Production, Manufacturing and Logistics
Locating alternative-fuel refueling stations on a multi-class vehicle transportation network

https://doi.org/10.1016/j.ejor.2017.02.036Get rights and content

Highlights

  • A multi-class vehicle transportation network is introduced.

  • Vehicles have different driving ranges and fuel tank levels at origins/destinations.

  • A binary linear programming model is proposed for locating refueling stations.

  • The objective of maximizing the total traffic flow covered.

  • The model is applied to the Pennsylvania Turnpike using the 2011 truck traffic data.

Abstract

The existing literature regarding the location of alternative fuel (AF) refueling stations in transportation networks generally assumes that all vehicles are capable of traveling the same driving range and have similar levels of fuel in their tanks at the moment they enter the network and when they exit it. In this article, we relax these assumptions and introduce a multi-class vehicle transportation network in which vehicles have different driving ranges and fuel tank levels at their origins and destinations. A 0-1 linear programming model is proposed for locating a given number of refueling stations that maximize the total traffic flow covered (in round trips per time unit) by the stations on the network. Through numerical experiments with the 2011 medium- and heavy-duty truck traffic data in the Pennsylvania Turnpike, we identify the optimal sets of refueling stations for AF trucks on a multi-class vehicle transportation network.

Introduction

Compressed natural gas (CNG) and liquefied natural gas (LNG) have recently been considered as candidate next generation fuels to improve fuel economy and produce lower greenhouse gas emissions than traditional fossil fuels, such as gasoline and diesel. In particular, LNG is the top alternative fuel (AF) for diesel-powered trucks, which move approximately 90% of the freight tonnage in the US, because LNG has higher energy density than other AFs (Whyatt, 2010). LNG engines are suited for mid- and heavy-duty trucks, which are classified by the Federal Highway Administration (FHWA) into classes 6–10 according to the number of axles and trailer units (Randall, 2012, Appendix A), as shown in Fig. 1. LNG-powered trucks can reduce up to 16% of greenhouse gas emissions and 73% of volatile organic compounds emissions compared to diesel-powered trucks (Tiax LLC, 2007). Furthermore, the low fuel price of LNG compensates for the high cost of purchasing LNG-powered trucks (Garthwaite, 2013). Myers et al. (2013, Appendix C) state that trucking companies can reduce operational costs if the LNG price is at least $0.52 per diesel gallon equivalent less than diesel price, given that trucks travel at least 120,000 miles annually over 6 years.

A proper AF refueling availability is necessary to encourage the use of AF vehicles, including LNG-powered trucks. There exists a variety of approaches to develop an AF infrastructure on a transportation network. Vehicles may need multiple refuelings for long-distance trips because fuel tank capacities are limited; the driving range of AF vehicles is, in fact, even shorter than that of traditional fuel counterparts. A set of refueling stations must be located along a path to cover the corresponding traffic flow when the path distance is longer than the driving range. Kuby and Lim (2005) develop the flow refueling location model (FRLM) to locate AF refueling stations on a transportation network with the objective of maximizing the total traffic flow covered by the stations. The FRLM requires a pre-generation stage to establish the combinations of refueling stations that can cover vehicles on each path for a given driving range. Evaluating the station combinations on all paths of a given network requires a large computational effort. To resolve the computational burden of the FRLM, Lim and Kuby (2010) suggest the use of three heuristics, namely greedy, greedy substitution, and genetic algorithms, and Kuby et al. (2009) integrate these heuristic algorithms to a geographic information system to analyze scenarios and evaluate the tradeoffs for the development of a hydrogen refueling infrastructure in Florida. As an alternative approach to reduce the complexity of the FRLM, Capar and Kuby (2012) propose an efficient formulation of the FRLM. Since their model does not need the pre-generation stage of feasible refueling station combinations, it is capable to efficiently find exact solutions for large-scale network problems.

While the FRLM mainly finds the locations of refueling stations that maximize the origin–destination (OD) flow refueled, a set-covering formulation of the problem can also be applied to locate the stations with the objective of minimizing the total cost of building the refueling stations to cover all traffic flow on a given network. In general, the set-covering approach uses the OD distance matrix, instead of the OD flow volume matrix required by the FRLM. OD distances are easily collected, while OD flow volumes are usually estimated, as it is difficult to obtain their exact values or probability distributions. We note that the set-covering approach also requires the use of the OD flow volume matrix when the set-covering approach defines path coverage with respect to station capacity. Considering the advantage of the set-covering approach on collecting the OD distance matrix, Wang and Lin (2009) extend the basic concept of the set-covering problem to formulate a mixed-integer programming model that determines locations of AF refueling stations with the objective of minimizing the total building cost of the stations. The model evaluates whether a vehicle at a given site can arrive to the next site with the fuel remaining on the tank. This evaluation procedure for each path is, however, very computationally costly. To reduce the computational burden of the set-covering approach, MirHassani and Ebrazi (2012) provide a new reformulation of the set-covering model for AF refueling stations, which is able to solve large-scale set-covering problems much faster. Also, the new reformulation can be simply changed to a flow-base maximum coverage model.

In addition to the solution approaches for the AF refueling station location problem discussed above, there exist several extensions of the FRLM that consider additional situations. First, some drivers may be willing to detour from their pre-planned paths for refueling. According to a survey that compares spatial refueling behaviors between CNG and gasoline vehicle drivers, CNG vehicle drivers seem to detour more than gasoline vehicle drivers do for refueling services (Kuby, Kelley, & Schoenemann, 2013). In order to account for driver deviation behavior, Kim and Kuby (2012) propose the deviation version of the FRLM with the objective of maximizing the total traffic flow covered by the stations on deviation paths. Kim and Kuby (2013) then develop heuristic algorithms for the deviation version of the FRLM to solve large network problems. Second, external restrictions on setting up refueling stations can be considered in real-world networks. Upchurch, Kuby, and Lim (2009) consider capacity constraints that limit traffic flow volumes at the refueling stations, and Capar, Kuby, Leon, and Tsai (2013) consider a budget constraint to analyze the effects of different land values. Third, it may be possible to cover more traffic flow volume when refueling stations are able to be located along the arcs. Kuby and Lim (2007) propose an approach for adding a single site on the middle of paths and suggest two dispersions methods, one minimizes the maximum length of subdivisions of the original arcs and the other maximizes the minimum length of subdivisions of the original arcs. The FRLM with original and additional candidate sites can provide better optimal locations for AF refueling stations to maximize the traffic flow volume covered by stations. Ventura, Hwang, and Kweon (2015) introduce the continuous version of the refueling station location problem where a single refueling station can be located anywhere on a tree transportation network. Lastly, there are other station location network design studies considering different initial states of charge of electric vehicles at origins and integrated decision-making models for marketing, engineering, and operational decisions (Kang et al., 2015, Lee et al., 2014).

In order to invigorate the use of AF vehicles in intercity freight transportation, Hwang, Kweon, and Ventura (2015) propose a new mathematical model for developing AF infrastructures on directed (symmetric) transportation networks when vehicles traveling the network have the same driving range and similar fuel levels at ODs. A directed transportation network consists of two divided-pathways, which are separated by a traffic barrier, and is only accessible from entrance and exit ramps, so that vehicles can drive at high speed safely for long-distance travel without any interruption such as traffic signals and intersections. Such a transportation network is called a dual carriageway or a divided highway, and many countries apply this road system to motorways, freeways, expressways, and toll roads. In general, a directed transportation network has built-in service facilities that provide service such as travel information, restrooms, food, and fuel for drivers’ convenience, so that drivers use these facilities on the network without deviating from their preplanned trips. Built-in service facilities are classified according to accessibility; a single-access service facility can provide refueling service only to vehicles in one driving direction, while a dual-access service facility can offer its service to vehicles in both driving directions.

This paper proposes a new mathematical model for a refueling station location problem on a directed transportation network where AF vehicles have different driving ranges and fuel tank levels at the entrances and exits. In general, some vehicles have higher fuel efficiency or carry a larger fuel tank than others, so that vehicles have different driving ranges depending on vehicle classes. The information on traffic flow distribution of the vehicle classes in a road system is easily obtained from federal agencies or related corporations. For example, in case of Pennsylvania, the information on the traffic flow distribution of vehicle classes is available from Pennsylvania Spatial Data Access (Pennsylvania Spatial Data Access, 2016). Korea Expressway Corporation (2014) also annually publishes a summary of the traffic flow statistics in South Korea.

Next, we consider that a vehicle has different remaining fuel tank levels at the entrances and exits of a transportation network. A vehicle would depart from its home location, such a transportation company, travel to a road network, go through a particular entrance and exit pair of the network, and then exit the network to reach a customer location. After that, the vehicle would return to the home location. During this round trip, the vehicle may be refueled outside the road network in or near its home location and customer locations, so that it is reasonable to consider different entry and exit fuel levels for vehicles on the transportation network. Note that, for convenience, we regard entrances and exits of a transportation network as origins and destinations (ODs) of traffic flow, respectively.

We suggest three methods to estimate fuel tank levels at OD pairs. First, we can survey drivers at each entrance and exit tollbooth in toll roads or at refueling stations in regular transportation networks asking how much fuel is left in their tank. Sperling and Kitamura (1986) and Kuby et al. (2013) surveyed drivers at refueling stations in the San Francisco Bay Area and Los Angeles County asking for their refueling patterns and preferences. Secondly, using a global positioning system tracker for drivers can be another way to estimate fuel remaining in the tank at OD pairs. Note that, for mobile device users, Google Map currently provides the Timeline service that tracks users’ itineraries (Google, 2016). By investigating where drivers have refueled before entering or after exiting a transportation network, fuel tank levels at OD pairs can be estimated. Lastly, fuel consumption data can be collected from an on-board diagnostics (OBD) system, which monitors emissions, speed, mileage, and other useful data on vehicles (Alessandrini, Filippi, & Ortenzi, 2012). By US Federal Law, all light-, medium-, and heavy-duty vehicles in the US produced after 1996 support an OBD system primarily for emissions inspections (Environmental Protection Agency, 2015). The statistics of fuel tank levels can be obtained and analyzed through an OBD acquisition tool.

In this paper, a directed transportation network with multiple vehicle classes and different fuel levels at ODs is defined as a multi-class vehicle transportation network. The objective of the problem is to determine the locations of the AF refueling stations that maximize the total traffic flow covered on the multi-class vehicle transportation network under consideration. The remainder of the paper is organized as follows. In Section 2, we first describe the general problem settings and assumptions. Next, we group OD pairs into two types depending on the OD distance. Then, covering conditions for round trips are established for each type of OD pair. Considering the specific covering conditions, a 0-1 linear programming model is formulated for the refueling station location problem on a multi-class vehicle transportation network. Section 3 describes the Pennsylvania (PA) Turnpike and discusses an approach to reduce the size of the network. Then, the proposed model is applied to the simplified PA Turnpike under different settings in terms of vehicle classes and available fuel tank levels at ODs. We also consider random fuel tank levels to test the robustness of the model. Lastly, Section 4 provides conclusions and topics for future research.

Section snippets

Model development

Let G(V, E) be a directed (symmetric) transportation network with set of vertices V  for the origins and destinations (ODs) and set of edges E={(vi,vj)|forsomevi,vjV}, where |V|=nV and |E|=nE. The distance between origin vi and destination vj is denoted by d(vi, vj), and it is considered to be the length of the shortest path between vi and vj. Note that, since network G is symmetric, (vi, vj) ∈ E if and only if (vj, vi) ∈ E; in addition, d(vi,vj)=d(vj,vi). Instead of distance, the length of a

Computational experiments

The PA Turnpike road network is chosen as the case study network to find the locations of AF refueling stations for LNG trucks. The proposed model is applied to a simplified version of the turnpike network with a reduced number of (aggregated) interchanges considering multiple truck classes using the 2011 truck volume data (Myers et al., 2013). Three truck classes with different limited driving ranges and four different fuel tank combinations are considered, so as to analyze the effect of fuel

Conclusions

In this article, we have introduced a multi-class vehicle transportation network, where vehicles have different driving ranges and fuel tank levels at ODs on a directed-transportation network with single-access and dual-access candidate sites for locating AF refueling stations. Vehicles are first grouped into multiple classes depending on their limited driving ranges. Since all vehicles are assumed to travel between ODs in round trips, a set of four different fuel levels remaining in the tank

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