Network planning of fuelling service stations in a near-term competitive scenario of the hydrogen economy

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Socio-Economic Planning Sciences 43 (2009) 55–71 www.elsevier.com/locate/seps

Network planning of fuelling service stations in a near-term competitive scenario of the hydrogen economy Chiara Bersania,b,, Riccardo Minciardia,b,c, Roberto Sacileb,c, Eva Trasforinib,c a

CIELI Centro Italiano di Eccellenza sulla Logistica Integrata, Italy DIST Department of Communication, Computer and System Sciences, University of Genova, Italy c CIMA Centro di Ricerca Interuniversitario in Monitoraggio Ambientale, Italy

b

Available online 13 March 2008

Abstract Hydrogen can be viewed as the flexible automotive fuel of the future. However, many issues related to its use have not been sufficiently investigated. One such issue concerns hydrogen logistics and distribution throughout a territory. One near-term scenario over the next decade is likely to include distribution procedures that are similar to those currently used for petrol products. In this scenario, the conversion of petrol service stations into hydrogen distribution points will progressively be implemented. Petrol companies will then represent one of the major categories of hydrogen producers. They will thus have to select, from a cost/benefit standpoint that accounts for competing companies expected to offer the same service throughout a territory, the most convenient and effective locations for hydrogen distribution. The current paper presents a model for planning a network of service stations of a given company within a competitive framework. A case study of a specific territory in northern Italy is presented and discussed. r 2008 Elsevier Ltd. All rights reserved. Keywords: Hydrogen economy; Hydrogen logistics; Hydrogen transport; Decision support systems; Optimisation

1. Introduction There is broad consensus that hydrogen can be regarded as the flexible automotive fuel of the future [1]. Research programs for the implementation of a hydrogen-based transportation system are already running in many countries, and the first practical applications are expected by 2015–2020. In that period, a considerable number of hydrogen-powered vehicles should begin to circulate, while infrastructures to produce and distribute hydrogen will likely emerge. Despite this promising scenario, the logistics on which the hydrogen economy [2] is to be based remains a matter of investigation. Some debate continues to about possible alternatives for production (e.g., centralised or on-site hydrogen production), storage (liquid, gaseous, or solid using some hydrogen-adsorbing material, etc.), and distribution (by hydrogen pipeline, natural gas pipeline, trucks, etc.). Corresponding author at: CIELI Centro Italiano di Eccellenza sulla Logistica Integrata, University of Genova, Via Bensa 1, 16124 Genova, Italy. E-mail address: [email protected] (C. Bersani).

0038-0121/$ - see front matter r 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.seps.2008.02.001

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While centralised production has the advantage of lower initial costs, the hydrogen thereafter requires transport to service stations. On-site production and dispensing, on the other hand, carry the drawbacks of high installation costs [3] and poor economies of scale, yet pose no transport costs. Interested readers may refer to Ref. [4] for a detailed discussion of future logistics scenarios. In addition, major economic stakeholders face the following decisional impasse: before investing, vehicle manufacturers require a high density refuelling network, while energy companies require profitable demand levels. Recent work by Hugo et al. [5] investigated, in some detail, the problem of hydrogen infrastructure strategic planning. They proposed an optimisation-based model to aid the long-term decision-making process for identifying the most energy efficient, environmentally benign, and cost effective pathways for delivering hydrogen to the consumer. In another paper, Melaina [6] developed three approaches for estimating the sufficient number of service stations required to initiate a hydrogen infrastructure for fuel cell vehicles. The approaches evaluate the existing populations of petrol service stations, the metropolitan land areas, and the lengths of principal arterial roads. Locating service stations on such roads, in 10–20 miles intervals, appears to represent the most logical structure. Melaina’s approaches provide a starting point for analysis, but they fail to account for customer refuelling behaviours and the exact placement of stations. In Ref. [7], Nicholas et al. provide an analytical framework for locating hydrogen fuel stations assuming that the existing petrol infrastructure is strongly related to needed hydrogen infrastructure of the future. Despite such recent research, the vision of future hydrogen logistics is far from clear. From a logistics standpoint, it is important to understand the function of the service station, which may be simply a dispensing station, or both a production and dispensing point [1]. In the first case, the transport of hydrogen plays a fundamental role, and, within both short- and long-term visions, tank trailers still represent a valid alternative to pipeline. The preferred mode of hydrogen transport will be dictated by economic and other, particularly safety, considerations [1]. While some studies (e.g., Ref. [8]) report that long distance hydrogen transport will likely rely on interstate pipelines, medium-to-short routes will exploit tank trailers transported by road, and containing either liquid or gaseous hydrogen as an economic, albeit hazardous, means to deliver the fuel [9–11]. It thus appears that, in the short- to mid-term, a blend of scenarios will be present. One of these will entail the gradual replacement of petrol service stations with stations dispensing only hydrogen [12], fed by tank trailers transported by road, and thus similar to the logistics model currently used for the distribution of petrol products. In this paper, a short-term scenario requiring the conversion of petrol service stations to hydrogen stations is considered. A territory with no existing logistical infrastructure to enable hydrogen distribution is assumed. The problem is thus to support decision-makers regarding the gradual transformation of an existing petrol service station network into one including hydrogen dispensing stations, in line with a 2015–2020 vision of the hydrogen economy [2]. According to this scenario, and to the assumption that petrol service stations are already strategically situated in locations suitable for hydrogen distribution, petrol companies will have to identify those existing stations that are most appropriate for hydrogen fuel distribution. This will involve converting a limited number of them by considering initial construction costs of the new network in maximising satisfaction of customer demand. The expected prominent role of petrol companies in hydrogen distribution under this short-term scenario is based on at least two phenomena: (1) in the near future, most hydrogen production will derive from petroleum refinement processes (similar to what exists at present); and (2) petrol companies already boast long-standing experience in fuel distribution. From this perspective, the problem bears several similarities and, at the same time, some peculiarities, with respect to classic facility location problems (FLPs). Before presenting our proposed model formulation, the literature on FLPs is briefly surveyed in the following section. 2. Facility location problems In an FLP, the objective is to choose those geographic locations where a certain number of service facilities (SFs) can be set up to optimally satisfy customer needs with respect to a specific demand, taking into account different criteria, and fulfilling a given set of constraints [13]. The literature on the subject offers a large number of mathematical programming models to represent a variety of FLPs. In the proposed approaches, the first step in formalising an FLP is to choose an adequate topological model of the territory, either as a

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continuous plane or as a network. In the former, an SF can be located on each point of the plane by defining two coordinates. In the latter case, the vertices of the network may represent both eligible SFs and demand points, while edges between vertices reflect their distances. When the FLP involves transportation, as in the current study, a network representation is usually preferred, owing to the natural topology of the transportation system. In the multiple facility location problem (MFLP) [14], the objective is, as in the previous cases, to locate SFs such that they optimally serve a given set of customers whose locations and needs are known. However, in this case, in addition to decisions regarding optimal locations, the demand to be satisfied by each SF must be defined, thereby introducing a location-allocation problem [14] to be solved. In common applications of industrial MFLPs, it is assumed that customers are positioned at the nodes of a transportation network; all the company then needs do is choose those new SF locations that serve them at minimum cost. The objective is to minimise the sum of the total setup/maintenance and transportation costs, which often depend only on the geographical locations chosen for the SFs. The problem studied here might fall within the bounds of an MFLP were it not for factors that should be included in the decision model; namely, the unknown number, and behaviour of, customers to be served (i.e., the demand), as well as competitors’ ventures in the territory. Regarding users’ behaviour with respect to the choice of a specific SF, an important factor affecting an MFLP is the presence of competitive offers in the same market of the same territory. In the competitive FLP, SFs compete against each other by attempting to attract as many customers as possible in order to maximise their market share and profit [15]. Competitive models based on SFs’ attraction, which is the ability to ‘‘capture’’ customers closer to them, are usually designed to solve the flow-capturing location problem (FCLAP) [16]. An example can be found in recent work by Kuby and Lim [16] who focus on the problem of optimally locating refuelling facilities for alternative fuels such as hydrogen and natural gas. In Ref. [16], the proposed model seeks to maximise the total flow of demand captured by new SFs, which are owned by a single company under no competitive assumption, while including constraints on travel distance. In particular, it locates plants to serve the maximum number of moving costumers, taking into account the limited fuel distance of the new hydrogen-based vehicles. The assumption that ‘‘the probability that a customer will patronise a facility is proportional to the facility attractiveness and inversely proportional to the distance from it’’ [17] supports use of the spatial construct known as the ‘‘gravity model’’. A more realistic approach to such models was later introduced by Huff [18], who suggested that customers share their patronage among competing facilities based on probabilities generated by a gravity-based formula. The Huff formulation uses distance (or travel time) from consumers’ residences to SFs, and states that the probability to be served by a specific SF is equal to the utility ratio of that SF to the sum of utilities of all SFs considered by the consumers in question. Several variants of this model have since been developed (e.g., Refs. [19–23]). Based on this earlier research, an original approach to support decisions within a future near-term scenario of hydrogen distribution for automotive use is proposed. The originality of the work entails at least two features. First, the application context, in itself, is original, since, despite the abundant literature on hydrogen economics, few works have addressed the logistics problem, at least within a detailed near-term vision. Moreover, to the authors’ knowledge, no previous optimisation work on hydrogen logistics has considered the location of competitors. Secondly, from a methodological standpoint, the proposed model integrates, into a single approach, key characteristics present in several well-known MFLPs that can be applied to the early transition stages of any alternative vehicle fuel. In the following sections, the proposed decision model will be introduced and discussed in detail, and an application via a case study presented. 3. The system model 3.1. Problem definition The scenario of interest here, and the related decision problem of locating service stations distributing hydrogen for automotive use, can be defined as follows: a company wishes to locate a set of SFs in connection

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with the introduction of a new product, in this case hydrogen. To formulate the decision problem mathematically, several simplifying assumptions must be introduced. 3.1.1. Eligible locations In theory, on a territory, each point might be an eligible place to dispense hydrogen. As a matter of fact, there are several constraints that limit such installations to safe locations. In a near-term scenario, it is realistic to assume that petrol companies will also be the first candidates to provide this service. Since many of the existing petrol service stations are already subject to safety criteria in terms of their locations, it is reasonable to assume that, in the years to come, some of them will be ‘‘converted’’ to dispense hydrogen. So, as our first simplifying assumption, it is presumed that those existing service stations (distributing petrol products in the current application) represent the only possible locations to distribute hydrogen for vehicles. Service stations that only dispense, but do not produce, hydrogen are thus taken into account. 3.1.2. Hydrogen demand model Hydrogen demand is assumed to be known, and estimated as a percentage of existing demand for petrol products. The latter is based on historical data for each petrol station of the company in question. This simplifying assumption seems reasonable, since, in the near term, hydrogen vehicles will represent a certain percentage of the existing petrol based traffic. Further, there does not appear to be justification, a priori, to assume that the distribution of hydrogen vehicles will be more prevalent in some areas rather than others. When the location of an SF is chosen, it is assumed able to satisfy the demand for that location. If a location is not chosen because it is deemed inconvenient for an SF installation, the demand at that location is assumed split based on a two-step elastic model: Up to a specified percentage, the demand is satisfied by the closest competitor SF, while the remaining part is met by other SFs of the company under consideration. Geographic distribution throughout the territory of competitor SFs is assumed to be known. While the effective location of those SFs actually distributing petrol products can be known, in practice, identifying which will be converted to hydrogen distribution in a near-term scenario may be difficult. Under a worst-case scenario, the competitor SF nearest to each chosen SF has been assumed converted to hydrogen distribution, and that the optimal set of chosen SFs has no ability to attract those new customers who are usually served by competing companies. This simplifying assumption is due to the fact that it is difficult to have complete understanding of competing companies’ ‘‘hydrogen’’ strategies. If this assumption were to result in a loss of customers, it still seems unrealistic that such a condition would directly translate into gains for competing companies. On the other hand, if, under the best of circumstances, we knew the hydrogen-based strategies of the competition, we might still account for the ability of the optimal set of SFs to attract those new customers who are usually served by competing companies. 3.1.3. Petrol vs. hydrogen distribution as two independent markets Despite the intrinsic common origin of petrol products and hydrogen in the near-term scenario, it seems reasonable, for several reasons, that the two products would follow independent markets. First, an integrated distribution of both petrol products and hydrogen in the same SF is not considered feasible for safety reasons. Second, according to several studies evaluating the future performance of road vehicles equipped with different fuel technologies, it is reasonable to assume that, in a scenario in which facilities and infrastructures to support hydrogen distribution will effectively work, only pure hydrogen vehicles will dominate the automotive market vs. hybrid (gasoline and electric) and bi-fuel (hydrogen and gasoline) technologies [24]. In addition, for those early petrol SF installations that are converted to hydrogen, such a strategy may not be economically advantageous, although it might be of value from a wider viewpoint, e.g., company image, experience with new forms of distribution, etc. With this rationale in mind, the distribution of hydrogen as an auto fuel will here be modelled as an independent activity from the delivery and sale of petrol at SFs. 3.2. Model formulation We now proceed to formulating our decision problem so that it considers two formal objectives.

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The first aims to minimise the costs of transforming some existing SFs from petrol to hydrogen dispensing facilities by reducing, as much as possible, the loss of customers purchasing hydrogen from other companies. The second objective maximises income from hydrogen distribution. This will be correlated with available inventory since, in existing fuel distribution systems, higher incomes generally result from those fuel SFs with larger inventories. Since both of these objectives can be expressed as cost/income with the same unit of measure (for example, euros), they can be merged into a unique objective function, to be minimised. A pivotal piece of information of the proposed model is the weekly hydrogen demand Di associated to vertex i, which can be considered inelastic. Under a simplifying assumption, Di may be evaluated on the basis of: (a) the current demand for petrol fuels at the ith SF (by converting this demand to units of hydrogen). This number is derived from data on average weekly consumption at every SF owned by the company; (b) an estimate of the percentage of motorists that, in the considered territory, and in the represented scenario, will have converted their vehicles from petrol to hydrogen fuel consumption. The basic decision variables of the problem are defined as follows:



yi, i ¼ 1, y, N: binary variables associated with the ith SF. Specifically, yi ¼ 1 when the ith SF is selected for hydrogen dispensing, whereas yi ¼ 0 when the ith SF is not selected. In addition, the model requires determination of four additional variables:

   

tmin i : distance of the ith SF from the closest SF of the considered company, and is dependent on decisional variables yi , i ¼ 1, y, N; di: hydrogen demand at the ith petrol SF; xij: binary variable representing the fraction of demand associated with the jth SF served by the ith SF; and Ai: inventory capacity of the warehouse at the ith SF.

3.2.1. Minimum distance between the ith SF and the closest operating SF The variable tmin i , as suggested above, can be obtained as a function of the variables yi, i ¼ 1, y, N, by computing the distance between the ith SF and the closest operating SF. A possible exposition of tmin is given i by Eq. (1), where M is an arbitrarily large number with respect to all tij values, which represent the shortest path from the ith to jth SF: ¼ M  maxfðM  tij Þyj g; tmin i jai

i ¼ 1...N

(1)

3.2.2. Hydrogen demand at the ith SF Hydrogen demand is assumed equal Di, demand associated with the ith SF, which has been selected to distribute hydrogen; specifically, when the ith SF is chosen to dispense hydrogen, yi ¼ 1, and, consequently, the associated demand is di ¼ Di. Alternatively, when the ith node is not selected to dispense hydrogen, Di is presumed to be at least partially lost since customers may turn to competitors’ SFs in surrounding areas. Under such circumstance, di(oDi) represents the remaining demand that must be satisfied by SFs of the considered company. The binomial logit model, commonly used in transportation theory [25,26], is employed here to define the loss of demand towards competitors. This is assumed possible when the ith node is not selected to distribute hydrogen. Thus, di is computed as d i ¼ Di

1 1 þ ri e

comp Wi ðtmin Þ i ti

ð1  yi Þ þ Di yi ;

i ¼ 1...N

(2)

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where

   

tmin i computed in Eq. (1), represents the distance of the ith SF to the closest SF of the considered company; tcomp is the distance of the ith SF to the closest SF belonging to competitor companies (this is assumed to be i known for all SFs of the considered company); ri is a positive parameter related to the perceived quality of service offered by the considered provider, and by the competitors. Values lower than 1.0 indicate that the quality of the service provider is perceived better than competitors, while values higher than 1.0 indicate the opposite; and Wi is a positive parameter expressing the sensitivity of customer choice to the difference between distances ðtmin  tcomp Þ. i i

Note that Eq. (2) is structured so that, in accordance with earlier comments, when yi ¼ 1, all, demand at the ith SF (di ¼ Di) is satisfied, while yi ¼ 0 suggests demand decreases in accordance with the logit model [25]. 3.2.3. Fraction of demand associated with the ith SF The variable xij, with values between 0 and 1, represents that fraction of demand associated with the jth SF (yj ¼ 0), which is to be served by the ith SF if the latter is selected for hydrogen distribution (that is, when yi ¼ 1). A representation of demand assignment in the system model, and the related variables and parameters, are sketched in Fig. 1. It is assumed that attrji yi ð1  yj Þ xij ¼ PN ; i¼1 attrji yi

j ¼ 1 . . . N;

i ¼ 1 . . . N;

iaj

(3)

where attrji is the attraction of the ith SF on customers whose demand is initially associated with the jth SF. Such attraction is based on the gravity model as a distance decay function [27]; that is attrji ¼

1 ; tji

j ¼ 1 . . . N;

i ¼ 1 . . . N;

iaj

(4)

3.2.4. Inventory capacity of the warehouse at the ith SF Ai represents the inventory capacity of the warehouse at the ith SF, when it is selected to dispense hydrogen (that is, when yi ¼ 1). It is assumed that the average permanence time (for example, a week) of hydrogen in the tanks is known, such that the inventory capacity of the warehouse can be considered equal to the sum of:

 

the overall weekly hydrogen demand at the ith SF (that is, Di); and the fractions of the demands dj relevant to those jth SFs in the territory that are not selected to dispense hydrogen. Under these assumptions, the capacity, Ai, is defined as Ai ¼

N X

xij d j þ Di yi ;

i ¼ 1...N

(5)

j¼1 iaj

Note that Eqs. (3) and (5), together, require that, if an SF is not selected for hydrogen dispensing (yi ¼ 0), its capacity is null (Ai ¼ 0). 3.2.5. Objective function The decision maker’s objective is to limit investments incurred when structuring nodes of the logistics network, while maintaining, to the best extent possible, his/her company’s market share, i.e., minimising the

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A1 = D1 + ∑ x1hdh h

COMPETITOR A

y1 = 1

D1

Dk x1kdk

yk = 0

Dj − ∑ xij dj i

x1j dj

x2kdk

Dk − ∑ xikdk i

yj = 0

Dj

x2j dj

COMPETITOR B

x1LdL y2 = 1 D2

x2LdL

DL −∑ xiLdL i

yL = 0

DL A2 = D2 + ∑ x2hdh h

yi = 1

yi = 0

COMPETITOR

Di

i-th node chosen to install a hydrogen SF

i-th node not chosen to install a hydrogen SF

competitor SF

demand in the i-th service station

Ai = Di + ∑ xihdh

Inventory capacity of the i-th SF

h

Fig. 1. A functional view of the proposed system model with related variables and parameters.

loss of demand. The cost to install an SF to dispense hydrogen is characterised by fixed set-up and variable costs depending on the size of the inventory. An additional objective is to maximise satisfaction of customer demand, whose economic value can be directly related to the size of the inventory in each SF [28].

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The objective function can be written as a weighted sum of the above two objectives, namely ( ) N N X X ðki yi þ hi Ai Þ  G Ai min i¼1

(6)

i¼1

where

  

ki is a positive parameter that represents the fixed cost of installing new equipment in the ith SF to distribute hydrogen (unit of measure is h); hi is a positive parameter related to the storage cost for each unit of product at the ith SF (unit of measure is h/l); G is a weight that balances the two objectives of the function (unit of measure is h/l). It guarantees that both addenda in the objective function represent economic and investment value.

The parameters ki and hi depend on the ith SF, since, respectively: the fixed cost of installing equipment may vary by location and geomorphologic characteristics of the soil where the hydrogen storage tanks are buried. Further, storage costs may vary by SF due to differences in both equipment efficiency and electric energy costs required to maintain proper cryogenic temperatures. The parameter G allows for greater storage capacity in order to enhance customer satisfaction. Its more attractive solutions may, however, be penalised by the parameter hi. In other words, greater storage may not be recommended due to higher variable costs (as expressed through hi); on the other hand, this may be outweighed by customer preferences. Although G is expressed in h/l, its real value can be difficult to defined, It thus, the focus of a sensitivity analysis of our model’s solutions. For example, imposing G ¼ 0 means that no emphasis is given to dimensions of the hydrogen storage tank in attempting to attract customers, G ¼ N, on the other hand, means that the only goal is to maximise storage capacity (and, consequently, customer satisfaction) independent of any possible changes in cost. In summary, the objective function (6) is subject to definitions/conditions (1)–(5), that will be used as constraints in the proposed decision model. 3.2.6. Other constraints of the problem Other constraints to be taken into account in model formulation of the decision problem are the following:



A constraint requiring that a minimum number (nmin) of SFs dispensing hydrogen is opened: N X

yi Xnmin

(7)

i¼1



where nminAZ+. An upper bound on inventory capacities: Ai pB;

i ¼ 1 . . . N,

(8)

where B is a suitable value, equal for all inventories.

3.2.7. Overall formulation of the decision problem For the sake of readability, the overall formulation of the proposed decision model is reported below: ( ) N N X X ðki yi þ hi Ai Þ  G Ai (6) min i¼1

i¼1

tmin ¼ M  maxfðM  tij Þyj g; i jai

i ¼ 1...N

(1)

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d i ¼ Di

1 1 þ ri e

comp Wi ðtmin Þ i ti

attrji yi ð1  yj Þ xij ¼ PN ; i¼1 attrji yi attrji ¼

Ai ¼

1 ; tji

N X

ð1  yi Þ þ Di yi ;

j ¼ 1 . . . N;

j ¼ 1 . . . N;

xij d j þ Di yi ;

i ¼ 1 . . . N;

i ¼ 1 . . . N;

i ¼ 1...N

i ¼ 1...N

iaj

iaj

63

(2)

(3)

(4)

(5)

j¼1 iaj

N X

yi Xnmin

(7)

i¼1

Ai pB;

i ¼ 1...N

yi 2 f0; 1g;

i ¼ 1...N

(8) (9)

Note that this model formulation is based on both binary and continuous decision variables. The objective function is linear, but several constraints are non-linear. Thus, the problem is a mixed-integer type. It can be optimally solved (using suitable optimisation software tools) only when the problem dimension is quite limited, and, even in this case, by paying close attention to avoid selecting a local optimum. For this reason, the case study presented in the following section is of ‘‘reasonable’’ dimension. 4. Case study An application of the proposed decision model (1)–(9) seeks to represent the real needs and user requirements of a major Italian logistics company that distributes petrol products. The model’s quantification was developed in conjunction with experts from this company. These details reflect the feeling that, in the very near future, the logistics scenario for distribution of automotive fuel across a territory will change significantly. This is the case since hydrogen has intrinsic characteristics that make the necessary logistics completely different from existing fuels. New decision support tools will surely be required under an emerging hydrogen economy, with design of the distribution network obviously being one of the first processes needing such support. In order to make our application more realistic, a case study format is proposed. As noted above, the necessary data have been obtained directly from the petrol company of interest, beginning with the current scenario for distribution of its products. 4.1. Description The proposed approach was applied to the existing scenario of consumption of common fuels (gasoline and unleaded petrol) in northwestern Italy, specifically, in the districts of Torino, Aosta, Asti, Cuneo, Biella and Vercelli (see Fig. 3). A network of 430 service stations was considered across this territory. Data regarding the location, and related demand patterns for common fuels at all service stations in these districts were made available. In order to reduce the set of SFs, and consider the most significant ones, two different pre-selections were performed (Fig. 2). First, 233 stations were chosen according to eligibility criteria related to a minimum quantity of fuel sold (approximately 50,000 l), while the demand, Di, for the remaining 197 SFs was not taken into account here.

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This lower bound of 50,000 l of common fuel sold per week thus allowed us to reduce the number of eligible SFs. In the territory of interest, weekly fuel sales generally falls between 12,000 and 300,000 l (with a maximum 630,000 l). Although the eliminated 197 SFs represent 45% of all facilities, they only account for 20% of total system demand. Eliminating these sites was done by assuming that the new hydrogen service stations will/should be located where demand for existing petrol was higher. This assumption is justified, we feel, in that the greater demand stations will be placed at strategic nodes of the road network. Moreover, the presence of basic infrastructure to dispense fuel will generally control start-up costs when the hydrogen is provided by that company owning the service stations in question. Thus, the first selection was made given the hydrogen infrastructure’s options for each eligible SF (implemented with a lower bound on fuel sold) in order to reduce the number of eligible SFs and to reduce computational effort. Subsequently, an additional selection was made to best cover the affected territory. This decision was provided by formalising a set covering problem [29] with a specified coverage distance of 10 km, resulting in a new subset of 56 SFs. The goal of this (optional) selection was to reduce computational time (from several days to a few hours on common PC architectures) given demand storage and competition (Fig. 2), i.e. by reducing the number of feasible alternatives given the need to load vehicles on long paths.1 The problem formulation described in Section 3 was then applied to the resulting set of 56 feasible SFs. Di, the total amount of hydrogen requested at the ith SF, was computed as proportional to the current demand for gasoline and unleaded petrol. Fixed (ki) and variable (hi) are the costs required to adapt the current SFs to hydrogen distribution taking into account the investment (i.e., fixed the set-up costs) and the management/ maintenance costs. Specifically, we set ki ¼ 150,000 h and hi ¼ 0.5 h for every kilogram of stored hydrogen. Using data from a study of refuelling hydrogen cell vehicles in Italy [31], the capital costs for installation of a liquid hydrogen SF is taken here to be 150,000 h. An inventory cost of 0.5 h/kg per week takes into account the need to refrigerate liquid hydrogen to 2531, or to maintain sufficient pressure for storing gaseous hydrogen [9]. 4.2. Implementation and results A decision support system (DSS) consisting of three different modules was constructed. The first, involving a Geographic Information System (GIS), computed all needed distances. It was implemented using an MS Vbasic routine and the MS MapPoints 2006 library. A relational database module was then created with MS Access used to store relevant system parameters and variables. Finally, an optimisation module was implemented using Lingo 10.0 software to locate (local) solutions of non-linear mathematical programming problems with binary and continuous decision variables. Lingo has a multi-start feature that restarts the nonlinear solver from a number of intelligently generated points. This allows the solver to identify several locally optimal points and select the best of those. This procedure thus does not guarantee the global optimum, but rather a ‘‘good’’ local solution. Using the parameter values listed in Table 1, a test was carried out with the objective of minimising plant costs, i.e., setting G ¼ 0 in Eq. (8), with nmin ¼ 1. Under these conditions, 77% of the original demand is maintained for the considered company, at an overall cost of approximately 11 Mh. Specifically, the DSS suggested opening 26 optimal SFs, located as shown in Fig. 3 (triangular icons). These are SFs whose positions would be more affected by the presence of competitors as they seek to maximise the number of ‘‘faithful’’ customers while minimising the possible loss of demand in the territory. From Fig. 3, it can be shown that the maximum distance between the nearest SFs available to dispense hydrogen along the main road is about 70 km. This result should allow the driver of a hydrogen vehicle to stop after less than 70 km for refilling. Given current technology, this distance does not exceed the fuel autonomy of new hydrogen vehicles. In fact, a hydrogen fuel cell propulsion system is about twice as efficient as a conventional internal combustion engine, so the new hydrogen vehicles could provide a fuel autonomy, which 1

A near-term fuel cell transit bus is assumed to have 10–13 kg of hydrogen storage capacity and fuel autonomy of 300 km while a fuel cell car can store approximately 6–9 kg of gaseous or liquid hydrogen in order to cover nearly 350 km [30].

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Fig. 2. DSS implementation.

allows it to travel more than 150 km. However, in a near-term scenario, it seems clear that the very limited autonomy of hydrogen vehicles will condition their use simply on the basis of road infrastructures adequately equipped for their refilling. Accessibility of territories with inadequate SF covering is thus viewed as a given. 4.3. Cost/benefit analysis A cost/benefit analysis was subsequently performed, varying the value of parameter G, and constraining the 26 initially chosen SFs to be selected in all further tests (that is, imposing yi ¼ 1 8i 2 S 26 , where S 26 is the set of the initially 26 chosen SFs). Note that an increase in G increases the importance of maintaining demand. Fig. 4 shows the percentage of demand and the respective number of SFs to be converted to hydrogen distribution obtained with different values of G. As expected, the increasing captured demand by all SFs produces an increase in the number of hydrogen SFs needed to satisfy customers’ demand; in particular, from 26 to 32 (the six added SFs appear in Fig. 3 as circled numbers) with a maximum value of 93% captured demand. According to the model, the maximum value of captured demand is limited because the presence of competitors in the territory affects (even) loyal clients with respect to the realistic behaviour of selecting the closest SF. The rapid inclination of the function from 31 to 32 opened SFs on the abscissa axis can be justified P because an increasing G emphasises the second term of the objective function related to the maximisation of N i¼1 Ai . This implies that the second addendum of the first term of the objective function (related to minimisation of variable costs for greater values of G), becomes negligible. Fig. 5 presents a sensitivity analysis viewed from a cost/benefit perspective. Specifically, it shows the percentage of lost demand vs. the total fixed and variable costs obtained by varying G, and with introduction of the six additional activated SFs. Note that an investment of more than 10 Mh allows the capture of 77% demand with an increase of 2 Mh for each SF added to the 26 already in the optimal solution. 5. Conclusions In this paper, a variant of the classic MFLP applied to a short-term scenario of hydrogen distribution for automotive use was presented. With respect to the wealth of literature on future hydrogen scenarios, this work aims to evaluate a concrete, detailed, operative planning phase within a given territory. The paper’s main contribution is on the modelling side, since an original formulation of a relevant decision problem is provided, and a realistic application to a case study is discussed. In fact, the model of the decision problem is rather complex due to non-linearities in some constraints, and to the presence of binary decision variables. At the same time, the application involves rather practical conditions.

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Table 1 Variable and parameter values obtained for the optimal solution with G ¼ 0 ID

yj

di (H2 kg/1000)

Ai (H2 kg/1000)

Di (H2 kg/1000)

tcomp ðkmÞ i

ðkmÞ tmin i

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56

1 0 0 1 1 1 0 0 0 0 1 0 0 1 1 1 1 0 1 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 0 0 1 0 1 0 1 1 0

63.00 0.47 22.95 16.00 14.00 15.00 4.82 14.31 16.98 89.92 17.00 43.00 7.89 42.00 18.00 33.00 25.00 13.25 77.00 38.33 44.00 25.05 20.04 15.00 2.75 16.92 25.00 8.92 2.99 14.00 14.00 25.97 15.97 34.00 33.00 12.37 4.04 58.00 15.00 18.00 12.91 15.89 56.73 70.00 11.57 19.00 25.00 14.93 2.02 29.00 21.69 18.00 9.0 19.00 28.00 11.57

91.89 0.00 0.00 29.37 33.09 55.81 0.00 0.00 0.00 0.00 29.53 0.00 0.00 70.87 34.99 57.57 46.50 0.00 92.85 0.00 67.93 0.00 0.00 0.16 0.00 0.00 57.72 0.00 0.00 37.35 30.71 0.00 0.00 50.33 0.00 0.00 0.00 97.82 45.23 36.37 0.00 0.00 0.00 101.91 0.00 44.51 40.55 0.00 0.00 47.09 0.00 29.82 0.00 33.64 50.92 0.00

63 22 23 16 14 15 21 21 17 90 17 43 33 42 18 33 25 14 77 45 44 58 31 15 17 17 25 17 14 14 14 26 16 34 33 60 21 58 15 18 28 17 65 70 17 19 25 133 18 29 22 18 16 19 28 14

1 10 50 40 20 5 7 15 60 55 80 90 10 4 7 14 10 25 30 18 3 17 20 1 10 50 40 20 5 7 15 60 55 80 90 10 4 7 14 10 25 30 18 3 17 20 4 7 14 10 25 30 18 3 17 20

69 29 20 39 35 26 13 11 27 20 36 25 16 17 16 17 24 11 12 9 35 18 17 41 18 23 13 20 12 22 12 27 23 9 11 17 11 33 32 11 26 17 8 13 13 18 9 17 24 11 4 27 16 25 35 12

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Fig. 3. Optimal 26 service facilities (triangular icons) from the original 56 in the Piemonte region.

A key assumption of the model is that the choice of SF by the customer is contingent on distance and not price. This seems reasonable as it appropriately reflects what has happened (and, in many cases, still happens) for petrol fuels. Nevertheless, it seems appropriate to distinguish customer attraction to an SF of the considered company from that of competitors’ SFs, and to model it in different ways, since, for marketing reasons, the company name should also play a role.

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Percentage of captured demand

Percentage of captured demand as a function of number of activated service facilities 95 93 91 89 87 85 83 81 79 77 75 25

26

28 30 27 29 31 Number of activated service facilities

32

33

Fig. 4. Optimal number of activated service facilities.

Percentage of lost demand as a function of the total cost Percentage of lost demand

13.0 12.5 12.0 11.5 11.0 10.5 10.0 7.0

9.0

11.0

13.0 15.0 17.0 19.0 Total cost (million of euro)

21.0

23.0

Fig. 5. Percentage of lost demand as a function of total cost.

Assuming the location of competing companies’ SFs is also seen as reasonable if viewed from a planning perspective. On the other hand, in a dynamic, changing world of hydrogen distribution, different decision models (e.g., ones based on bidding and/or game mechanisms) might be more pertinent in future contexts. Another important aspect of the current problem scenario is the centralised vs. decentralised technologic alternatives to produce, transport, and store the hydrogen. In this work, no decentralised hydrogen production in the SF, has been taken into account, as in a preliminary wide-scale application on a short-term scenario, hydrogen distribution from a centralised site production to service stations may represent a more concrete and less costly alternative. The proposed model can also be applied to the optimal location of hydrogen service stations by type of production or storage for the hydrogen. From a transport viewpoint, both the supply of liquid or gaseous hydrogen to service stations by tanks, and/or the on-site production by methane steam reformation could be accounted for in the proposed model. At this time, small-scale, on-site reformers appear to be the most attractive alternative on a long-term cost basis; however, investment, operating and maintenance costs remain higher than for other options. Delivered hydrogen stations benefit from decades of experience in the industrial gas industry to supply common fuels. This, in itself, should suggest that the distribution of liquid hydrogen is likely the best solution from a cost/benefit standpoint for the first near-term scenario [32]. It is quite reasonable, in fact, to assume that petrol companies will also manage the distribution of hydrogen, where the logistics/distribution method would be based on tank truck deliveries as they are now with petroleum-based fuels. Further, given the important role of petrol companies in a short-term scenario within a hydrogen economy, it is reasonable to assume that hydrogen SFs will be set up where petrol service stations are currently operational. Importantly, both in the US and in European countries [6], the first hydrogen stations are appearing in locations where both demand and accessibility are high. (See, for example, the stations at the

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Berlin airport and in Milan, Bicocca District [33].) The choice for this kind of locations can be justified for at least two reasons: the first is that preliminary evaluations have defined these locations as being suitable for the distribution of automotive fuel, regardless of whether it is petrol or hydrogen [34]; secondly, petrol companies already own these service stations, thus facilitating the hydrogen SF installation process. A final, most important aspect in planning hydrogen logistics is to predict when and how the new hydrogen economy will begin. The European Hydrogen and Fuel Cell Technology Platform (HFP) [35], established at the end of 2003, will likely be instrumental in structuring socio-economic and technical research on hydrogen and fuel cells in Europe, as well as stimulating public and private investment in R&D. In particular, HFP aims to facilitate and accelerate the development and deployment of cost-competitive, world-class European hydrogen and fuel cell-based energy systems and component technologies for applications in transport, stationary and portable power. Participants should represent a balance of expert knowledge and stakeholder interests, including the research community, industry, public authorities, and civil society. At the same time, governments should evaluate the social impact of hydrogen transportation market access scenarios, perhaps using coordinated systems analyses that encompass the three affected entities: vehicles, fuel, and society. The projects carried out by HFP may encourage strong community programs to develop, to serve market development needs, and to increase the understanding of all stakeholders. In conclusion, while many aspects of the hydrogen economy are still unknown and/or difficult to predict, the proposed DSS can be an important instrument in helping determine optimal placements of service stations within a hydrogen economy. Acknowledgements This work was carried out in collaboration with FEEM (Fondazione ENI Enrico Mattei, http:// www.feem.itwww.feem.it) and Praoil S.p.A. (ENI Group). We would like to thank Dr. D. Pizzorni and Dr. G. Vicini for their help in developing the research effort. The project was also supported by the INTERREG—ALCOTRA Programme 176 on hazardous material transportation. Appreciation is offered to two anonymous reviewers for their helpful comments, and to the Editor-in-Chief, Dr. Barnett R. Parker, for his overall editorial assistance and guidance. References [1] T-Raissi A, Block DL. Hydrogen: automotive fuel of the future. Power and Energy Magazine, IEEE 2004;2(6):40–5. [2] Andrews CJ, Weiner SA. Visions of a hydrogen future. Power and Energy Magazine, IEEE 2004;2(2):26–34. [3] Berry GD. Hydrogen as a transportation fuel: costs and benefits. UCRL-ID-123465. Lawrence Livermore National Lab, CA, USA, 1996. [4] Padro´ CEG, Putsche V. Survey of the economics of hydrogen technologies. Technical report. National Renewable Energy Laboratory, 1999. [5] Hugo A, Rutter P, Pistikopoulos S, Amorelli A, Zoia G. Hydrogen infrastructure strategic planning using multi-objective optimization. International Journal of Hydrogen Energy 2005;30(15):1523–34. [6] Melaina MW. Initiating hydrogen infrastructures: preliminary analysis of a sufficient number of initial hydrogen stations in the US. International Journal of Hydrogen Energy 2003;28:743–55. [7] Nicholas MA, Handy SL, Sperling D. Using geographic information systems to evaluate siting and networks of hydrogen stations. Transportation Research Record 2004;1880:126–34. [8] Birgisson GE, Lavarco WE. An effective regulatory regime for transportation of hydrogen. International Journal of Hydrogen Energy 2004;29(7):771–80. [9] Amos WA. Costs of storing and transporting hydrogen. National Renewable Energy Laboratory of Colorado, US Department of Energy, 1998. Available at: /www.nrel.govS. [10] Bersani C, Fazio D, Minciardi R, Paladino O, Pizzorni D, Sacile R, et al. Cost/benefit analysis in hydrogen logistics. Chemical Engineering Transactions 2004;4:501–6. [11] Bersani C, Giglio D, Minciardi R, Paladino O, Pizzorni D, Sacile R, et al. A decision support system for the evaluation of future scenarios in next-generation hydrogen fuel station networks. Chemical Engineering Transactions 2004;4:507–12. [12] Maack MH, Skulason JB. Implementing the hydrogen economy. Journal of Cleaner Production 2006;14(1):52–64. [13] ReVelle CS, Eiselt HA. Location analysis: a synthesis and survey. European Journal of Operational Research 2005;165(1):1–19. [14] Levin Y, Ben-Israel A. A heuristic method for large-scale multi-facility location problems. Computers and Operations Research 2004(31):257–62.

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Chiara Bersani is a Ph.D. student in the Department of Communication, Computer and System Sciences, University of Genova. She received her Italian Laurea in Computer and System Science Engineering at the University of Genova, Italy. Ms. Bersani’s research interests involve transport and logistics systems, with special reference to hazardous material management and inventory routing problems. She is working with CIELI, Italian Excellence Center on Integrated Logistics, on development of an Internet-based port and maritime database for the Greater Caribbean, which is being, financed by the Association of Caribbean States, Ms. Bersani’s research has appeared in Chemical Engineering Transactions.

Riccardo Minciardi is Professor of Modelling and Simulation, Department of Communication Computer and System Sciences, and former Dean of Computer Science Engineering, University of Genova, Italy, where he received his Italian laurea in Electronic Engineering. He is also a member of the Great Risks Committee of the National Civil Protection Department, and of the Italian Centre of Excellence on Integrated Logistics. Professor Minciardi’s current research interests include modelling and control of automated manufacturing systems, transport planning in urban systems, risk management, and environmental decision support systems. His research has appeared in journals such as IEEE Transactions on Automatic Control, IEEE Transactions on Robotics and Automation, European Journal of Operational Research, International Journal of Adaptive Control and Signal Processing, Information and Decision Technologies, and Automatica. Professor Minciardi’s professional affiliations include IEEE and CIRA (Italian Group of Research in Automatica).

Roberto Sacile is an Assistant Professor, University of Genova, Italy, holding the professorships of Computer Science Fundamentals, Geographic Information Systems and Models and Methods for the Management of Environmental Systems. He received his Italian Laurea in Electronic Engineering at the University of Genova, Italy, his Ph.D. at Politecnico of Milan, Italy, and a post-doc specialisation at INRIA (the French National Institute for Research in Computer Science and Control). Professor Sacile manages a research contract between Praoil (Eni group, the most important Italian petrochemical company) and University of Genova on various aspects of hazardous material transport. His main research interests are related to computer-based and decision support methodologies and their integration

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within an information system, with specific applications to the environmental and transport fields. Professor Sacile’s research has appeared in journals such as Decision Support Systems, Journal of Cleaner Production, Environmental Modelling & Software, and Resources, Conservation and Recycling; Waste Management. He is a coauthor of ‘‘Agent-Based Manufacturing and Control Systems’’ CRC Press, 2004. Professor Sacile is member of AICA (Italian Group of Research in Computer Science), and the NATO Environmental Security Panel.

Eva Trasforini is a Researcher at CIMA (Centro Interuniversitario di ricerca in Monitoraggio Ambientale) and a Lecturer in the course of Environmental and Industrial Risk Management. She received her Italian Laurea in Environmental Engineering at the University of Genova, Italy. Ms. Trasforini received her Ph.D. in Methods and Technology for Environmental Modelling from the University of Basilicata Region, Italy. Her main research interests include decisional and modelling issues related to environmental systems, and to resource allocation for risk mitigation. Ms. Trasforini’s research has appeared in Environmental Modelling & Software, European Journal of GIS and Spatial Analysis, and Natural Hazards and Earth System Sciences. Her professional affiliations include IEMSS (International Environmental Modelling and Software Society).