A hazmat multi-commodity routing model satisfying risk criteria: A case study

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Journal of Loss Prevention in the Process Industries 21 (2008) 345–358 www.elsevier.com/locate/jlp

A hazmat multi-commodity routing model satisfying risk criteria: A case study Sarah Bonvicini, Gigliola Spadoni Dipartimento di Ingegneria Chimica, Mineraria e delle Tecnologie Ambientali, Alma Mater Studiorum Universita` di Bologna, via Terracini, 40131 Bologna (BO), Italy Received 5 September 2007; received in revised form 5 November 2007; accepted 5 November 2007

Abstract The risk caused by transportation of hazardous materials can be reduced by routing, that is by the choice of alternative less risky paths than those usually preferred by truck drivers. In order to solve the routing problem a new model named OPTIPATH has been developed, offering a wide set of different optimisation strategies, optionally including compliance with risk acceptability criteria. The OPTIPATH methodology has been integrated in the TRAT4-GIS software for transportation risk analysis. In this paper the application of OPTIPATH to a complex Italian real-life scenario is outlined. The main aim of the work is to show the capability of the methodology in highlighting the trade-offs among strategies for the selection of the preferred solution and the importance of TRAT4-GIS in offering help to administrators involved in the decision-making process which characterises land-use and transportation planning activities. r 2008 Published by Elsevier Ltd. Keywords: Hazardous materials; Risk criteria; Routing; Optimisation; Transportation

1. Introduction The control and the reduction of the risk in a zone with a high concentration of process industries can generally be achieved also by lowering the risk caused by the hazmat transportation activities through the area (CCPS, 1995; Egidi, Foraboschi, Spadoni, & Amendola, 1995). One way to decrease road transportation risk consists in routing hazmat vehicles on less risky paths than those chosen by truck drivers (List, Mirchandani, Turnquist, & Zografos, 1991). For solving this risk-based routing optimisation problem, a new methodology named OPTIPATH has been developed. The main innovative features of the model are briefly reported in the following, whereas a detailed description of its theoretical fundamentals can be found in Bonvicini and Spadoni (2008). A first distinctive aspect of OPTIPATH lies in the definition of the network arc attributes, which is heavily drawn on the risk indexes traditionally adopted in quantified risk Corresponding author. Tel.: +39 051 2090235; fax: +39 051 2090247.

E-mail addresses: [email protected] (S. Bonvicini), [email protected] (G. Spadoni). 0950-4230/$ - see front matter r 2008 Published by Elsevier Ltd. doi:10.1016/j.jlp.2007.11.009

analysis. Despite the fact that the routing problem has been mainly faced by operations researchers, OPTIPATH has been developed in the context of transportation risk analysis. Individual risk measures and societal risk profiles are carefully evaluated as functions of both the frequency of an incident and its damage effects. A second strength of OPTIPATH is given by the possibility of the optimal tank truck distribution to guarantee compliance with risk acceptability criteria. In the absence of Italian limit values, the Dutch criteria for the transport of hazardous substances have been applied (Ministry of Housing, Planning and Environment & Ministry of Transport and Public Works, 1996). The Dutch individual risk threshold is equal to 1  106 events yr1. Instead, the limit for the societal risk caused by hazmat vehicles is established for road segments of unitary length (i.e. of 1 km): the F(N) curve of each road segment must lie under the limit curve, which has the following expression: Farc limit (N) ¼ 102 N2 events yr1 km1. This curve is called the arc societal risk limit in the following. The presence of risk limits, which is assured by specific constraint equations, splits the tank truck flow on more than one path from an origin to a destination node, producing a

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Nomenclature area F(N) curve curve of the cumulated frequency of having fatalities XN due to total hazmat transportation in the area, area F in events yr1 F cumulated frequency of having fatalities XN, events yr1 Farc limit(N) curve limit curve for the F(N) curve of network segments of unitary length, Farc limit in events yr1 km1 FREQTOT total value of the accident frequency, events yr1 LTOT total value of the travelled distance, km yr1 N number of fatalities, persons OLPOPTOT total value of the exposed on-line population density, persons yr1 OOPETOT total value of the out-of-pocket expenses, h yr1 RRCTOT total value of the risk-related costs, h yr1 TACTOT total value of the total-arc costs, h yr1 TIMETOT total value of the travelling time, min yr1

more homogeneous risk distribution over the area than an all-or-nothing assignment to a unique optimal route. The third feature of OPTIPATH is represented by its implementation in the Windowss-based TRAT4-GIS software, which has two interacting modules, RISK (evaluating risk to people) and OPTIPATH (performing optimisation). This implementation is essential to make the methodology capable of handling realistic networks, and not just small hypothetical cases or made-up numerical examples. Both the RISK and the OPTIPATH modules run under the ArcViews 3.2 GIS software (ESRI, 1999). In addition, OPTIPATH requires CPLEXs 6.52 (ILOG Inc, 1999) for the solution of the routing problem. In fact, from a mathematical point of view OPTIPATH is a multi-commodity and multiple-origin/destination-pairs network flow problem (Ahuja, Magnanti, & Orlin, 1993), offering different optimisation strategies and the possibility to assure compliance with risk limit values. Each optimisation criterion refers to the minimisation of a different objective function corresponding to a specific arc attribute. One of the objective functions (i.e. one of the arc attributes) is given by the risk-related costs (minRRC criterion), which represent a monetisation of the societal risk caused by hazmat transport (Bonvicini & Spadoni, 2008). The other default objective functions are the out-of-pocket expenses (minOOPE criterion), the travelling time (minTIME criterion), the transport distance (minL criterion), the accidental frequency (minFREQ criterion), the on-road population density (minOLPOP criterion) and the total-arc costs (minTAC criterion), expressed as the sum of the riskrelated costs (RRC) and the out-of-pocket expenses (OOPE). In addition, it is possible to require the optimal solution to satisfy risk acceptability criteria: or the arc

ir-lim

optimisation strategy honouring the individual risk limit value ir-lim+sr-lim optimisation strategy honouring both the individual and the arc societal risk limit value minFREQ optimisation strategy minimising the total value of the accident frequency minL optimisation strategy minimising the total value of the travelled distance minOLPOP optimisation strategy minimising the total value of the exposed on-line population density minOOPE optimisation strategy minimising the total value of the out-of-pocket expenses minRRC optimisation strategy minimising the total value of the risk-related costs minTAC optimisation strategy minimising the total value of the total-arc costs minTIME optimisation strategy minimising the total value of the travelling time sr-lim optimisation strategy honouring the total value of the arc societal risk limit value

societal risk limit (sr-lim) or the individual risk limit (ir-lim) or both (sr-lim+ir-lim). The TRAT4-GIS menu for the selection of the optimisation strategies is shown in Fig. 1. Through the TRAT4-GIS software the OPTIPATH methodology has been applied to a complex real-life routing scenario, namely the Italian area of Ravenna, in order to put in evidence the usefulness of the routing model and of the software tool in giving support to the decision makers involved in land-use planning activities where industrial risk has to be taken into account. The application of OPTIPATH to Ravenna is outlined and discussed in this paper. It is organised as follows. In Section 2 a description is given of the features of the area. Section 3 contains information about the current hazmat shipments. The results of optimisation are reported in Section 4. Finally some concluding remarks are provided in Section 5. 2. Description of the area of Ravenna Ravenna is an Italian town located in the southern part of the Plan of the Po, near the Adriatic sea. It has an important harbour, which is connected through a channel to the main industrial zones, where huge amounts of hazardous materials are yearly processed, shipped and stored. There are more than 130 fixed plants, mainly operating in the field of petrochemical, agricultural and inorganic products as well as in the food industry. Transportation is performed by road, rail, pipeline and ship. Ravenna has approximately 90,000 inhabitants, to which 400,000 tourists have to be added during the summer bath season. It has been the main western centre of the Byzantine culture, as testified by some areas of great cultural and architectural interest. For these reasons the

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Fig. 1. TRAT4-GIS software: menu for the selection of the optimisation strategies.

area of Ravenna has already been the object of previous risk analysis studies performed with the ARIPAR-GIS software (Egidi et al., 1995; Spadoni, Egidi, & Contini, 2000; Spadoni, Contini, & Uguccioni, 2003). However the application of OPTIPATH requires additional information with respect to a risk analysis study. Due to the partial availability of all real data, their realistic values and plausible hypothesis have been adopted where real information is missing. For this reason, the application of OPTIPATH to the area of Ravenna has the main purpose of highlighting the capabilities of the model and not of solving a real routing problem, which currently does not exist at all, since neither risk analysis studies for transportation networks (with a final comparison of risk indexes to threshold values) nor the evaluation of alternative paths are compulsory by law in Italy. In the following, a description is given of all the data (both real and realistic ones) and hypotheses which have been adopted for the area of Ravenna. 2.1. Transportation network The area considered in this study measures 28,800 m  26,000 m. To describe its road network, 143 arcs and 111 nodes have been considered. Not all considered arcs are currently suitable from a structural point of view for heavy good vehicles, as tank trucks. They have been taken into account as possible alternatives to the current set of paths, though opportune modifications would be necessary for them. The area of Ravenna and its road network are shown in Fig. 2. The arcs of the network have been assumed as belonging to three different classes: motorway arcs, national road segments and urban streets. For each category a different accident frequency per unit tank truck and unit length has been assumed, adopting data derived from (Cozzani, Bonvicini, Vanni, Spadoni, & Zanelli, 2001a, b). The release probability, conditioned to the occurrence of an accident, has been taken equal to be 0.139 for atmospheric tank trucks and to 0.050 for pressurised ones, on all network arcs (Cozzani et al., 2001a, b). In order to evaluate the time required by a tank truck to run along each arc, different characteristic speed values have been adopted for the arcs as a function of the class

they belong to. Typical speed values, which are not necessarily coincident with limit values, have been assumed. The values of the accident frequency and of the characteristic speed of the three arc classes, together with the on-road population density introduced further on, are summarised in Table 1. 2.2. Meteorological conditions Three different pairs ‘‘Pasquill class–wind speed’’— called meteorological classes—have been chosen as representative of the meteorological conditions of Ravenna: B–3 m s1, D–5 m s1 and F–2 m s1. A detailed wind rose has been considered for the area, assuming 16 different wind sectors. 2.3. Population distribution In order to evaluate societal risk measures, data about the population distribution in Ravenna are required. For risk evaluation purposes, population has been assumed to be uniformly distributed inside rectangles or clustered in centres of aggregated population (CAPs) or linearly distributed along the road network. In TRAT4-GIS, different population categories can be defined, each characterised by different values of the indoor and outdoor presence probability. To describe the population of Ravenna, six population classes have been taken into account, as listed in Table 2. Data about the indoor and outdoor presence probabilities of the various population classes were derived from the ARIPAR study (DICMAUniversita` di Bologna, Protezione Civile Emilia Romagna, & Regione Emilia Romagna, 1992). These values are typical, considering the habits of Italians living in a town sited in the North of Italy and the open times of the public places described as CAPs. To describe Ravenna, more than 850 population rectangles have been defined (the major part of them measuring 400 m  400 m), with a population density (always belonging to category 5) ranging from 6.25  106 to 1.32  102 persons m2. Further, about 250 CAPs have been taken into account, distributed between population categories 1–4, with persons ranging form 10 to 1419. Finally ‘‘motorists’’ (belonging to population category 6)

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Fig. 2. The area of Ravenna assumed for optimisation. Table 1 Accident frequency per unit tank truck and unit length, characteristic speed and linear population density values as a function of the arc class Arc class

Accident frequency (events vehicle1 km1)

Characteristic speed (km h1)

Linear population density (persons m1)

Motorway National road Urban road

3.31  107 3.67  107 6.60  107

100 50 30

0.05 0.07 0.09

Table 2 Population categories in the area of Ravenna Population category

Description

Indoor presence probability

Outdoor presence probability

Category 1

Students, supermarket customers and staff Hotel guests and staff People at monumental sites People in stadium Residents Motorists

1.00

0.00

0.67 0.33

0.33 0.67

0.00 0.95 0.00

1.00 0.05 1.00

Category 2 Category 3 Category 4 Category 5 Category 6

Those CAPs (about 70) with a population greater than 100 persons have been chosen as the set of points where the individual risk limit has to be verified, if a ir-lim or a sr-lim+ir-lim criterion is adopted. The population rectangles and the CAPs taken into account in the risk evaluation of Ravenna are shown in Fig. 2. 3. Hazmat tank trucks in Ravenna With regard to the dangerous goods shipped in the area of Ravenna (which amount nearly to 3,000,000 tonnes, referring to a database of 1995), attention has been focused on the bulk transport of liquids and liquefied gases. 3.1. Hazmat shipments

have been assumed as present on the whole transportation network, with a linear density varying with the arc class, as reported in Table 1.

As usual in risk analysis, different substances have been grouped into four clusters according to their physical–

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chemical properties and their hazard characteristics in terms of flammability and/or toxicity. For each cluster a key substance has been chosen, namely chlorine (as representative of toxic gases), LPG (as representative of flammable liquefied gases), gasoline (as representative of flammable liquids) and methanol (as representative of flammable and toxic liquids). As shown in Fig. 2, eight origin/destination points of hazmat tank trucks have been considered, among which only points numbered 7 and 8 are inside the area, the others being on the border. The border points represent for the tank trucks intermediate points (without stop) on the route from Ravenna to the final destinations (or from the initial origins to Ravenna). Instead, points numbered 7 and 8 correspond to the entrances of the two industrial areas to which tank trucks are directed (or from which they come from). After clustering the chemicals into groups represented by key substances and merging the plants into two groups, depending on whether they belong to the first or the second of the two industrial zones, the shipments turn out to be 35, involving 85,712 vehicles yr1. Each shipment represents a commodity and refers to a specific chemical and a specific origin/destination pair: 1 shipment involves chlorine, 14 LPG, 8 gasoline and 12 methanol. The data characterising each shipment, i.e. the substance, the origin/ destination nodes and the number of vehicles to be shipped between them, are summarised in Table 3. 3.2. Accidental scenarios of hazmat tank trucks For each key substance, the consequences analysis has been performed, taking into account all accidental scenarios which can originate from a tank truck. Since the Dutch risk acceptability criteria have been applied in OPTIPATH, for reasons of consistency and coherency, the characterisation of the loss of containment events (LOCs) and of the event trees has been performed according to the Dutch guidelines (Committee for the Prevention of Disasters, 1999). The consequence evaluation for the final scenarios (pool fire, flash fire, fireball, toxic cloud) has been performed through the software EFFECTS 2.1 (TNO, 1996) and TUTUM (DICMA-Universita` di Bologna, 2002), in order to obtain, for each final event and each meteorological class, the vulnerability map, that is the distribution of the death probability around the release point, evaluated from the distribution of physical effects through the probit equations developed by TNO (Committee for the Prevention of Disasters, 1992). Vulnerability maps represent input data for the RISK module of TRAT4-GIS. As an example, in Fig. 2 the spatial death distribution caused by the toxic puff developing after the catastrophic rupture of a chlorine tank truck in the F–2m s1 meteorological class, in the case of wind coming from the north-eastern direction and the incident occurring in the middle point of arc 49 is shown: the outer curve refers to a death probability value of 0.01, the intermediate one to a value of 0.50 and the inner one to 0.90.

349

Table 3 Hazmat shipments data assumed for optimisation in the area of Ravenna Shipment or commodity

Key substance

Origin node

Destination node

Road tank trucks (vehicles yr1)

CL1 Gaso1 Gaso2 Gaso3 Gaso4 Gaso5 Gaso6 Gaso7 Gaso8

Chlorine Gasoline

7 5 7 7 7 7 7 7 7

5 7 4 5 3 6 2 5 1

20 19 4313 26,894 5884 5973 8434 5068 6692

LPG1 LPG2 LPG3 LPG4 LPG5 LPG6 LPG7 LPG8 LPG9 LPG10 LPG11 LPG12 LPG13 LPG14

LPG

5 7 7 7 7 7 7 8 8 8 8 8 8 1

8 5 3 6 2 5 1 5 3 2 1 4 5 8

1083 2004 543 248 544 541 1561 210 995 550 930 450 214 290

Meta1 Meta2 Meta3 Meta4 Meta5 Meta6 Meta7 Meta8 Meta9 Meta10 Meta11 Meta12

Methanol

7 5 7 3 7 6 7 2 5 7 7 4

5 7 3 7 6 7 2 7 7 1 4 7

8340 323 1091 402 16 166 251 124 603 534 56 346

Total

85,712

3.3. Risk-related costs As a first result of the application of OPTIPATH to Ravenna, it is useful to show and justify, for the four goods shipped through the area, the values of the risk-related costs, which represent a monetisation of the societal risk due to hazmat transport. For each key substance, the arithmetic mean values—evaluated on all network arcs—of the risk-related costs (RRC), of the out-of-pocket expenses (OOPE) and of their sum, representing the total-arc-costs, have been calculated. These mean values are shown in Fig. 3. Looking at this graph, it is possible to note that the arithmetic mean value of the RRC is greater for chlorine than for the other chemicals, while gasoline has the minimum value, more than one order of magnitude smaller than that of chlorine. This difference can easily be justified since the RRC represent a measure of the hazard of the

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Mean total arc cost (Euro/veh)

350

8 RRC OOPE

7 6 5 4 3 2 1 0

Methanol

Chlorine

Gasoline

Table 4 Minimum, maximum and arithmetic mean values of the societal-riskbased arc capacities for each key substance Societal-risk-based arc capacity values (vehicles yr1)

Chlorine

Gasoline

LPG

Methanol

Minimum Maximum Arithmetic mean

0 4563 883

2897 402,109 263,054

513 44,597 32,743

477 129,590 73,583

LPG

Current flow - area F(N) curve

Fig. 3. Mean contributions of the risk-related costs (RRC) and the out-ofpocket-expenses (OOPE) to the mean total-arc costs for each key substance.

3.4. The societal-risk-based arc capacities As a further result, the minimum, the maximum and the mean value (evaluated among all network arcs) of the societal-risk-based arc capacities are listed in Table 4 for the four key substances. Though major details about their evaluation and meaning is reported in Bonvicini, Vezzani, and Spadoni (2002), it is worth saying here that these capacities represent flow restrictions which are necessary in order to comply with the arc societal risk limit. It is possible to note that the mean value of the societal-riskbased arc capacity for chlorine is at least two orders of magnitude smaller that the mean values of the capacities of the other goods, confirming the extremely hazardous properties of chlorine. Moreover, the minimum value of the societal-risk-based arc capacities of chlorine is equal to zero, meaning that on at least one arc not even a single vehicle per year of chlorine can travel without exceeding the arc societal risk limit curve. In particular, the arcs with small arc capacities are those with high societal risk values, i.e. those crossing the zones of Ravenna with a high population density. 3.5. Risk due to the current flow distribution Preliminarily to the determination of the optimal flow distributions on the basis of the various optimisation criteria available in OPTIPATH, the risk distribution corresponding to the current flow has been determined, since the current situation and the risk values due to it represent the term of comparison for all other flow distributions. In the absence of information about the

F (events/year)

substance. It can be further noted that the values of the OOPE are the same for all substances: in fact for the area of Ravenna these expenses have been assumed as independent of the commodity. Nevertheless, the contributions of the OOPE and of the RRC to the total-arc-costs are different for each chemical: chlorine is the unique substance for which the contribution of the RRC to the total-arc-costs is not negligible, being equal to 45.3%.

1,E-01 area F(N) curve

1,E-03

Dutch area limits

1,E-05 1,E-07 1,E-09 1,E-11

1

10

100 N

1000

10000

Fig. 4. Area F(N) curve of the current flow distribution and Dutch limit curves for an area.

current paths of hazmat shipments through Ravenna, it has been supposed that the current flow corresponds to the minimum distance criterion without any type of constraint. For the current flow distribution, a risk evaluation has been performed first of all. In Fig. 4 the societal risk caused by total hazmat flow over the area, expressed as the area F(N) curve, is reported. In this figure also, the Dutch limit curves for the societal risk of an area (Pasman, Duxbury, & Bjordal, 1992) are depicted. Above the upper limit curve there is the ‘‘intolerable risk zone,’’ under the lower limit curve there is the ‘‘negligible risk zone’’ and inside the two curves there is the ALARP zone, that is the zone where risk has to be reduced ‘‘as low as reasonably possible.’’ It can be immediately noticed that the current area F(N) curve lies entirely in the intolerable risk zone. In addition, the arc societal risk limit curve is violated along some arcs and in particular along the arcs 35 and 49 (which are evidenced in Fig. 2). Fig. 5 shows the Dutch limit curve for the arc societal risk and the F(N) curves evaluated for the more risky segment of unitary length for the arcs 35 and 49, considering all the hazmat tank trucks travelling on these arcs in the current flow distribution. Instead, in Fig. 6(A) the individual risk mapping of the current flow distribution is depicted. It can be seen that on some arcs there are risk values in the range 1  104–1  103 events yr1, with a maximum value of 2.8  104 events yr1. Though the individual risk decreases to negligible values by moving away from the road (it is smaller than the Dutch limit at a distance of 200 m from

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the arc with the highest individual risk value), some of the CAPs which are very close to the road experience individual risk values greater than the threshold. As a further result useful for judging alternative flow distributions, the total values of the default arc attributes are reported in Table 5 for the current flow distribution. The total value of an arc attribute is given by the sum on all network arcs and all commodities of the product of the attribute value of the commodity on the arc and the total number of hazmat tank trucks of the commodity yearly travelling on the arc. The symbols FREQTOT, LTOT, OLPOPTOT, OOPETOT, RRCTOT, TACTOT and TIMETOT are used, respectively, for the accidental frequency, the transport distance, the on-road population density, the Current flow - F(N) curves of the most risky unitary length (1 km) segment

F (events/year/km)

1,E-01

1,E-05 1,E-07 1,E-09 1,E-11

1

10

100 N

1000

out-of-pocket expenses, the risk-related costs, the total-arc costs and the travelling time. As an example, LTOT represents the total distance yearly travelled in Ravenna by all 85,712 hazmat tank trucks, expressed in km yr1; whereas FREQTOT, expressed in events yr1, is the frequency with which accidents involving one of these vehicles yearly occur in the area. 4. Hazmat routing in Ravenna: presentation and discussion of results Through OPTIPATH various optimal flow distributions have been obtained for the area of Ravenna, applying different routing strategies. 4.1. Routing strategies applied to Ravenna

arc 49 arc 35 Dutch arc limit

1,E-03

351

10000

Fig. 5. Examples of F(N) curves of the most risky unitary length (1 km) segments of arcs 49 and 35 due to the current flow distribution and Dutch limit curve for an arc.

Optimisation has been performed considering all the default optimisation strategies, i.e. the criteria minFREQ, minL, minOLPOP, minOOPE, minRRC, minTAC and minTIME, each one referring to a different arc attribute. For each objective function, four options about the respect of risk limit values have been considered: no compliance with risk limits (no-lim), compliance only with the limit on the arc societal risk (sr-lim), compliance only with the limit on individual risk (ir-lim) and compliance with both the individual and the arc societal risk thresholds (sr-lim+ ir-lim). In this way, 28 routing criteria have been applied to Ravenna. It is necessary to say that there is no flow distribution which, even without any restriction on societal risk, guarantees the respect of the individual risk limit in all 70 risk control points, that is all ir-lim strategies (and thus

Fig. 6. Individual risk distribution (events yr1): (A) current flow distribution and (B) [minRRC, sr-lim+ir-lim] strategy.

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Table 5 Total values of the arc attributes for the current flow distribution RRCTOT (h yr1)

FREQTOT (events yr1)

LTOT (km yr1)

OLPOPTOT (persons yr1)

TIMETOT (min yr1)

OOPETOT (h yr1)

TACTOT (h yr1)

2.75  105

6.41  101

1.76  106

1.17  108

1.49  106

3.62  106

3.89  106

Fig. 7. Paths of the chlorine shipment CL1 obtained through different optimisation criteria.

also all sr-lim+ir-lim) violate the threshold at least in one risk control point. For this reason the maximum acceptable individual risk value in the control points has been increased and put equal to 1  105 events yr1. This choice, though surely somewhat arbitrary, is justified by the fact that it seems not reasonable to forbid hazmat transportation through the area of Ravenna; furthermore, this threshold violation is limited to a small number of hot spots. A good emergency preparedness to hazmat incidents occurring near these few critical points could surely compensate for this fact. With this modification all 28 routing problems have a solution. The criterion [minL, no-lim] corresponds to the current flow distribution. The more interesting results of this application are reported and discussed in the following, putting in evidence which considerations can be assumed as generally valid (and thus also averted from the specific case of Ravenna) and which instead are specific for this area.

4.2. Results of general validity First of all it has to be noted that generally each criterion produces a different flow distribution. As an example, the paths of the chlorine shipment CL1 (cited in Table 3) are shown in Fig. 7 for all the 28 routing strategies. As a second comment, it should be kept in mind that generally, once an optimisation strategy with risk limits has been chosen, the path of a commodity shipped alone through the area is different from the route the commodity would follow in the optimisation problem with the simultaneous presence of all the commodities. This fact is pointed out in Fig. 8, which refers to the criterion [minRRC, sr-lim] and shows the flow distribution of the methanol shipment META1 (whose data are reported in Table 3) in the case of all 35 commodities travelling on the road network of Ravenna and in the case of shipment META1 travelling alone.

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353

Fig. 8. [minRRC, sr-lim] criterion, flow distribution of shipment META1: (A) routing problem with all 35 shipments to be optimised and (B) routing problem with only shipment META1 to be optimised.

Third, when considering those of the no-lim strategies whose objective function is based on the arc attributes which are not dependent on the key substance (that is the criteria minFREQ, minL, minOLPOP, minTIME and minOOPE, since the accident frequency, the length, the on-line population density, the travelling time and the outof-pocket expenses are, for each arc, the same for all substances), the best path between a specific origin/ destination pair is the same for all substances. Instead if the strategies minRRC and minTAC are considered (always in the case of the no-lim strategies), due to the fact that the risk-related costs and thus also the total-arc-costs depend on the substance, different commodities might have different optimal routes between the same origin/ destination nodes. As a fourth issue it can be noted that in all no-lim solutions there is a unique path for each shipment: the best route for a specific commodity between a specific origin/destination pair can be travelled by an infinite number of vehicles. Instead, the presence of risk limits causes the trucks of a commodity to be split on more than one path between their origin and destination nodes. In this way, risk is more uniformly spread over the whole area. As a fifth consideration it can be noted that in all no-lim solutions, comprising the solution corresponding to the [minRRC, no-lim] criterion, there could be arc unitary length segments with F(N) curves exceeding the arc societal risk limit. This means that the minimisation of the riskrelated costs without any societal-risk-based constraint does not guarantee the compliance with the arc societal risk limit value. 4.3. Comparison among routing strategies In order to compare to each other the various routing strategies, a comparison of the total values of the arc attributes and of the risk values of each criterion has to be performed. In Table 6 the percentage differences of the total values of the arc attributes for the different optimisation criteria are reported and evaluated with respect to the corresponding total values of the current

flow distribution listed in Table 5. Table 6 is divided into four parts, referring to the no-lim, the sr-lim+ir-lim, the sr-lim and the ir-lim strategies. It has to be noted that, inside each part of the table, the criteria minL and minOOPE produce identical percentage variations of the total arc attribute values. This can be easily justified, since for Ravenna it has been assumed that the out-of-pocket expenses are independent of the substance. As a consequence, for a given flow distribution, the total arc attribute values OOPETOT and LTOT are, in this specific case, simply proportional. Further, in the case of Ravenna also the minTAC criterion gives the same variations as the minL and minOOPE strategies inside each part of the table. The value of TACTOT is given by the sum of OOPETOT and RRCTOT. Since in Ravenna chlorine is the only commodity whose risk-related costs are of the same order of magnitude than the out-of-pocket expenses and there is a unique shipment of chlorine, which contributes, with its 20 yearly tank trucks, for only 0.02% to the total number of hazmat vehicles travelling through the area, the contribution of RRCTOT to TACTOT is practically negligible. Thus, in this area, the minimisation of TACTOT gives a flow distribution whose total values of the arc attributes are nearly equal to those produced by the minimisation of OOPETOT. It is necessary to say that the total value of the arc attribute corresponding to the objective function in the case of the no-lim criteria is always smaller than (or equal to) its value in the current flow distribution, whereas it could be also greater than it in the case of sr-lim+ir-lim, sr-lim and ir-lim strategies. In the latter cases the optimisation of the objective function has to simultaneously satisfy a set of constraint equations: as obvious, constraints increase the value of the objective function. In fact it can be noted that the percentage variations of the arc attribute corresponding to the objective function in the no-lim criteria (which have been italicised, in the first part of Table 6) are all negative or null, whereas, in the sr-lim+ir-lim, sr-lim and the ir-lim cases, they can be also positive. The fact that in the no-lim criteria the total value of the arc attribute corresponding to the objective function is not greater than its value in the current flow distribution

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Table 6 Percentage differences of the total values of the arc attributes for different optimisation criteria LTOT (%)

OLPOPTOT (%)

Total values of the arc attributes-

FREQTOT (%)

k Optimiz. criterion k

No respect of risk limit values (no-lim)

[minFREQ, no-lim] [minL, no-lim] [minOLPOP, no-lim] [minOOPE, no-lim] [minRRC, no-lim] [minTAC, no-lim] [minTIME, no-lim]

3.9 0.0 6.2 0.0 4.5 0.0 1.9

[minFREQ, sr-lim+ir-lim] [minL, sr-lim+ir-lim] [minOLPOP, sr-lim+ir-lim] [minOOPE, sr-lim+ir-lim] [minRRC, sr-lim+ir-lim] [minTAC, sr-lim+ir-lim] [minTIME, sr-lim+ir-lim]

5.7 0.0 4.0 0.0 13.1 0.0 10.8

1.7 0.0 10.3 0.0 6.8 0.0 6.0

OOPETOT (%)

RRCTOT (%)

5.7 0.0 4.0 0.0 13.1 0.0 10.8

25.1 0.0 10.5 0.0 37.8 0.0 24.7

TACTOT (%)

TIMETOT (%)

3.6 0.0 3.1 0.0 9.5 0.0 8.2

10.1 0.0 31.5 0.0 24.8 0.0 11.4

Respect of both the societal and individual risk limit values (sr-lim+ir-lim) 10.1 18.2 1.7 18.2 24.4 10.6 17.6 1.7 17.6 20.0 14.4 19.9 3.4 19.9 26.5 10.6 17.6 1.7 17.6 20.0 15.6 23.3 0.9 23.3 34.4 10.6 17.6 1.7 17.6 20.0 10.5 18.2 2.6 18.2 28.0

15.7 15.4 17.3 15.4 19.5 15.4 15.7

25.9 26.2 43.6 26.2 44.3 26.2 25.8

[minFREQ, sr-lim] [minL, sr-lim] [minOLPOP, sr-lim] [minOOPE, sr-lim] [minRRC, sr-lim] [minTAC, sr-lim] [minTIME, sr-lim]

Respect of the societal risk limit value (srlim) 10.1 18.2 1.7 18.2 10.6 17.6 1.7 17.9 14.4 19.9 3.4 19.9 10.6 17.6 1.7 17.9 15.6 23.3 0.9 23.3 10.6 17.6 1.7 17.9 10.5 18.2 2.6 18.2

24.7 23.3 26.9 23.3 34.5 23.3 28.4

15.7 15.2 17.2 15.2 19.5 15.2 15.7

25.5 26.2 43.6 26.2 44.3 26.2 25.5

[minFREQ, ir-lim] [minL, ir-lim] [minOLPOP, ir-lim] [minOOPE, ir-lim] [minRRC, ir-lim] [minTAC, ir-lim] [minTIME, ir-lim]

Respect of the individual risk limit value (irlim) 3.9 5.7 1.7 5.7 3.3 4.5 0.9 4.5 3.1 8.5 9.4 8.5 3.3 4.5 0.9 4.5 4.5 13.1 6.8 13.1 3.3 4.5 0.9 4.5 1.9 10.8 6.0 10.8

25.1 12.4 23.3 12.4 37.7 12.4 24.7

3.6 3.6 6.7 3.6 9.5 3.6 8.2

10.1 8.1 24.2 8.1 24.8 8.1 11.4

can be noticed by looking at Fig. 9, where the data of the first part of Table 6 (that is those of the no-lim criteria) are graphed in the form of a spider web. Each coloured polygon refers to a different objective function and the vertexes of each polygon on the axes represent the percentage variations of the total values of the arc attributes with respect to those of the current flow. Each polygon has a coloured dot, which refers to the percentage variation of the total arc attribute corresponding to the objective function: it can be noticed that the coloured dots lie all inside or on the 0% grid line. As a further confirmation of this fact, the minTIME strategies can be considered, for instance. In the [minTIME, no-lim] criterion, TIMETOT has a (negative) variation of 11.4% with respect to the value of 1.49  106 min yr1 of the current flow. In the criteria [minTIME, sr-lim+ir-lim] and [minTIME, sr-lim], TIMETOT increases by, respectively, 25.8% and 25.5%, whereas in [minTIME, ir-lim], TIMETOT decreases again by 11.4%. The more numerous are the constraints, the greater is the value of the objective function: for this

reason, for a given objective function, in the no-lim criterion the reduction of its value is greater than (or at limit equal to) its value in the sr-lim or the ir-lim case, and in these two cases it is greater (or equal) than in the sr-lim+ir-lim criterion. As an example, considering the minRRC strategies, in the no-lim case the reduction of the objective function is of 37.8% compared to the value of 2.75 105 h yr1 of the current flow. If the ir-lim constraint alone is added, the reduction is of 37.7%; instead,if the sr-lim constraint is considered, it is of 34.5%; finally in the sr-lim+ir-lim case it is of 34.4%. This can be seen also in the spider web graph of Fig. 10, where the percentage variation of each sr-lim+ir-lim criterion versus the corresponding no-lim strategy is reported. Each coloured polygon refers to an objective function and on each one there is a dot of the same colour, showing the percentage variation of the total arc attribute corresponding to the objective function: it can be noticed that all dots are outside the 0% grid line. In addition it can be noted that, considering the results of each part of Table 6, i.e. looking separately at the no-lim,

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355

Fig. 9. Percentage variations of the total values of the arc attributes of no-lim criteria with respect to those of the current flow distribution.

Fig. 10. Percentage variations of the total values of the arc attributes of sr-lim+ir-lim criteria with respect to those of corresponding no-lim criteria.

the sr-lim+ir-lim, the sr-lim and the ir-lim criteria, the greatest reduction—or, if there is no reduction, the slightest increment of the total value of an arc attribute between different optimisation criteria—corresponds to the criterion where this attribute is optimised. For instance, considering the sr-lim+ir-lim criteria, the major reduction of the total risk-related-costs RRCTOT occurs in the criterion [minRRC, sr-lim+ir-lim], being equal to 34.4%, whereas the slightest increment of the total travelling time TIMETOT occurs in the criterion [min TIME, sr-lim+ ir-lim], being equal to 25.8%. All the comments expressed till now to the data of Table 6, though derived from the case of Ravenna, have a general validity. Instead, referring to the particular case of this area, it should be noted that the percentage variations of the sr-lim criteria are always similar and very often identical to those of the sr-lim+ir-lim criteria. This means

that, for each objective function, the solutions of the sr-lim and the sr-lim+ir-lim routing problems are similar and thus the addition of the ir-lim constraint to a sr-lim routing problem only slightly modifies the solution, that is the solutions of the sr-lim problems nearly assure compliance also with the ir-lim constraint. In addition, it can be noted that, for each objective function, the variations of the ir-lim strategies are, in absolute values, smaller than those of the corresponding sr-lim strategies: for instance, considering the total attribute values of FREQTOT, in the ir-lim criteria the variations are in the range j3.9%j to 4.5%, while in the sr-lim strategies they are in the range 10.1% to 15.6%. This means that, for each objective function, the sr-lim solutions (and thus also the sr-lim+ir-lim ones, as previously stated) differ much more from the current flow distribution than the ir-lim solutions. As a consequence, in order to guarantee compliance with the arc societal risk

ARTICLE IN PRESS S. Bonvicini, G. Spadoni / Journal of Loss Prevention in the Process Industries 21 (2008) 345–358

threshold, the tank trucks have to be rerouted to a great extent to new paths with respect to those currently used by drivers. As a further consideration, since the current flow distribution violates the individual risk value of 1  105 events yr1 only in a few CAPs, the compliance with this threshold can be obtained by minor modifications of the current flow distribution. 4.4. The best routing strategy for Ravenna The question which spontaneously rises is which optimisation criterion has to be adopted in Ravenna. To give an answer to this question, a comparison of the total values of the arc attributes and of the risk values of the different criteria has to be performed. As a consequence of the consideration about risk distribution equity addressed in the former sections, a sr-lim+ir-lim criterion should be adopted. Focusing attention on the second part of Table 6, it is necessary to evaluate which objective function should be chosen, i.e. which criterion is the best one among minFREQ, minL (or minOOPE or minTAC), minOLPOP, minRRC and minTIME. It can be noted that, considering the sr-lim+ir-lim criteria, the various objective functions produce similar variations of each total arc attribute: these variations are in the ranges 10.1% to 15.6% for FREQTOT, 17.6% to 23.3% for LTOT, 3.4% to 2.6% for OLPOPTOT, 18.2% to 23.3% for OOPETOT, and 15.4% to 19.5% for TACTOT. For all these attributes the different objective functions produce total values, whose difference with respect to the current flow value is, in absolute value, of about 5% and often smaller than it. Instead, the percentage variations the various sr-lim+ir-lim criteria cause to RRCTOT are in the range 34.4% to 20.0% (i.e. they can differ till 14.4%) and to TIMETOT in the interval 25.5% to 44.3% (i.e. they can differ till 18.8%). It has to be noted that the greatest reduction of RRCTOT (equal to 34.4%, occurring, as obvious, in the [minRRC, sr-lim+ir-lim] criterion), corresponds to the greatest increment of TIMETOT, equal to 44.3%, and of LTOT, equal to 23.3%: this fact could induce to judge the solution of the [minRRC, sr-lim+ir-lim] criterion as not practicable. Though looking at the percentage differences of the sr-lim+ir-lim strategies, the [minRRC, sr-lim+ir-lim] criterion seems the best for Ravenna. In fact, considering the current flow distribution, the arithmetic mean time each vehicle spends travelling through the area of Ravenna (obtained by dividing the value of TIMETOT of Table 5 by the total number of vehicles reported in Table 3), is equal to 17 min. An increment of 44.3% (which could be judged as enormous), corresponds to about 8 min, that is to a value which is negligible, compared to the total travelling time of each vehicle between a first point inside the area of Ravenna and a second point corresponding to its final destination (or initial origin) in Italy, which is at least of some hours. In the same manner also the increment of LTOT (and thus of OOPETOT) in the [minRRC, sr-lim+ ir-lim] strategy, which is of 23.3%, corresponds to less than

5 km (being the mean distance travelled through Ravenna, obtained analogously as the mean time, equal to about 20 km). Considering the total distance travelled by each vehicle between a first point inside the area of Ravenna and a second point corresponding to its final destination (or initial origin) in Italy, which is at least of some hundreds of kilometres, the increment of 5 km is negligible at all. As a conclusion of these considerations, it is possible to say that the solution of the [minRRC, sr-lim+ir-lim] strategy, which is for Ravenna the best one on the base of risk, remains feasible from an economical and a practical point of view. In order to take a final decision, some considerations have to be made also about the risk values of the different criteria, both in terms of area F(N) curves and individual risk distributions. In Fig. 11 the area F(N) curve of the sr-lim+ir-lim strategies and the Dutch limit values for the societal risk of an area are reported. It can be immediately noticed that no criterion guarantees the area F(N) curve to be at least inside the ALARP zone. Though as obvious, all these strategies honour the arc societal risk limit on all arcs. The unique way to move these curves inside the ALARP zone would be to reduce the flow of hazmat through Ravenna, independently of the distribution of the tank trucks on the network. The criterion, among the sr-lim+ ir-lim strategies, which brings the area F(N) curve nearest to the ALARP zone is the minRRC one. By performing a comparison among the area F(N) curves of all the 28 solutions, it is possible to note that the area F(N) curve of the [minRRC, sr-lim+ir-lim] strategy is the lowest of all. Through a comparison of Figs. 11 and 4 (which refers to the current flow), it can be seen that, except for values of No10, the [minRRC, sr-lim+ir-lim] criterion causes a reduction in the values of the frequencies F of nearly one order of magnitude, together with a reduction of the maximum value of N (from 5000 to 3000 fatalities). It has be noted that, once an objective function has been chosen, the criteria corresponding to the four risk limit options produce very similar area F(N) curves. This can be seen in Fig. 12, where, for instance, the area F(N) curves Optimized flows,sr-lim+ir-lim criteria - area F(N) curves 1,E-01

F (events/year)

356

minTIME minRRC

1,E-03

minL, minOOPE, minTAC minFREQ minOLPOP

1,E-05

Dutch area limits

1,E-07 1,E-09 1,E-11

1

10

100 N

1000

10000

Fig. 11. Area F(N) curve of the different sr-lim+ir-lim strategies and Dutch limit curves for an area.

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obtained for the [minTAC, no-lim], [minTAC, sr-lim+ ir-lim], [minTAC, sr-lim] and [minTAC, ir-lim] criteria are reported. Considering the other objective functions, analogous results are obtained. For a further validation of the [minRRC, sr-lim+ir-lim] criterion, a comparison of the corresponding flow distribution on the network, compared to the flow of the current situation, has to be performed. Relatively to chlorine, the two routes are shown in Fig. 8. It can be noted that in the current case the chlorine vehicles travel near the town centre, while with the [minRRC, sr-lim+ir-lim] strategy they use a longer route, far away from the more densely populated zones. The same consideration can be made also for methanol looking at Fig. 13, where the flow distribution of the tank trucks of the 12 shipments of methanol in the current situation and in the [minRRC, sr-lim+ir-lim] strategy are shown: preference is given to paths cutting off the town centre. Similar results are obtained also for LPG and gasoline. A further confirmation of this is given also by the individual risk distribution of the [minRRC, sr-lim+ir-lim] criterion reported in Fig. 6(B): by comparing it to the individual risk distribution of the current flow reported in Optimized flows, minTAC criteria-area F(N) curves

F (events/year)

1,E-01

no-lim sr-lim+ir-lim

1,E-03

sr-lim ir-lim

1,E-05

Dutch area limits

1,E-07 1,E-09 1,E-11

1

10

100 N

1000

10000

Fig. 12. Area F(N) curves obtained for the [minTAC, no-lim], [minTAC, sr-lim+ir-lim], [minTAC, sr-lim] and [minTAC, ir-lim] criteria.

357

Fig. 6(A) it is possible to notice that risk is shifted from the town centre to suburban zones. Since the outskirts are less populated than the central quarters, this displacement produces the already evidenced reduction of societal risk. Further, though on some arcs the individual risk still reaches very high values, there is a minor concentration of CAPs along the paths running in the suburban zones and for this reason the flow distribution of the [minRRC, sr-lim+ir-lim] strategy guarantees in each CAP an individual risk value inferior to 1  105 events yr1. 4.5. Details on the computational effort In the end some remarks about the computational time are necessary, though they strictly refer to the case study of Ravenna. The application of TRAT4-GIS to this area has been performed on a 3.07 GHz Mobile IntelsPentiums4 personal desktop with 448 MB RAM. The calculation of the input data of the optimisation problem requires about 1 h. This time is spent especially for the evaluation of the risk variables, which is related to the dimensions of the network, the number of substances to be shipped, the number of risk control points and the accuracy of the description of the impact area, particularly of the population distribution. After evaluating all the data for optimisation, the solution of the routing problems corresponding to the various optimisation criteria is obtained very quickly, since each problem is solved in less than 3 min. The computational effort is thus attributable to the calculation of risk and not to optimisation itself. This time value seems absolutely acceptable, keeping in mind that OPTIPATH is intended for helping decision makers in planning transportation activities once for all over a long period, as 1 yr. 5. Conclusions The application of the TRAT4-GIS code to the case study of Ravenna has put in evidence that this software, with its

Fig. 13. Flow distribution of all the 12 methanol shipments: (A) [minL, no-lim] criterion, i.e. current situation and (B) [minRRC, sr-lim+ir-lim] criterion.

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interacting modules RISK and OPTIPATH, represents an efficient, flexible and simple code for hazmat transportation risk analysis and routing, capable of handling realistic networks. It surely constitutes a useful tool for persons involved in land-use planning activities, due to the support it can give in the decision-making processes where industrial risk has to be taken into account. In fact the considerations about the violation of risk acceptability limits in Ravenna highlight the critical situation of this area (with the assumed tank truck flow) from the point of view of the risks due to hazmat transportation. The current transportation risk values fully justify the application of OPTIPATH to the area, in order to determine less risky paths for hazmat shipments. Though there is no solution which assures compliance with the Dutch limits for individual risk and for the area F(N) curve, the respect of the arc societal risk limit is possible for all arcs of the network. Furthermore, OPTIPATH allows the development of an alternative distribution of hazmat shipments (with respect to the current one), which, in addition to the highest possible risk reduction, remains feasible from an economical and practical point of view. Acknowledgements This research has been supported by a grant of the Italian National Research Council (CNR-GNDRCIE): this support is gratefully acknowledged. Thanks are due to Alice Andrenacci for her help in the application of OPTIPATH to Ravenna. References Ahuja, A. K., Magnanti, T. L., & Orlin, J. B. (1993). Network Flows. Englewood Cliffs, NJ, USA: Prentice-Hall. Bonvicini, S., & Spadoni, G. (2008). A hazmat routing model satisfying risk criteria. In Transportation research trends. New York, USA: Nova Science Publishers. Bonvicini, S., Vezzani, E., & Spadoni, G. (2002). Hazmat transportation in populated areas: are routing criteria useful to reduce risks? In Decision making and risk management, Proceedings of the ESREL’02 conference, Lyon, France, 19–21 March 2002 (pp. 557–564).

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