Let’s walk! The fallacy of urban first- and last-mile public transport

Abstract

In recent years, there has been an upsurge in intelligent mobility solutions that provide door-to-door services. Although these services offer convenience to certain individuals, it is frequently overlooked that they can lead to welfare losses when accounting for the reduced health benefits that result from reduced physical activity. In this paper, we derive a welfare function of introducing first- and last-mile public transport services. By comparing possible health gains from walking with corresponding accessibility losses, we identify the distance boundaries under which the service fails to be socially beneficial. The results are based on a simulation study and draw on further insights from a recent agent-based model from Copenhagen focusing on first- and last-mile public transport. Although the model is intentionally stylized and may not apply universally to all scenarios featuring diverse population densities, demographic profiles, or transport network layouts, the fundamental conclusion presented in the paper is that first-mile services have minimal welfare impact for average trip distances below 1 km, appears robust even under conservative assumptions. In this case, the probability of failure is almost 100% for any realistic parametrization. This finding implies that planners and researchers should focus on the design of main transit networks and the access and egress of active modes to and from the stations. In particular, door-to-door services covering shorter distances should not be the priority of public funding unless in particular situations or contexts.

Introduction

Mobility solutions that provide door-to-door services (Alonso-González et al. 2018), first- and last-mile public transport services (Venter 2020; Zhang et al. 2015), and public transit feeder services Chandra et al. (2013) have received increasing attention in recent years. This study will refer to these services as first- and last-mile (FLM) services. However, it is essential to note that there are differences in whether these services operate on a demand-responsive basis, essentially covering door-to-door routes, or if they adhere to a specific route pattern with stops. While FLM services may be convenient for certain user segments, it is often forgotten that such services, besides the operational costs, come at a reasonably sizable welfare loss that results from adverse health effects. This loss is generated from users being less physically active when using these FLM services. Until now, the literature has not examined this loss in societal efficiency, despite the growing recognition of the positive health impacts associated with walking and cycling (Breda et al. 2018; Rich et al. 2021). This awareness provides some rationale for exploring this aspect further.

In this paper, we hypothesize that factoring in the aforementioned welfare loss might result in scenarios where FLM services become inefficient from a welfare perspective when employed for shorter distances. This results from substitution effects from active modes to the FLM service and the welfare losses and operational performance resulting from this shift.

Therefore, the study aims to study the societal welfare contribution of adding an FLM service by including active modes’ external positive health effects. In particular, using realistic yet conservative assumptions regarding the accessibility and cost of the service, the region under which such service is likely to fail from a welfare efficiency point of view is studied using concepts from the scenario discovery literature (Lempert et al. 2006) and simulation. Based on a standard discrete choice model and welfare economic theory, we show that the failure regime correlates with shorter distances where active modes are competitive. It suggests a distance threshold of approximately 1 km under which FLM services are largely irrelevant from a welfare-economic perspective. This finding is relevant for several reasons. Firstly, it suggests that from a societal point of view, it is more relevant to support the development of an overall public transit network that operates at a granularity above the minimum threshold rather than spending resources on FLM solutions below such threshold and door-to-door transport services in specific. Second, investments that focus on improving the accessibility of active modes to and from main stations should be an area of priority (Ha et al. 2023; Jiang et al. 2012). This taps into a more fundamental discussion of MaaS services in the Smart City sphere and how such services compete with active modes and main transit lines as also advocated in Currie (2018).

The paper is organized as follows. In Sect. “Literature review”, we study the literature with reference to scenario discovery and the evidence for positive health effects of active transport. Last, in the section, we dive into the FLM literature and how it relates to the current paper. In Sect. “Methodology”, we present the underlying welfare economic model and discuss the assumptions. Section “Results” presents results from the simulation study. In Sect. “Discussion”, a discussion is offered, including a discussion of results from a recent agent-based model from Copenhagen on FLM transport. Finally, in Sect. “Conclusions and future work”, we conclude and offer a perspective on future research avenues.

Literature review

The literature review is divided into three separate parts. First, we refer to the growing literature on scenario discovery methods, which form part of the methodological basis of this paper. Secondly, since the study is strongly dependent on recent evidence on the health benefits of active modes, we provide an overview of this literature and its main finding. Finally, we give an overview of the FLM literature and consider the current research directions and the relationship between this literature and the current paper.

The Scenario discovery literature

From a methodological perspective, this paper relates to a growing literature centred around the title "scenario discovery analysis" (Lempert et al. 2006), which aims at exploring scenarios and policy options that could result in negative consequences or system breakdowns (Groves and Lempert 2007). The underlying idea is that by simulating and analyzing these scenarios, researchers and decision-makers can gain insight into the conditions under which certain policies might fail or lead to adverse outcomes. This methodology has found numerous applications in climate assessment studies (Shortridge and Guikema 2016; Gerst et al. 2013), in biodiversity studies (Rosa et al. 2020), in transportation contexts, such as in the logistics sector (Halim et al. 2016), and as a method applied to the study of land use policies (Ariza-Álvarez 2021) to mention a few.

In this paper, unlike many large-scale studies, where simulation runs are expensive and time-consuming and where tailored statistical methodologies are applied to interpolate the solution space (Kwakkel and Jaxa-Rozen 2016; Kwakkel 2019), we face a situation where simulation runs are fast and rather simple. This allows us to enumerate the solution space quite accurately over the parameter space and under the assumptions set before the experiment. However, the idea is entirely similar to the original idea of Lempert et al. (2006) in that we study failure regions under uncertainty and use this insight to provide policy recommendations.

Health effects of active travel

Evidence suggests that biking and walking as active forms of transportation positively impact health (Brown et al. 2016; Fishman et al. 20185). A recent large systematic review of reductions in all-cause mortality from walking and bicycling (Kelly et al. 2014) shows that the effects are substantial. However, there is a large degree of variation between the different studies. The HEAT assessment model (Breda et al. 2018; Martin et al. 2006) estimates that for a person travelling 1 km by bicycle daily at a speed of 14 km/h, the total health benefits amount to 337 euros per year. The main factor is decreased premature fatalities by 0.0000800 and a monetized value of a statistical life (VSL) of 4,540,000 euro/death. Assuming an average travel distance of 4 km per day, the average health benefit per km is approximately 1 euro/km. A recent Danish study (COWI 2020) finds that the external costs of conventional bike riding are around 0.9 euros/km, which is largely similar to the values estimated in the HEAT assessment model (Breda et al. 2018; Martin et al. 2006). The Danish study also distinguishes between the external costs of conventional biking and e-biking, finding that the costs of e-biking are approximately half those of conventional biking. The values are used in a recent study of supercycle highway infrastructure in Rich et al. (2021), where the significance of the health effects is demonstrated. The estimated values in COWI (2020) are based on updated values from the recent review in Foley et al. (2018) and Foley et al. (2019), which link the effect of exercise with specific diagnoses such as cancer, diabetes, and heart disease and monetize the results in a Danish unit value per kilometre applying the value of a statistical life that is to be used in official project evaluations of infrastructure projects in Denmark (organized by the Ministry of Transport in Denmark). In addition to the positive health benefits of cycling, there are also negative effects due to increased accident rates. The cost of these accidents is based on the estimated production loss for different types of accidents (fatal, seriously injured, and injured) and the cost of treatment. In the Cowi study, estimates are adjusted to account for the systematic under-reporting of nonfatal accidents and the differences in accident risk between bikes and e-bikes. The difference between the external benefits of walking and bicycling introduces another source of uncertainty. The HEAT assessment model (Breda et al. 2018) estimates the health benefits of walking at 337 euros per year per person travelling 1 km daily at a speed of 6 km/h. This suggests that the underlying health costs of biking and walking are similar, which is also reflected in current Danish practice (TRM 2019).

First- and last-mile literature

As evidenced in Table 1, there is a strong research interest for papers considering different variants of FLM solutions compared to papers on "mass transit". Then, it appears to be opportune and pertinent to study the efficiency of these services in more detail and to characterize the failure region (Lempert et al. 2006) of transport scenarios involving these services by using scenario discovery methods as referred to in Sect. “The Scenario discovery literature”. In particular, because, up to this point, studies that address the link between mode substitution and health-related effects (as described in Sect. “Health effects of active travel”) for FLM transport have been absent from the literature.

Table 1 Google Scholar citations for selected the exact quotes represented in the columns of the table, e.g. ’door-to-door transit’, relating to first- and last-mile transport

Many research papers have been published on FLM transportation and on-demand services revolving around the "smart city" concept. These efforts aim to create and investigate a unified digital platform where users can plan, book, and pay for various services in a multi-modal environment (Mladenović 2021). The effect and impact of such systems have been widely investigated (Atasoy et al. 2015), often using operational research (Cordeau and Laporte 2007) to frame the problem into variants of travelling salesman problems (Sawik 2016) or using simulation methods (Quadrifoglio et al. 2008) to allow uncertainty and heterogeneity in the assessment. Scheltes and de Almeida Correia (2017), as an example, uses an agent-based modelling approach and reveals that a system in the city of Delft can only compete with the walking mode. Mostly, studies focus on efficiency from an operational perspective, such as in Gupta et al. (2010), or benchmark operational performance between different types of services (Rahimi et al. 2018), or focus on specific metrics such as utilization and trip completion Liyanage and Dia (2020). As seen in Table 1, many studies could have been referenced. However, as virtually none of these addresses the welfare loss stemming from reduced use of active modes when deploying FLM services, we see little value in including additional studies.

However, some articles have raised criticism and concerns about the potential of FML services. We can refer to Currie (2018), who questions the focus on FLM transport solutions instead of the focus on main transit lines. It is argued that there are few examples of viable public FML services in urban contexts due to poor scalability and efficiency. This echoes an earlier study by Enoch et al. (2006), which delved into the reasons behind the failure of FML services by examining 72 distinct demand-responsive projects. The study argues that a perilous temptation exists to provide excessively flexible services and incorporate costly technological systems that may not be necessary. However, a somewhat divergent conclusion is presented in the study by Perera et al. (2020), who investigates a demand-responsive service in Sydney. Their findings suggest that while FML services hold promise in connecting individuals from less accessible areas to public transport hubs, they must be economically viable and subject to proper regulation. It is worth noting, however, that the service discussed in this study primarily operates on a stop-to-stop basis, unlike a door-to-door service. Typically, door-to-door services necessitate a more extensive fleet of vehicles to cater to the demands (Badia and Jenelius 2021; Enoch et al. 2006), thus making it a more demanding and challenging service. Another paper is Rich et al. (2023), which applies an agent-based simulation model for the city of Copenhagen and shows that accounting for health losses significantly reduces the competitiveness of the last-mile service. The current study, however, goes further by embedding this research question into a welfare economic framework. This allows us to consider the trade-off between health effects and accessibility across various parameters.

While this paper intentionally focuses on a somewhat simplified scenario where walking is compared to an FML service, it is worth noting that there exists a growing body of literature on the choice of mode for first and last-mile trips. Some of these papers raise questions that could be pinpointed in future research avenues. Some studies (e.g., Rahman et al. (2022); Badia and Jenelius (2021)) propose that access and egress behaviours often differ when considering mode choices, with walking used more frequently on the egress trip. Other studies consider e-scooters and shared e-bikes as potential mode choices, attempting to anticipate future transportation trends (Stam et al. 2021; van Kuijk et al. 2022; Tzouras et al. 2023; Fan and Xumei Chen 2019) in this market. At this point, however, it should be noted that e-scooters will not generate a health surplus and are, therefore, quite different from active modes. Also, shared e-bikes require the availability of such services at the stop. Another study that can be mentioned is Thorhauge et al. (2022), who consider the FML choice of mode in a context with an autonomous service and finds that walking is the main substitute and that the main transport modes are largely unaffected by changes in FML attributes.

Drawing upon the literature cited above, this paper makes the following contributions. Firstly, it illustrates the importance of considering health impacts when planning public transport services in urban areas, particularly those covering distances where active travel is a viable alternative. Utilizing simulation techniques and insights from scenario discovery literature, we assert that the failure of such services, from a welfare economic standpoint, is critically dependent on including health considerations. Secondly, this finding bears substantial implications, potentially reshaping urban transit systems’ optimal design and granularity. We advocate for a shift towards prioritizing main transit lines and enhancing active mode access to stations, thus redirecting resources accordingly. Lastly, we hope that the simplicity of the proposed model framework can inspire other researchers to further explore similar failure patterns in diverse urban transit contexts through simulation methodologies.

Methodology

The analysis is based on a mode-choice comparison between a baseline and a scenario as presented in Fig. 1.

Fig. 1

A mode choice model for first- and last-mile transport, segmented into primary and feeder modes. The feeder mode in the baseline is represented by walk, while in the scenario, the feeder modes are represented by walk and FML

The baseline represents car and public transport as the main transport modes, with walking being the only mode of access to public transport. The scenarios have identical main modes but differ, including a second first and last-mile (FML) mode. The FML mode and walk compete for the access- and egress market. The analysis aims to explore the possible welfare consequences of introducing the FML mode over a spectrum of potentially different users and conditions. The aim is to illustrate precisely those conditions for which the FML fails from a welfare economic perspective. The model is presented in Sects. “Theoretical model–Limit cases”, while a discussion of the most important assumptions is left Sect. “Framing and assumptions”.

Theoretical model

The following section presents a simple random utility model from which we derive the consumer surplus function over a spectrum of heterogeneous users and services. This allows us to compare a baseline where walking is the only access mode to public transport with a scenario where this alternative is supplemented with a combination of FLM and public transport, as shown in Fig. 1.

Consider a trip with the following main transport modes $j=\{1,2\}$ with $j=1$ representing “car” and $j=2$ representing “public transport”. In addition, consider two potential access trip modes conditional on using public transport: $i=\{1,2\}$ with $i=1$ representing “walk” and $i=2$ representing an “FLM service” to the station. The reader is referred to Table 7 for a notation list.

For the main trip between the station and the end destination, let $TT_{n,j}$, and $C_{n,j}$ represent travel time and cost for user n and alternative j. If we let $VoT_n$ express the value of time for user n, the generalized time function (refer, e.g. to Rich (2021)) for main mode j, can be stated as

$$\begin{aligned} GT_{n,j}=TT_{n,j}+C_{n,j}/VoT_n \end{aligned}$$

(1)

For the conditional access trip linked to public transport, define the access walking time as $WT_{n,i=1}$ and let $TTF_{n,i=2}$, $CF_{n,i=2}$, and $WTF_{n,i=2}$ define the corresponding conditional access travel time, travel cost, and waiting time of the FLM service.

As the walking alternative has zero costs, it will have a generalized time that is simply equal to $WT_{n,i=1}$, whereas the generalized time for the feeder trips is equal to

$$\begin{aligned} GTF_{n,i=2}=TTF_{n,i=2} + WTF_{n,i=2} + CF_{n,i=2}/VoT_n \end{aligned}$$

(2)

Here $CF_{n,i=2} = \mu Dist_{n,walk}$ with $\mu$ representing the operational cost per km for the FLM service.

Utility functions can be stated as the choice of main mode in combination with the conditional choice of access mode for all individuals as shown below in Eq. (3)

$$\begin{aligned} U_{n,i|j} = V_{n,i|j} + \epsilon _{n,i|j}, \forall n,i,j \end{aligned}$$

(3)

Clearly, the indirect utility functions can be formulated for both the baseline and the scenario presented in Table 2. For simplicity, we assume that the error terms $\epsilon _{n,i|j}$ are IID-Gumbel distributed, aligning the underlying choice demand model with an MNL model. While more complex models, such as the nested-logit model, could have been chosen, particularly given its alignment with the structuring of conditional probabilities in Fig. 1, we lack the data necessary to support such hypotheses. Such models could potentially capture the imperfect substitutability between cars and public transport. Additionally, including a logsum parameter of less than one for the upper nest would reduce the demand substitution effect at that level, favouring the FML scenario due to a higher degree of substitution. However, without sufficient data to validate these assumptions, we prefer to maintain a conservative approach based on the MNL framework.

The indirect utility functions $V_{n,i|j}$ are presented below in Eqs. (4–8) in Table 2;

Table 2 Overview of indirect utility functions for the baseline and the scenarios. Only two alternatives are available for the baseline, whereas three are available for the scenario

It is assumed that people do not consider health effects in their mode choice. However, the welfare effect related to health is included as part of the welfare function, to be presented below.

The objective in the following is to analyze the cost-effectiveness of incorporating the FML alternative across various sets of parameter values, which reflect positive external impacts on health and accessibility. The research hypothesis is that, for most shorter distances, health benefits will significantly outweigh the improved accessibility benefits. This suggests that as a society, we need not overly prioritize FLM services and door-to-station transports except in particular circumstances.

The welfare function

To assess the impact of introducing the FML alternative compared to the baseline scenario from a welfare economic standpoint, we formulate the welfare function utilizing a rule-of-the-half approximation (Kidokoro 2004). While we typically seek to maximize the welfare function across various policies, in this instance, we focus on evaluating the welfare function across different parameter combinations, each representing distinct assumptions. We aim to identify conditions where the service fails to yield positive welfare and vice versa.

The welfare function depends on prices and demand in both the baseline and alternative scenario, as outlined in Eq. (9). Note that prices and demand follow the notation in Table 2.

$$\begin{aligned} Z = {\sum _{n}\sum _{i,j}} (p_{n,i|j}^0-p_{n,i|j}^1) \cdot \frac{(d_{n,i|j}^0 + d_{n,i|j}^1)}{2} \end{aligned}$$

(9)

Because we assume that the price of driving by car remains unchanged, i.e., $p_{n,j=1}^0=p_{n,j=1}^1$, the car alternative effectively cancels out. Additionally, since the walking access distance remains constant between the baseline and the scenario, the combination of public transport and access walking similarly cancels out. As a result, the welfare function is significantly simplified, leading to a reduced form expressed in Eq. (10).

$$\begin{aligned} Z = {\sum _{n}} (p_{n,i=1|j=2}^0-p_{n,i=2|j=2}^1) \cdot \frac{(d_{n,i=1|j=2}^0 + d_{n,i=2|j=2}^1)}{2} \end{aligned}$$

(10)

With

$$\begin{aligned}{} & {} p_{n,i=1|j=2}^0 = WT_{n,j=2}VoT_n - \theta Dist\_walk_{n,i=1|j=2}, \forall n \end{aligned}$$

(11)

$$\begin{aligned}{} & {} p_{n,i=2|j=2}^1 = GTF_{n,i=2|j=2} VoT_n, \forall n \end{aligned}$$

(12)

$$\begin{aligned}{} & {} d_{n,i=1|j=2}^0 = \frac{exp(V_{n,i=1|j=2})}{exp(V_{n,j=1}) + exp(V_{n,i=2|j=2})}, \forall n \end{aligned}$$

(13)

$$\begin{aligned}{} & {} d_{n,i=2|j=2}^1 = \left( \frac{exp(V_{n,i=2|j=2})}{exp(V_{n,i=1|j=2}) + exp(V_{n,i=2|j=2})} \right) \left( \frac{exp(V_{n,j=2})}{exp(V_{n,j=1}) + exp(V_{n,j=2})} \right) , \forall n \end{aligned}$$

(14)

In Eq. (11) $\theta Dist\_walk_{n,j=2}$ expresses the health benefits of walking ($\theta$ is the external monetary welfare contribution of one kilometre of walking and has the opposite sign as travel time and cost). In principle, it may be argued that people substitute active transport behaviour for other fitness activities, based on which we should expect only a fraction of $\theta$ to enter the surplus function. However, here, we only refer to the official Danish number (TRM 2019), which we vary downwards to investigate the effect of other parameter values.

In Eq. (12), we translate the generalized access time of using FML into monetary terms by multiplication with official values-of-time.

Equation (13) expresses that because walking is the only available access alternative in the baseline, the conditional probability of choosing to walk is equal to 1. Hence, only the main mode probability is effectively used.

Finally, Eq. (14) represents the choice probability of choosing the FML alternative over walking. As discussed above, this is expressed as a simple MNL probability.

Extending the above welfare function to include level-of-service changes for the main mode is straightforward. Such effects could result from changes in congestion patterns, or it could reflect that by improving access conditions.

On the welfare contributions from health and accessibility

Considering the average surplus for a representative consumer n it follows that Eq. (9) can be reduced substantially. If we define ${\widetilde{d}}_n = \frac{1}{2} ( d_{n,i=1|j=2}^0 + d_{n,i=2|j=2}^1)$ then, based on the simplified welfare function in Eq. (10), the condition for a positive welfare contribution from a representative consumer n can be stated as

$$\begin{aligned}{} & {} 0 \le {\widetilde{d}}_n ((WT_{n,j=2} - GTF_{n,i=2|j=2})VoT_n - \theta Dist\_walk_{n,j=2}) \Rightarrow \end{aligned}$$

(15)

$$\begin{aligned}{} & {} 0 \le Dist\_walk_{n,j=2} \left( \frac{60 \cdot VoT}{ws} - \frac{60 \cdot VoT}{fs} - \theta -\mu \right) - WTF_{n,i=2} \cdot VoT) \Rightarrow \end{aligned}$$

(16)

$$\begin{aligned}{} & {} \theta Dist\_walk_{n,j=2} \le Dist\_walk_{n,j=2} \left( \frac{60 \cdot VoT_n}{ws} -\frac{60 \cdot VoT_n}{fs} -\mu \right) - WTF_{n,i=2} \cdot VoT_n \end{aligned}$$

(17)

Where in Eq. (16) ws is walking speed, fs is the speed of the feeder mode, and $\mu$ is the cost of the feeder mode per km. Note also that although we can eliminate the scaling of demand, given by ${\widetilde{d}}_n$, when considering a single individual n, we cannot eliminate the scaling when considering the aggregated surplus function. This is because ${\widetilde{d}}_n$ is a function of travel time components and distances, which will affect the weight of the contributions from each user. In other words, for simulation purposes, we maintain the scaling of demand to correctly calculate the weighted consumer surplus over the population.

The interpretation of Eq. (17) is straightforward. It says that the service will be beneficial only if the monetized travel time savings of the feeder service are greater than the monetized health benefits of walking minus the monetized travel time. The equation lends itself nicely to the concept of a frontier where health effects on the left-hand side are compared to accessibility on the right-hand side.

Limit cases

Note first that if $Dist\_walk_{n} \rightarrow 0$ then $Z_n \rightarrow 0$. In this situation, while walking has no health benefits, nothing is gained from implementing the feeder service because of waiting time and the cost of ordering the service. If such positive start-up costs exist, there should be a region of shorter trips for which the service should fail.

Two things will happen if $Dist\_walk_{n} \rightarrow \infty$. Firstly, if the feeder mode is more competitive over longer distances, the waiting time cost should offset the slower walking speed. However, concurrently, the cost also escalates for the feeder mode. Consequently, the delicate balance between travel time savings and operational costs ultimately dictates the service’s viability.

If VoT $\rightarrow \infty$, more emphasis is put on accessibility. This suggests that the region in which the service fails is when VoT is small.

Parameters of cost and time in the utility functions only affect demand. Although it does affect the aggregated consumer surplus somewhat, it turns out that the overall welfare optimization is not overly dependent on specific beta parameters as long as these are within a realistic range. We apply generalized cost parameters from Hallberg et al. (2021) to maintain a realistic range.

Results

This section outlines the key assumptions underlying the study, with a discussion of how these assumptions might influence the direction of the findings. We then present the simulation analysis results.

Framing and assumptions

Several assumptions are introduced to simplify the analytical model presented in Sect. “Methodology” while preserving the general direction of the results. In instances where these assumptions tend to support the FML case (or vice versa), we explore their impact, probable consequences, and potential methods for alleviation.

• 1. Only walk: We focus only on walking as the feeder mode in the baseline and exclude bicycles. One reason is that we consider relatively short distances for which walking is the preferable option (Christiansen and Baescu 2020). More importantly, however, biking and walking offer similar external health benefits (Breda et al. 2018; COWI 2020), and are usually not associated with travel costs. The higher travel speed of bicycles makes it a more desirable option in terms of travel time. Excluding cycling likely results in the FML service appearing slightly more favourable from a welfare economic standpoint. This is primarily because the travel time of the competing alternatives, against which it’s assessed, is slightly overestimated.

• 2. No distinction between access and egress: While these are likely to differ, as discussed in Sect. “First- and last-mile literature”, it makes no difference in this simplified case where only walk and FML are considered.

• 3. Shorter distances only: We limit the study to shorter distances between 0-2 km and deliberately discard more specialized FML services that operate over longer distances and often in rural areas. Such services are quite different and may not comply with the idea of an FML service that operates only on the journey’s first (or last) part.

• 4. FML distances: We assume that walking distance is equivalent to the distance of the door-to-station service. This is a conservative assumption, as walking distances are often more direct than road distances. In dense urban areas, FML services could face one-directional roads or other network obstacles that do not apply to walking.

• 5. Main mode demand effects are included: When the FML alternative is introduced, it generally causes the public transport nest to be more retractable, and we include this by representing the increase in demand. However, this effect is small because the level of service for main modes is unchanged and represents a significant portion of the total level of service. This is consistent with Thorhauge et al. (2022) suggesting that the overall elasticity of demand for primary trips remains largely unaffected by FML services.

• 6. Cost structure assumes autonomy: The operational cost of the FLM service is based on a simple total cost of operating the vehicles. This includes depreciation, repair, fuel, and other things. In this setting, we assume the shuttle is autonomous and discard any wage costs to the driver. This assumption tends to favour the FML service over the alternatives as its cost is underestimated compared to a present-day scenario.

• 7. While there is evidence that transfer penalties exist when shifting between public transport modes, e.g. as in Nielsen et al. (2021) that finds a minimum penalty corresponding to 5.4 min of in-vehicle-time, it is here neglected. The FML context is slightly different from many other transfer contexts, and how to set this parameter is unclear.

• 8. The ’cognitive cost’ of booking an FML service and the uncertainty of it arriving on time is not considered. The literature on these aspects is not well developed. However, this would likely be an important element, particularly on shorter trips.

Regarding the cost structure (Assumption 6), which favours the FML service by assuming autonomy, it should be noted that, ideally, these costs should be shared among passengers. However, as shown in Rich et al. (2023), utilization rates for a similar on-demand shuttle service in Copenhagen were around 10%. Given the shorter distances in this experiment, it is reasonable to assume that these shuttles will, on average, serve one passenger at a time due to the empty runs required to provide the service. Part of the simulation study involves varying the operational costs, which corresponds to changes in the utilization rate.

To summarise, the first and second assumption is mostly a framing of the study; assumptions three and four slightly favour the FML, assumption five is neutral, while assumptions six, seven and eight strongly favour the FML. Consequently, we believe it is safe to assume that the FLM service (in this specific framing) is included on neutral terms and, if anything, favours the FML service rather than the opposite.

It should be noted that while ticket prices negatively impact consumer surplus, they also generate income for the state. As a result, this transfer cancels out in the welfare function.

Simulation results

As described in Sect. “Methodology”, we study the trade-off between the benefit-cost rate of establishing the door-to-station service and the distance of the access trip. In other words, the aim is to identify the regions for which the service is likely to fail from a welfare perspective. As commented, these regions are expected to be characterized by low distances, low VoT, a high positive health external effect $\theta$, and a high operation cost of the service $\mu$. For further details on the data-generating process of the simulation experiment, we refer the reader to Tables 5 and 6.

Below, we present the market shares of the different mode combinations in the baseline and the scenario. As it appears from Eqs. (5) and (8) in Sect. “Methodology” it is assumed that the alternative specific constant of the walking alternative and the FML alternative are identical and equal to zero. However, in reality, this assumption is improbable. In real-world scenarios, the walking mode, inherent flexibility and absence of booking and waiting requirements should encounter fewer unobserved variables working against it.

Note that there is a small substitution effect at the level of the main modes when introducing the FML. The overall market share of public transport increases from 18% to slightly over 21% as seen in Table 3. This is included in the welfare evaluation as described earlier in Sect. “Methodology”.

Table 3 Inferred market shares in the simulation

In Fig. 2, we present the result of the first simulation. The figure depicts the average consumer surplus return as a function of the access distance and three different value-of-time categories. The figure is based on 20,000 simulated trips, and for Fig. 2, we have maintained the average operating cost of $\mu = 5.9$, which corresponds to Bösch et al. (2018) and Rich et al. (2023).

Note that results are not deterministic as we apply random sampling concerning access distances and the waiting time of the feeder transport mode. In the Figure, we applied beta parameters corresponding to the values in Table 5. However, experiments with alternative parameter values largely leave the pattern unchanged.

Fig. 2

Simulation of average consumer surplus $Z_n$ per access trip (DKK/trip) as a function of access distance (km) and value-of-time segments (DKK/min). A: $\theta = 0$, B: $\theta = 2.25$ DKK/km, C: $\theta = 4.5$ DKK/km, D: $\theta = 6.75$ DKK/km. For all figures $\mu$ = 5.9 DKK/km

Several observations are revealed in Fig. 2. First, the region where the service fails to make any societal contribution is characterized by low VoT and low access distances. Moreover, if the positive external cost of walking $\theta$ is high, then this further hammers the profitability of the service. Sub-Figure D illustrates the situation where the currently recommended value is applied. Therefore, with conservative parameter values, there is almost no region for which the service is profitable if the average service distances for passengers are less than 1 km.

As there is quite some uncertainty for the operational cost $\mu$ it is reasonable to examine the region of failures for a wider interval of $\mu$. This is particularly true as it may reflect revenue, as discussed earlier. This is presented in Table 4. In addition, we now consider the aggregated surplus over the different segments in the analysis.

Table 4 Aggregated surplus Z for different parameter combinations and distance segments

Conclusions largely correspond to that of Fig. 2 except that operational cost roles now become clearer. The bottom line is that even in the most optimistic scenario, every service that operates below 0.5 km fails. It might be argued that an operational cost of $\mu = 2.95 DKK/km$ is also very optimistic. Therefore, the realistic failure rate for trips less than 1 km is almost 100%.

Discussion

The paper sheds light on the societal performance of FLM solutions and the failure region of these services. If we account for lost health benefits, it is shown that there is an almost 100% risk of failure when distances are less than 1 km and if we apply commonly accepted operational cost estimates for such services. This taps into a more general discussion of public transport and how such services should be designed in urban areas. While it may be relevant for special groups, such as elderly people or disabled people, it is highly questionable if these services provide net benefits for society at large. Below, we offer four perspectives on the findings and their wider implications.

Viable business models may exist

Just because society should not invest in FML services based on a welfare assessment, it is not the same as saying that it might not present a viable business case. The feasibility largely hinges on-demand elasticity, pricing dynamics, and operational expenses. However, exploring these aspects falls beyond the scope of this paper. It entails validating the demand model through empirical data and gaining comprehensive insights into the operational efficiency of such services, which can vary significantly across different locations.

There are many other examples in society where goods or services may not align well with societal welfare objectives yet remain financially viable from a purely business-oriented standpoint. The distinction lies in the fact that the external effects, whether positive or negative, may diverge from the perceived costs associated with the service. One prominent example is the tobacco industry. Indeed, cigarette manufacturers can generate substantial profits despite the well-documented negative health effects associated with smoking. However, the societal costs in terms of healthcare expenditures due to smoking-related illnesses and lost productivity are significant, which is why the state tends to internalize some of these negative effects through taxes. In this case, we do not consider taxation as public transport is mainly subsidized. Rather, we ask whether such services should be subsidized and conclude that this depends on the granularity of the main transit network. However, in all likelihood, and most cases, there is no welfare contribution to these services if they are below a distance threshold of 1 km.

FLM versus mass transit

The paper argues against relying on on-demand mobility as a first-mile/last-mile (FML) solution, particularly for shorter distances. This does not mean all solutions should be based solely on traditional mass transit. Smart solutions that integrate with the mass transit system are still very much warranted, as suggested in recent papers by Ng et al. (2024), Fielbaum and Alonso-Mora (2023), and Calabrò et al. (2023).

However, this raises an interesting debate about prioritizing mass transit and FML services. Often, instead of allocating resources to FML services, it may be more beneficial for societies to invest in efficient mass transit systems with a network of well-defined stations and enhance the accessibility of active modes to and from these stations, as highlighted by Ha et al. (2023); Jiang et al. (2012). This recommendation is valid as long as the mass transit network covers access trip distances adequately, which depends on the specific context and the operational performance of the mass transit system.

Generally, FML services cater to a much smaller audience and are not scalable to the same extent as mass transit, as noted by Currie (2018). This observation underscores the broader discussion of services for the many versus services for the few. With public transport systems facing increased stress due to a lack of public funds and the aftermath of COVID-19, it is crucial to eliminate inefficiencies in the public transport sector. Consequently, more frequent investigations of areas where services are failing should be conducted.

The population density of a city significantly influences its transportation needs. In larger cities, the case for mass transit over FML services is even stronger Enoch et al. (2006). Higher density reduces travel distances, enhances mass transit performance, and increases congestion for many FML services. Thus, despite the rising number of research papers on "last-mile transit" compared to "mass transit," a redirection of research efforts might be warranted in several cases.

Door-to-door versus other types of FLM services

Another discussion regards the type of FLM services, of which there can be many. To facilitate this discussion, we will here present a cost-benefit analysis for an autonomous FLM service in Copenhagen, where a flexible door-to-station and a station-to-stop were considered (Rich et al. 2023). This case is interesting because the distances in this network are between 0 and 2 km and correspond to the distances analyzed in the simulation model. The study examines an FLM service in a new area in Copenhagen, e.g., The Hersted Industrial Park, close to a new light rail corridor. Using an agent-based model, different feeder services are compared to a baseline where people only walk. The analysis covers two different route patterns, e.g. fixed routes (between nine predefined stops) and door-to-station services. It accounts for waiting-time loss, operational costs, and the health benefits that result when people are walking.

Based on a large transport model, we apply realistic arrival time patterns in the simulation. It is worth mentioning that while bus operating costs are similar to those of Table 5 the health costs are slightly higher and correspond to those of the HEAT project (Breda et al. 2018). Furthermore, as the analysis investigates scenarios for 2035, a complete cost-benefit analysis is performed where everything is converted to a net present value term.

The four scenarios are investigated.

• 1. Scenario 1: Only trips from Station to Stops (StS) and vice versa. These leave out shorter trips between stops.

• 2. Scenario 2: Travelling between all stops (BS). Here, we allow trips between daily stops, making trips shorter.

• 3. Scenario 3: Travelling from Station to Stops + 20% of trips between all Stops (StS + BS). This is a hybrid scenario between Scenario 1 and 2 and generally implies that a fraction of shorter trips between stations is also considered. Hence, it results in shorter trips but also trips that are more evenly spread out across the day.

• 4. Scenario 4: This is a continuation of Scenario 3, where distances increased by 100%. This essentially increases urban sprawl and considers the service over longer distances.

The intricate workings of the underlying model, particularly the agent-based simulation, can be studied in Rich et al. (2023), but are not crucial at this juncture. Instead, we will focus on the primary inference drawn from this model as it incorporates the lost health benefits in a similar way as in this paper. Two main conclusions stand out. Firstly, if health benefits are included in the calculation, it substantially diminishes the societal profitability of the new service. This is seen by comparing the blue and the orange bars in Fig. 3. The other important observation, which speaks to the comparison of different types of services, is that for this system, the on-demand services are less efficient than fixed route operations. This speaks to the challenges of door-to-door services, which necessitate a larger fleet of vehicles to serve demands, thus making it a more demanding and less efficient service to provide (Badia and Jenelius 2021; Enoch et al. 2006). Once more, while this observation doesn’t pertain to the design of any particular system, it does raise doubts about the broader applicability of flexible FLM systems.

Fig. 3

Simulation of cost-benefit performance for Scenario 1 - 4 for fixed routing and a station-to-door service. Blue bars represent B/C rates for the service when health costs are not included, while orange bars represent the B/C rates when health costs are included (refer to Table 5 for the specific value)

A final comment is that across the scenarios and service types shown in Fig. 3, there is no region where the new service does not fail. We can also see that, unlike Table 4 and Fig. 2, where larger distances were always better, the results are slightly more ambiguous here. This is the result of waiting time dynamics in the system, the high cost of operating the vehicles, and the specific OD pattern that is simulated in this system. However, this underlined once again that we need to consider health loss when examining FLM solutions.

The broader implications for the design of public transport networks

The broader implications of this study have already been touched upon in the previous sections. However, a summary is in place at this stage. Firstly, it is essential to emphasize that this paper does not rule out the use of FML services in the future. Anticipated technological advancements and cost reductions will pave the way for their adoption. However, the market for these services will likely be driven by commercial activities with little involvement from the state. At least, as demonstrated in this paper, if we include losses in health effects, it is not apparent that such services pose a net benefit for the state when operated on shorter distances and, therefore, should be subjected to subsidies. The paper offers a straightforward approach to assessing this, although refinement of the model and inputs is essential to account for specific contextual factors. This implies that while the state should not obstruct or object to such services, they should direct their attention and subsidies to main transit lines. Moreover, the state should make it easy to get to and from the stations to support active modes and their resulting positive welfare contribution. Finally, we believe that examining transport policies through a lens of both failures and acceptances can provide additional insights. This approach aids in averting wasting public funds and ensures resources are allocated to areas where they have the most value for society.

Conclusions and future work

In the paper, we investigate the welfare performance of first- and last-mile public transport services by accounting for welfare losses that result from reduced walking. The probability of failure of these services is examined over a wide range of parameters by considering the aggregated welfare function. It is concluded that while such services can be justified for certain groups, they are likely to fail for almost any reasonable parameter combination as long as the average trip length is below 1 km. This is a consequence of high operating costs and waiting time, but most importantly, due to the loss of health benefits resulting from reduced walking mileage. The latter effect has not been studied in the literature in the context of first- and last-mile transit until now, although recent research suggests that the benefits are significant. The main planning implication from the paper is that rather than being obsessed with first- and last-mile public transport services, the research community should pay more attention to efficient mass transit solutions for the many and design efficient routes to and from stations to support usage of active modes. This does not mean that FML services will not play an essential role in the future as costs are reduced and technology is improved, but it emphasizes that state subsidies may not be warranted for these types of services.

Future work may consider; i) The relaxation of some of the limitations as references in Sect. “Framing and assumptions” to further investigate failure regimes under different and possibly less conservative assumptions, ii) the extension of the problem to a network representation where agents and first- and last-mile services are simulated over a geographical space and in connection to a public transit network. This might be used to determine the optimal granularity of main transit networks for a given urban context, iii) The inclusion of the entire transport chain from home to the end destination to properly reflect the first- and last-mile service component in such transport chains to further reflect on the flexibility issues and the need to be on time for such services.

Appendix A. Parameters and data generating processes used in simulation framework

See Tables 5, 6 and 7.

Table 5 Parameters used in simulations

Table 6 Derived variables applied in the simulation

Table 7 Acronyms and mathematical notation are used throughout the paper