 30-60 min during periods of low demand. In high-demand and limited-source scenarios, the selection of balanced trips is recommended. Another important finding is that relocation cases yield higher profits compared to self-balanced cases, indicating that vehicle relocation has a significant impact on earnings and meeting demand while costs remain relatively unaffected. Consequently, vehicle relocation is crucial for maximizing profits and accommodating demand. This study is unique in providing a comprehensive formulation encompassing strategic, tactical, and operational decisions, as well as offering flexibility in trip selection.

Previous research works have addressed strategic and operational decision-making challenges in the context of uncertain demand. Another dimension of uncertainty arises when implementing electric vehicle (EV) deployment for one-way carsharing, particularly when taking into account the state of charge (SOC) of individual vehicles.

The authors in [46] work have addressed the station location selection, optimal fleet size, and vehicle balancing problem to minimize the overall costs associated with these decisions under stochastic demand. To solve a large-scale problem, the authors proposed a continuum approximation model under stochastic and dynamic trip demands. The location problem is NP-hard, i.e., a problem hard to solve in a polynomial time; therefore, the authors proposed a continuum approximation approach to overcome the modeling challenges. This work may not considered be under mathematical modeling. A main drawback of this study is that it was assumed that an EV is not available until it is fully charged. By adopting this assumption, there will be no need to track the vehicles’ SOC. This considerably reduces the model scale; however, in reality, an EV can be utilized and fulfill demand requests even if it is not fully charged. Therefore, vehicle utilization is reduced, and more vehicles are deployed to meet the commuters’ demand requests.

To overcome the aforementioned problem, the authors in [42] proposed a mixed-integer non-linear program (MINLP) to optimize the fleet size, station capacity, and vehicle relocation by considering a time-varying SOC of vehicles. However, a huge computational burden is caused by continuously tracking the vehicle charge state. This necessitates the development of a hybrid heuristic method to handle the computation burden. In particular, the model is split into two subproblems: One focuses on determining the strategic decisions of fleet sizing and number of parking spaces, which is referred to as station capacity. The second one deals with the operational-level decisions regarding vehicle rebalancing. It is crucial to optimize both levels jointly.

More explicitly, at the strategic level, the model calculates the upper and lower bounds for the fleet size. These bounds are determined by assuming that EVs are fully charged before departure or by disregarding the constraints related to the battery capacity, respectively. Once the fleet size and station capacity are known, a set of small-scale linear programs is created to determine how to relocate vehicles effectively to meet travel demand within a rolling time frame. The model utilizes a shadow price algorithm and a golden-section line search method to optimize station capacity and fleet size, aiming to maximize the overall profit. Results indicate that allocating only a few vehicles or providing limited parking spaces for high demand will result in numerous unfulfilled requests. Conversely, an excessive allocation of vehicles and parking spaces might result in the system being underutilized. It should be noted that the authors have not optimized the stations’ locations and numbers.

The authors in the previous study adopted a heuristic approach to handle the computation burden due to tracking the SOC. Some other research studies have simplified the charging requirements by proposing a traceable EV relocation problem as in the work of [47,48]. The authors considered a vehicle as available only when a specified charge level was achieved. Another stream of researchers, as shown previously in Section 2, tracked the SOC of vehicles through time–space network constraints as in the work of [26,31].

Table 2. Strategic and tactical decisions while considering vehicle relocation.

Reference	Strategic Decisions		Tactical Decisions		Additional Decisions	Objective Function	Application	Main Outcomes
	(1)	(2)	(3)	(4)
[49]	✓	✓	✓	✗	No. of parking spaces Vehicle inventory at each station at each time step	Max profit	A case study from Lisbon, Portugal	Demand variability should be considered during the design of CS as it directly impacts the profit.
[12]	✗	✓	✓	✗	No. of parking spaces Fleet allocation	Max profit	A case study from Lisbon, Portugal; 75 candidate station locations, 1777 trips	Relocation operations should be considered during CS design (i.e., deciding the SV station locations).
[46]	✓	✗	✓	✗	-	Min costs	A case in Sioux-Falls City, US; 24 nodes	Proposed continuum approximation model to design CS that solved for a large scale, obtaining a near-optimum solution.
[48]	✓	✓	✓	✗	Trip selection	Max profit	A case from Vienna, Austria Candidate station locations: 693	The proposed exact approach performs well for medium-size instances. CS stations located in small districts are not profitable compared to locating them next to established projects.
[50]	✓	✗	✓	✗	Trip selection	Max profit	A case from Manhattan, US	Proposed a Bender decomposition approach to solve the problem. Station opening and SV costs, walking times, and demand variation have a direct impact on the CS profitability.
[51]	✓	✓	✗	✗	Charging station allocation No. of parking spaces	Max no. of EV trips Min no. of unserved commuters	Survey data from Ontario, Canada	Creating a self-regulating network (that increases the flow balance and decreases the need for relocation) is not profitable. Vehicle relocation is essential.
[52]	✗	✓	✗	✗	No. of chargers to be installed Station upgrade with chargers of a certain type No. of vehicles with a certain battery level to be charged with a charger of a certain type	Max profits	Auto Bleue, Nice, France Tested on 10 and 20 stations out of 60 stations Each station has 3 parking lots	Proposed two heuristic methods to solve the problem. Mixed heuristics tested on a subset of stations gives quality solutions in a reasonable time. System’s performance is not sensitive to the fast-charger price.
[13]	✓	✓	✓	✓	No. and location of shared stations No. of served and unserved orders	Multi-objective: max operator profit and commuters’ benefit	A case from Nice, France Converted the existing two-way data to one-way	Proposed a multi-objective model that optimizes the operator’s and commuters’ benefits. This allows decision-makers to make trade-offs between operator’s and commuters’ benefits.
[41]	✗	✓	✓	✓	No. of parking spaces Vehicle movements Vehicle and staff allocation	Max profit	Two cases: toy network with 3 nodes; network of Manhattan with 13 nodes	Introduced service reliability concept to handle the complexities of strategic and operational decisions. The proposed model was shown to reduce the CS profitability.
[42]	✗	✓	✓	✗	No. of parking spaces in a zone Fleet size in a zone No. of satisfied travel demands	Max profit	A case from Suzhou, China 54 zones	The proposed strategic and operational framework was decomposed to find station capacity and fleet size first and then a rolling horizon approach to find the vehicle relocation. Results were obtained within less than 24 h when the state of charge was not tracked.
[8]	✓	✓	✓	✗	Fleet allocation; depot size; vehicle inventory; trip selection	Max profit	A case from Lisbon, Portugal 1776 trips	Inefficient vehicle relocations would result in huge profit losses even when charging high trip prices. A ratio of 22.7 vehicles to 100 trips is found to be ideal.
[44]	✓	✓	✓	✗	No. of stations No. of car parking spaces Vehicle allocation	Max profit	A case from Suzhou, China 104 zones	A customized gradient search algorithm is proposed to solve the design and operation problem when having non-linear demand. CS profit is maximized when CS share is 83%. The satisfied demand is reduced during peak hours due to vehicle availability. As CS pricing increases, the market share and profit decrease.
[53]	✓	✓	✓	✗	No. of chargers installed in a station Trip selection Trip assignment to vehicles	Max profit	Grid graph instances with 1000 random trips A case from Vienna, Austria	Tracked vehicles’ battery levels during the planning stage. Proposed two heuristics to derive quickly a feasible good solution. Instance difficulty is related to the no. of trips. The proposed heuristics solved up to 480 trips.
[54]	✓	✓	✓	✗	First level: no. of stations and their capacity, fleet size Second level: trip selection	Max profit	A case from Vienna, Austria	Variable neighborhood search was proposed to find station location, capacity, and no. of vehicles at the first level. For each first-level solution, a path-based heuristic is proposed to decide the accepted trips.
[55]	✓	✓	✗	✗	No. of vehicles being charged with a regular charger No. of vehicles being charged with fast chargers Trip assignment to a station	Max profit	A case from San Francisco, US	Proposed a decision support system for planning optimal CS station locations and capacity.
[40]	✗	✓	✓	✗	Vehicle allocation	Min costs	Planned CS in Singapore 20 zones	Developed a decision support system for designing and operating CS. Relocation should be considered during CS planning.
[45]	✓	✓	✓	✗	No. of parking spaces Vehicle allocation	Max profit	A case from Chengdu, Sichuan candidate station Locations: 40 travel demands Ranges (2335, 23,315)	A greedy-based heuristic algorithm to solve the joint problem. Vehicle relocation cost decreases with the increasing no. of trips and duration. Trip selection to have a balanced trip results in selecting long trips when there is low demand and limited resources, and the opposite is true. More profit is generated when relocating vehicles compared with selecting balanced trips.
[32]	✗	✓	✓	✗	Dynamic trip price from i to j in time t	Max revenue	EVCard in Chengdu	Dynamic pricing leads to better profit and greener mobility compared to fixed pricing. User-based relocation by dynamic pricing plays a vital role in relocation.

Note: (1) station/parking location, (2) station capacity, (3) fleet size, (4) staff size.

summarizes the research works that studied the tactical and operational decisions while considering the vehicle balancing decisions. It is noteworthy to mention that, for the sake of completeness, we have added references that are not reviewed in the text. In Table 2, we indicate, in the first column, the cited reference. Columns 2–5 include whether the cited reference covers the decisions regarding the station or parking location, station size, fleet size, and staff sizes, respectively. Column 6 covers the additional decisions that are optimized and are not included in Columns 2–5, such as the number of opened stations. Column 7 covers the objective function, while the case study or application settings under which the model is applied and tested are summarized in Column 8. Finally, the main research outcomes are summarized in Column 9.

6. Operators Decisions and Commuters Demand

The overall benefits for both the operator and the users while designing and operating CSSs have been studied. This is particularly important when considering that the system is subsidized with a public fund, which enables the decision-makers to evaluate a trade-off between the operator’s profit and commuters’ service level. In this section, we review three research works related to this topic. Moreover, research works in the previous sections have focused on optimizing the carsharing operator’s benefits by deciding on tactical and strategic decisions. However, it is vital to shed light on how these decisions would impact the carsharing ridership. Therefore, in this section, we summarize a selected number of research works that have considered the optimization of the operator’s and commuters’ benefits simultaneously.

The authors in [30,38] works have built a bi-level program to find the optimal configuration of a carsharing system by considering the commuters’ reaction to this configuration. The scope of the carsharing decisions is different in each work. To maximize the operator’s profit, the authors of [38] have optimized the fleet size, pricing, and vehicle relocation in the upper level while minimizing the corresponding users’ commuting costs in the lower level. We review [30] more thoughtfully.

The bi-level program involves the optimization of variables in one model, known as the lower level, based on the optimal solutions of another optimization model. The upper level encompasses the main objective function along with additional constraints. The problem considered in [30] is to maximize the operator’s rental revenue by determining station location, size, and vehicle inventories subject to budget constraints at the upper level. And in the lower level, the user’s travel and waiting times should be minimized.

More formally, the operator’s decision variables are $x_i$, $y_i$, and $z_i$, where $x_i$ is a binary decision variable indicating whether a station should be opened in location i, $y_i$ is an integer variable to indicate the capacity of station i, and $z_i$ is the number of vehicles located initially at station i. There is a cost associated with each decision. The costs are related to station setup costs $c_s$, additional parking space costs $c_p$, and the cost of deploying a shared vehicle $c_v$. The operator aims to find the optimal network configurations $(x,y,z)$, denoted by $\mathit{x}$, subject to budget constraints C, to maximize the revenue of the shared flows throughout the network. However, the operator does not determine the shared flows.

From the commuters’ perspective, the problem is finding the network flows to maximize their utility. For a given origin–destination (O-D) pair, indexed by k in the following, the commuters aim to minimize the traveling and waiting times. The demand from node i to the destination of index k is denoted by $D_{ik}$. Two continuous decision variable decisions are made by the commuters, $v_{ijk}$ and $w_{ik}$. $v_{ijk}$ indicates a flow from node i to j for demand pair k, while $w_{ik}$ presents the total waiting time at node i for a demand pair k. Therefore, the decisions made by the commuters at the lower level are ($v,w$), denoted by $\mathit{v}$.

To present the operator’s operational decisions, the authors defined a to present the checkout replacement ratio. For example, if a = 1, there exists enough capacity to handle vehicles’ checkouts and returns, while if a ≥ 1, returns may exceed the capacity. M is a very large number.

The bi-level network can be formulated as follows:

$$\begin{array}{}\mathrm{(38)}& \hfill \underset{x,y,z}{max}\sum _k^{}\sum _{(i,j)\in A_s}^{}{r}_{ij}{v}_{ijk}\hfill \mathrm{(39)}& \mathrm{s}.\mathrm{t}.\sum _{i\in V_s}^{}{c}_s{x}_i+c_p{y}_i+c_v{z}_i\le C\hfill \mathrm{(40)}& M{x}_i\ge y_i\hfill & \hfill i\in V_s\mathrm{(41)}& z_i\le y_i\hfill & \hfill i\in V_s\mathrm{(42)}& y_i\le y^{ub}\hfill & \hfill i\in V_s\mathrm{(43)}& x_i\in \{0,1\}\hfill \mathrm{(44)}& y_i,z_i\in {\mathbb{Z}}_{+}^n\hfill \end{array}$$

Lower level:

$$\begin{array}{}\mathrm{(45)}& \underset{w,v}{min}\sum _k^{}\left(\sum _{(i,j)\in A}^{}{c}_{ij}{v}_{ijk}+\sum _{i\in V}{w}_{ik}\right)\hfill \mathrm{(46)}& \mathrm{s}.\mathrm{t}.\sum _{j:(i,j)\in A}^{}{v}_{ijk}-\sum _{j:(i,j)\in A}^{}{v}_{jik}=D_{ik}\hfill & \hfill i& \in V,k\in K\hfill & \hfill \left({\alpha }_{ik}\right)\mathrm{(47)}& v_{ijk}\le f_{ij}{w}_{ik}\hfill & \hfill (i,j)& \in A\setminus \underline{A},k\in K\hfill & \hfill \left({\beta }_{ijk}\right)\mathrm{(48)}& M{x}_i\ge \sum _k^{}{v}_{ijk}\hfill & \hfill (i,j)& \in A_s\hfill & \hfill \left({\gamma }_{ijk}\right)\mathrm{(49)}& M{x}_j\ge \sum _k^{}{v}_{ijk}\hfill & \hfill (i,j)& \in A_s\hfill & \hfill \left({\delta }_{ijk}\right)\mathrm{(50)}& \sum _k^{}\sum _{j,(i,j)\in A_s}^{}{v}_{ijk}\le z_i\hfill & \hfill i& \in V_s\hfill & \hfill \left({\zeta }_i\right)\mathrm{(51)}& \sum _k^{}\sum _{j,(i,j)\in A_s}^{}{v}_{ijk}\le \alpha (y_i-z_i)\hfill & \hfill i& \in V_s\hfill & \hfill \left({\eta }_i\right)\mathrm{(52)}& w_{ik}\ge 0\hfill & \hfill i& \in V,k\in K\hfill & \hfill \left({\lambda }_{ik}\right)\mathrm{(53)}& v_{ijk}\ge 0\hfill & \hfill (i,j)& \in A,k\in K\hfill & \hfill \left({\mu }_{ijk}\right)\end{array}$$

The carsharing operator aims to maximize the rental revenue of the shared vehicles’ fulfilled requests for the set, $A_s$, which presents the vehicle sharing arcs. However, as indicated earlier, this is a commuter’s decision in response to the network configurations. The main constraints were considered in the upper-level decisions. It is noteworthy to mention that ${\alpha }_{ik}$, $\left({\beta }_{ijk}\right)$, $\left({\gamma }_{ijk}\right)$,$\left({\delta }_{ijk}\right)$, $\left({\zeta }_i\right)$, $\left({\eta }_i\right)$, $\left({\lambda }_{ik}\right)$, and $\left({\mu }_{ijk}\right)$ are necessary variables to replace the lower-level optimization model using the following KKT conditions:

• Budget constraints in (39).
• Parking slot availability only at opened stations in Constraints (40).
• Number of vehicles assigned to a station does not exceed its capacity in Constraints (41).
• Limiting the number of opened stations in Constraints (42).

Commuters react to the network’s settings $(x,y,z)$ in the lower level to minimize the travel and waiting times (45). The main constraints considered regarding the shared flow are as follows:

• Flow conservation for each node in Constraints (46).
• Relating the travel and waiting times for frequency-based links, $f_{ij}$, in Constraints (47).
• Flows are only between opened stations in Constraints (48) and (49)
• Capacity constraints for the shared stations in Constraints (50) and (51)

In a concise notations, the bi-level program is written in the following form:

$$\begin{array}{cc}\hfill \underset{x\in X}{\max }& F\left(\mathit{v}\right)\hfill \\ \hfill & \mathrm{s}.\mathrm{t}.G(\mathit{x},\mathit{v})\le 0\hfill \\ \hfill & \underset{\mathit{v}\in V}{\min }f\left(\mathit{v}\right)\hfill \\ \hfill & \mathrm{s}.\mathrm{t}.g(\mathit{x},\mathit{v})\le 0\hfill \end{array}$$

where upper and lower decision vectors are given by $\mathit{x}=(x,y,z)$ and $\mathit{v}=(w,v)$, respectively, while upper- and lower-level objective functions are given by $F\left(\mathit{v}\right)$ and $f\left(\mathit{v}\right)$, respectively. $G(\mathit{x},\mathit{v})$ and $g(\mathit{x},\mathit{v})$ are the upper and lower constraint sets, respectively. For a given feasible region of a network settings $\mathit{x}$, the commuters’ feasible region $\mathbf{\Omega }\left(\mathit{x}\right)$ is defined as the following:

$$\begin{array}{cc}\hfill & \mathbf{\Omega }\left(\mathit{x}\right)=\mathit{v}\mid g(\mathit{x},\mathit{v})\le 0,v\in V\hfill \end{array}$$

The commuters’ reaction set $\mathbf{\Psi }\left(\mathit{x}\right)$ is defined as the following:

$$\begin{array}{cc}\hfill & \mathbf{\Psi }\left(\mathit{x}\right)=\mathit{v}\mid \mathit{v}=\arg \underset{v}{min}f\left(\mathit{v}\right);\mathit{v}\in \mathbf{\Omega }\left(\mathit{x}\right)\hfill \end{array}$$

The set for which the operator optimizes the system settings for the given commuter’s choice from the reaction set is defined by the inducible region (IR) as follows:

$$\begin{array}{cc}\hfill & \mathrm{IR}=(x,v)\mid G(\mathit{x},\mathit{v})\le 0,\mathit{x}\in X,y\in \mathbf{\Psi }\left(\mathit{x}\right)\hfill \end{array}$$

The Karush–Kuhn–Tucker (KKT) approach for solving bi-level problems was applied in [30,38]. The method involves substituting the lower-level program with the KKT conditions. This would transform the bi-level model into a mathematical model featuring equilibrium constraints if the lower-level program is convex and satisfies the linear constraint qualifications [56]. This resulting program is a large MIP that existing solvers can solve. However, solving a network with more than 40 nodes within a reasonable time is hard. This formulation is considered optimistic as the model favors the user’s benefits over the operator’s.

Interesting research that simultaneously considered the operator’s and commuters’ benefits in a multi-objective MILP was performed by [13]. The authors used the weighted sum approach to combine the operator’s and commuters’ benefits into one scalar objective function. This approach allows for an efficient frontier generation that allows the decision-makers to explore the trade-offs between the operator’s profits and the user’s benefits.

From the operator’s perspective, the problem involves determining the strategic, tactical, and operational decisions. In particular, the operator aims to optimally find the location of sharing stations, their capacities, and fleet sizes while considering the dynamic relocation and the charging requirements to maximize their revenue. From the commuter’s perspective, the problem aims to maximize the user’s benefits of the monetary value of the utility gained for each fulfilled trip from origin to destination.

To cope with the size of real-world problems, the authors proposed an aggregate model to reduce the number of relocation variables by adopting the concept of a virtual hub. Instead of relocating between any two stations, the proposed virtual hub concept assumes that the relocated vehicles are accumulated at a virtual hub and then relocated to the stations. A sensitivity analysis based on real data from France was demonstrated. The authors varied the demand levels, the accessibility distance to the shared station, and the subsidy levels provided and observed the number of vehicles used, rentals served, relocations performed, and the utilization of vehicles and how those dimensions impact the net user and operator benefits. For an average of 150 trips in various scenarios, the runs were terminated when either reaching a 2% optimality gap or a 9 h run.

7. Future Research Directions

In this section, we shed light on various practical considerations that have received no or little attention in the literature.

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Fleet types: Most of the cited works have assumed the deployment of standard vehicle options, often in the form of sedans or compact cars. However, expanding the fleet to include heterogeneous vehicles of varying sizes and capacities can better accommodate the diverse needs of commuters and provide them with more tailored transportation options at various rental rates and energy consumption levels. For example, by providing SUVs for family outings or electric vehicles for environmentally conscious users, CSSs can effectively enrich commuters’ overall experience.

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Charging type: Another practical concern that has not received enough attention is the deployment of fast and slow charging stations when operating electric-vehicle-sharing systems. Most of the referenced research studies have overlooked the distinction between slow and fast charging methods when optimizing the operational dynamics of electric-vehicle-sharing systems. The distinction between fast and slow charging deployment plays a significant role in the operational and tactical decisions made. On one hand, deploying fast charging can significantly reduce the charging time. This will help in the better management of fleet operations by minimizing vehicle downtime. On the other hand, traditional or slow charging often necessitates larger fleet sizes to account for the time vehicles spend unavailable during charging. Addressing this aspect of operational design can significantly enhance the feasibility and appeal of electric-vehicle-based carsharing, fostering its sustained growth and acceptance among users.

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Prediction of commuting behavior: Research efforts should study the factors influencing commuter choice within a shared mobility system in more detail. Investigating the trade-offs commuters consider while commuting with a shared vehicle, such as cost, convenience, travel distance, and personal preferences, can help in predicting the travel market trends and the share of shared vehicle mobility in urban transportation networks over the years [57]. The authors in [58] have used a multiple linear regression model to determine the factors influencing carsharing travel demand. This ultimately can improve the system’s efficiency in terms of optimizing the carsharing design and user satisfaction.

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Travel demand forecasting: Apart from studying how well the market accepts carsharing and understanding the behavior of carsharing users over an extended period, there is a need for further research into predicting immediate spatial and temporal SV trips. In [16], the authors have optimized vehicle relocation based on car pickup forecasting. However, some other research works have focused on forecasting car pickup and car return demand, as in the work of [59]. The authors proposed a station-embedding-based hybrid neural network, and based on a case study from China, the hourly demand forecasting error was reduced by about $56.5\%$ compared to conventional forecasting methods. The main drawback of this method is that vehicle relocation was not studied in the study. To the best of our knowledge, the research effort by [57] stands as the only study incorporating vehicle pickup and return demand forecasting alongside the optimization of vehicle relocation within the context of one-way carsharing. The authors introduced a multi-phase optimization approach aimed at reducing the emissions generated. Results based on a real case study from China showed that this approach maximized the order satisfaction rate and vehicle utilization, hence enhancing the sustainable operation of carsharing systems. This area of research should be further investigated.

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Carsharing in a multi-modal transportation network: The operation of carsharing in a multi-modal transportation system and how it impacts urban mobility in urban settings should also be studied in more detail. Urban planners can improve mobility through synchronized services developed through collaboration with other mobility providers such as public transport. Therefore, a wider range of commuters can be considered.

8. Conclusions

To conclude, we reviewed the main operational research problems that arise in the design and operation of one-way carsharing systems. We reviewed the models and the approaches to solve them. Although this area has been theoretically covered in [19], our aim was to review the main operational research issues that arise in this field. In particular, we have reviewed the tactical decisions related to resource dimensioning and allocation and trip pricing while explicitly considering vehicle balancing as a main decision variable. Moreover, we have reviewed the strategic decisions related to the location of shared stations or parking stations, along with considering optimizing their capacity while also considering vehicle balancing. We have carried out thorough analyses regarding the reliability of the proposed models and the solution approaches considered by considering realistic scenarios of uncertain shared vehicle demand levels or a continuous SOC when operating EV-sharing systems.

We broaden our review to encompass the research studies that consider the impact of the operator’s decisions on commuters’ mobility experience. This is, in particular, a very important area of research that is usually overlooked when planning carsharing. Solely optimizing the carsharing benefits without regard to the commuters’ response to the optimized operational and strategic decisions would cause shared vehicles to lose their attractiveness.

Lastly, we shed light on some practical considerations overlooked in the literature that may interest researchers.