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An Interperiod Network Storage Location–Allocation (INSLA) model for rail distribution of ethanol biofuels
Journal of Transport Geography 18 (2010) 729–737
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Journal of Transport Geography journal homepage: www.elsevier.com/locate/jtrangeo
An Interperiod Network Storage Location–Allocation (INSLA) model for rail distribution of ethanol biofuels Jeffrey P. Osleeb a,*, Samuel J. Ratick b a b
Department of Geography, University of Connecticut, Storrs, CT 06269, United States Department of Geography and George Perkins Marsh Research Institute, Clark University, Worcester, MA 01610, United States
a r t i c l e
i n f o
Keywords: Ethanol logistics Unit train Multi-period optimization models
a b s t r a c t In response to the US federal renewable fuels standards, new ethanol plants of varying sizes are being established in the US. The transportation challenge is to decide on how best to move raw materials to these existing and new ethanol plants, and to ship the fuel from the ethanol plants to markets around the country. In this paper, we extend the Interperiod Network Storage Location–Allocation (INSLA) model formulation into a Rail-INSLA model to address the transportation/transshipment issues associated with the rail distribution of ethanol biofuels that include: transporting less than unit train quantities from each plant, developing new sidings at ethanol plants to accommodate a unit train, and determining the optimal number and locations for carrier operated terminals for the agglomeration of less than unit train size shipments into unit train shipments. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Increasing concerns for energy security in light of increasing oil imports, increasing costs, and oil supplies from increasingly unstable regions, has prompted the United States government to mandate that 30 billion liters of ethanol biofuels be produced domestically by 2009 (Energy Policy Act of 2005) and144 billion liters by 2022 (Amendment to the Energy Policy Act of 2005, 2008) and be added to gasoline in order to reduce our dependence on foreign sources. In response to these policies, new ethanol plants of varying sizes are being sited throughout the US, and particularly in the Midwest (the ‘‘Corn Belt”), to take advantage of the corn crop, currently the primary input in US-produced ethanol. Since ethanol is produced at geographically dispersed local ethanol plants, it must then be shipped to refineries where it is blended into gasoline. The transportation geography challenge in this growing market is to decide how best to transport raw materials to existing and proposed ethanol plants, and then how to ship the ethanol from these plants to refineries around the country. Currently, railroads represent the only means by which such large quantities of ethanol can be shipped efficiently.1 Depending on the size of the railroad tank car in which the ethanol is to be shipped, the 36 billion liters of ethanol mandated for 2008–2009 may require * Corresponding author. Tel.: +1 860 486 3656; fax: +1 860 486 1348. E-mail address: [email protected] (J.P. Osleeb). 1 A pipeline network to transport ethanol does not currently exist and it is doubtful, because of railroad right-of-way considerations. That they will be built in the future; there are also technical difficulties for pipeline shipments of this corrosive liquid. Barge transportation systems are currently at full capacity. 0966-6923/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jtrangeo.2009.09.011
between 300,000 and 900,000 tank car shipments from ethanol plants to refineries. While unit trains, which are composed of between 95 and 125 tank cars, provide the least transportation costs (lowest rates per tank car) for shipping ethanol, the size of many existing and proposed ethanol plants individually do not generate sufficient product to fill a unit train, and therefore, their shipments do not qualify for unit train rates. In response those shippers (ethanol plants) that are unable to generate sufficient volumes for unit trains can pay individual tank car rates (carload rates); invest in new rail sidings to store tank cars, or coordinate with other ethanol producers to agglomerate their output into unit train size shipments; or work with carriers to create unit train size shipments at central terminals. The significantly lower unit train rates would make them the preferred means of shipment. However, there are a number of other costs besides train rates that need to be factored into the decision. These costs include holding, demurrage and capital costs. Holding represents the opportunity cost of the ethanol, demurrage is the daily cost associated with a rail car that is either empty or waiting to be filled or filled and waiting to be transported; capital costs are associated with developing the proper length of rail sidings to store the tank cars until the unit train is assembled.2 In this paper, we develop a mixed-integer mathematical programming model to address the dynamic planning issues involved in the transportation/transshipment (Orden 1956) of biofuels from 2 Although tank storage of ethanol at supply nodes may be used to reduce demurrage costs it was not considered in this paper.
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plants to refineries. Our model is derived from the class of mathematical programming-based dynamic location–allocation models, termed ‘‘Interperiod Network Storage Location–Allocation models” (INSLA), designed to address the use of storage and agglomeration facilities to alleviate congestion on transportation networks, to allow for the realization of economies of scale in transportation, and to address the issues of cyclical supplies and demands (Ratick et al. (1987) and Osleeb and Ratick (1985, 1990)). We extend the INSLA model to determine the least cost transportation pattern for shipping ethanol on the Burlington Northern Santa Fe Railway (BNSF) from ethanol plants in the US Midwest to refineries in California, Illinois, Louisiana, Montana and Texas. The extended INSLA model formulation, Rail-INSLA, specifically addresses the location decisions and the costs and efficiency trade-offs involved in rail transportation of ethanol that include: transporting less than unit train quantities from each plant as is, developing new sidings at ethanol plants to accommodate a unit train, and determining the optimal number and locations for carrier operated terminals for the agglomeration of less than unit train size shipments into unit train shipments.
2. Background Adding ethanol to supplement petroleum in the production of gasoline in the US has spurred numerous debates concerning the unintended consequences for food production, world food prices, the environment, the chemical compatibility of ethanol with existing motors and fuel tanks (Hill et al., 2006) and the manner by which feedstock will be transported to ethanol plants. There is a long tradition in operations research and transportation geography that addresses many of the issues raised in the transportation of ethanol. We review some of these to highlight the issues raised and the manner by which they are addressed. Akinci et al. (2008) raise the issue of the sustainability of the entire ethanol enterprise, and conclude that ethanol production will be unable to sustain current US petroleum consumption patterns. Similarly von Blottnitz and Curran (2007) are concerned that human and ecological toxicology and acidification issues associated with ethanol production will outweigh the benefits derived from reducing green house gases. Black (2001) agrees with both studies arguing that the US cannot produce enough feedstock for ethanol to replace fossil fuels and that ethanol emissions are probably carcinogenic. Demirbas (2007) argues that the primary advantage of biomass fuels is the reduction of greenhouse gases and not necessarily a supplement to fossil fuels. A number of papers have addressed the issue of transporting feedstock to individual ethanol plants. Petrolia (2008) evaluates the input requirements for a typical ethanol facility in Minnesota that would produce ethanol from corn stover (cobs, stalks and leaves) and concludes that in most cases local farmers would be able to supply enough feedstock to prevent input costs from increasing significantly with the size of the ethanol plant. Kumar and Sokhansanj (2007) develop a model to evaluate different delivery systems for transporting switchgrass (another type of feedstock) to ethanol plants. Kumar et al. (2005) consider pipelines for the delivery of corn stover to ethanol plants and conclude they are cheaper than trucks and do not cause congestion, implying that ethanol plants can be larger in size than those previously served by trucks. Zhan et al. (2005) develop a GIS-based system to determine the procurements costs of switchgrass at potential ethanol locations, and conclude that there can be significant variations in procurement cost depending upon the locations of the ethanol plants. Ayoub et al. (2007) develop a decision support system to estimate biomass potential that includes the biomass supply chain, comprised of biomass resource suppliers, transportation and con-
version. They assume that transportation will occur in one type and size of vehicle. While this paper focuses on the transportation issues of supplying ethanol plants with feedstock, the transportation problems associated with distributing the ethanol to oil refineries is not addressed. Few studies have focused on the transportation logistics attendant upon shipping billions of liters of ethanol by rail from ethanol plants to oil refineries. To adequately address the problem of the distribution of ethanol, a logistics model that takes into account both time and space is required. It takes time to accumulate tank cars to make unit trains all the while incurring demurrage costs; and the tank cars must be moved over space from the ethanol plants to the refineries. Osleeb and Ratick (1985) and Ratick et al. (1987) developed a logistics modeling framework, Interperiod Network Storage Location–Allocation (INSLA), which simultaneously accounts for distribution and storage costs (inventory). Employing a similar approach, Hinojosa et al. (2008) suggests that customer demands can be dynamic and therefore the supply chain must change within a specified period of time to reflect the demand changes. This often requires the opening and closing of facilities over the planning horizon. Given the high costs associated with opening and closing facilities, their model prevents these adjustments from occurring over short time periods. A number of other papers have been published that address the space–time logistics problem. Yu et al. (2008) consider the inventory routing problem under a vehicle fleet size constraint. Their model addresses the availability of transport facilities and the tradeoff between delivering the product in the appropriate time period and transporting product in low demand periods when transport facilities are available but at the expense of carrying inventory. Another concern is the availability of capacity for multi-commodity transport. Al-Khayyal and Hwang (2007) consider the problem of shipping commodities between ports given commodity supplies, commodity demands, storage constraints at ports and the existing shipping capacity. They develop an efficient specially structured equivalent mixed-integer linear program formulation to solve this problem.
3. Model development The Rail-INSLA (R-INSLA) model developed in this paper is designed to find the least cost transportation pattern for shipping ethanol from supply plants to refineries, potentially utilizing storage at sidings and aggregation terminals to consolidate individual tank car shipments to unit train sizes. INSLA type models are designed over a closed dynamic cycle; that is, conditions in the last time period of a cycle form the initial conditions for the first period. For the transportation of ethanol, this might represent a typical week, month or year. R-INSLA can, however, be run under different scenarios in which the planning cycle – and network, supply and demand characteristics – are varied. The results of these scenario runs will allow users to determine which situation is most likely to occur and to plan according to that result. In our application presented later in this paper, the time unit (period) considered is two days, over a cycle of seven time periods, representing a typical two weeks in the operation of ethanol plants and refineries. The conditions at the end of the cycle, time period seven represents the initial conditions for next time period one. There are three types of nodes in our ethanol transportation network: (1) ethanol supply plants, (2) potential aggregation terminals run by the railroad to create unit trains, and (3) the refineries (final demand nodes). The considerations for investing to expand rail sidings to store ethanol-filled tank cars until unit train sizes are achieved can be modeled as a ‘‘logical sub-network” at supply nodes or agglomeration terminals (nodes), within this
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Fig. 1. Logical sub-network at a supply node.
overall transportation network (Osleeb and Ratick, 1990). Fig. 1 is an example of the logical sub-network at a supply node (to see examples of how logical sub-networks are embedded into the overall transportation/transshipment network see Ratick et al., 1987). Available supply in time period t can be shipped through the clearinghouse node to other nodes in the network (agglomeration terminals or final demand refineries) via carload trains, or stored in a rail siding at the ethanol plant. If storage is utilized, the accumulated ethanol-filled tank cars from previous time periods (Sjt) may be shipped, again through the clearinghouse node, to other nodes in the network via unit trains, taking advantage of the lower rates. If storage is utilized, a fixed investment cost is assessed, once for the cycle. Depending on the largest number of tank cars that need to be stored, Bj, this cost is indexed by location and not by time. Demurrage costs are also incurred and assessed each time period that a filled tank car is in storage. Logical sub-networks for railroad-operated agglomeration terminals on the network would be similar to the operation of a sub-network at a supply node (shown in Fig. 1) with the supply replaced by incoming flows of ethanol tank cars from ethanol production nodes in the network, and outgoing shipments only by unit train.3 Our extension of the original INSLA model framework consists of adding new variables and constraints that deal specifically with the agglomeration of carload trains to produce unit trains, which offer economies of scale in transportation. The formulation for the R-INSLA mixed-integer optimization model is given below: The total cost objective function (1) is comprised of five types of costs (the sum of expressions (i) through (v) below): Minimize:
i:
X X X ðC ijt X ijt þ C ijt X ijt Þþ t
i
ð1Þ
ji
Total transportation costs for unit train and less than unit train
ii:
X
SC j Bj þ
j2J
Total fixed costs for establishing sidings at storage nodes
iii:
XX j2J
Ajt X ijt
þ
t
3 We have in other applications allowed for supply nodes in the network to also be potential agglomeration nodes; in that case the input to the clearinghouse node would be both that node’s own supply and the amounts shipped from other supply nodes to that node.
Total initial demurrage costs for ethanol tank cars at storage nodes
iv:
XX
Ojt Sjt þ
t
j2J
Total sum of opportunity costs for storing ethanol and demurrage costs for tank cars at storage nodes
v:
XX j2J
djt Y jkt
t
The demurrage costs for unit trains at ethanol supply nodes Subject to the following constraints:
X
X ijt Eit
8i 2 E; t
ð2Þ
8j 2 DEM; t
ð3Þ
j2Mi
X
X ijt ¼ Djt
i2Nj
Sjt ¼ Sj;t1 þ
X
X X X ijt ½ X jkt þ X jkt 8j 2 J; t
i2Nj
Sj1 ¼ Sj;T þ
X
X ij1 ½
i2Nj
Sjt Bj
k2Uj
X
X jkl þ
k2Uj
8j; t
ð4Þ
k2CARj
X
X jk1 88j 2 J
ð5Þ
k2CARj
ð6Þ
X jkt ¼ CapUnit Y jkt
8j; k; t
ð7Þ
X jkt ; Sjt ; Bj 0 Y jt 2 fintg where: Decision variables Xijt = the number of tank cars of ethanol transported from node i to node j in time period t Sjt = the number of tank cars in storage node j in time period t Yjkt = the number of unit trains used to ship from node j to node k in time period t Bj = the maximum number of tank cars at storage node j in any time period. Parameters = C ijt C ijt
=
Eit
=
the cost per tank car for carload trains of ethanol shipped from node i to node j in time period t the cost per tank car in a unit train for ethanol shipped from node i to node j in time period t the maximum number of tank cars of ethanol that can be supplied from supply node i (ethanol plant) in time period t
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Djt
=
CapUnit
=
SCj
=
Ojt
=
Ajt
=
djt
=
Sets E
=
DEM J T Nj Uj
= = = = =
CARj
=
the number of tank cars of ethanol demanded at refinery j in time period t the number of tank cars of ethanol needed to make up a unit train the fixed cost per tank car slot for building a rail siding at storage node j the opportunity and demurrage costs for storing ethanol in tank cars at storage node j in time period t the initial demurrage cost/tank car at storage node j in time period t the demurrage charge per unit train at storage node j in time period t the set of all nodes i that can produce (supply) ethanol the set of all nodes j that have a demand for ethanol the set of all storage nodes j in the network the number of discrete time periods for the problem the set of all nodes i for which arc {i,j} is defined the set of all nodes k that can be reached from j via unit train the set of all nodes k that can be reached from j by carload trains
The constraints in (2) assure that the amount supplied from any ethanol plant i, in time period t, does not exceed that plant’s capacity in that time period in the cycle. There is one constraint for every plant in the network and for every time period – this would allow for a variable production schedule for ethanol. The constraints in (3) assure that the demands at nodes j (the refineries) are met in every time period; there is one constraint of this type for each demand node and for each time period. Constraints (4) and (5) are the continuity constraints for the INSLA time cycle. In (4) the amount in storage at the end of time period t (Sjt) is equal to the amount that was in storage in the previous time period, plus the amount shipped into storage node j in time period t, less the amount shipped out by unit and carload trains; one constraint of this type is needed for each storage node j and each time period t. Constraint (5) links the last period T to the first period in the cycle for all storage nodes (j in J). There is a storage node j associated with each ethanol plant node i, or as a free-standing agglomeration terminal in the network, at which tank cars of ethanol can be stored to produce unit size trains. Constraints (6) assures that the variable Bj – the size of the rail siding required at any storage node j – is at least as large as the maximum number of tank cars of ethanol stored at j in any time period. One constraint of this type is needed for each storage node j and each time period t. (Note that the variable Bj is not indexed by time.) The cyclic formulation in constraints (4) and (5) represents modal or average operating characteristics for ethanol production and distribution to refineries over the time horizon. The new ethanol tank car storage capacity at any node, Bj,4 would then be available at any time period in the cycle; this distinguishes the formulation of INSLAtype cyclical dynamic models from those associated with trends (Ratick et al., 1987 and Osleeb and Ratick, 1985, 1990).The constraints in (7) assure that each unit train is comprised of exactly the CapUnit number of tank cars, and that only full unit trains are transported from node j. This constraint along with constraints (4) and (5) assure
4 For the ethanol supply plants Bj represents the maximum number of tank cars from storage that needs to be added to that period’s supply to make a unit train. This assumes that the ethanol plants already have a large enough siding to accommodate one period’s supply.
that all ethanol shipped out of a storage node will be on either unit trains or carload trains (with less than CapUnit tank cars).
4. Case study application 4.1. Data The data required to undertake the analysis presented in this paper are varied and come from a number of disparate sources. Rail rate data for both single car and unit train movements were required as were data on the location and capacity of ethanol production and the location and refinery demand for ethanol. Since rail rate data for the Burlington Northern Santa Fe Railway (BNSF) were readily available on the internet (BNSF, 2008a), the BNSF Railway rail rates were used, as were ethanol plants and oil refineries that are accessible via the BNSF Railway. In some cases ethanol plants that could access the BNSF Railway via short lines were also used in the analysis. The BNSF Railway operates over 32,000 miles of main-line and haulage right agreements with Union Pacific (BNSF (2008b)). Fig. 2 is a map of the study area showing the primary routes of the BNSF Railway. For this study we are assuming that the BNSF Railway may agglomerate car loads from individual ethanol plants into unit trains at four yard locations: Council Bluffs, IA; Des Moines, IA; Lincoln, NE; and Minneapolis, MN. The ethanol plant data used in this analysis is a subset of the 76 ethanol plants that were listed as being in production or will be ready for production by the spring 2008 for the study area (Cummings, 2007). Of the 76 plants listed, this analysis included 25 of those plants that are located in Iowa, Minnesota, Nebraska, North Dakota and South Dakota. The daily ethanol output for each of those plants is given in Table 1. Their total daily output is approximately 176 tank cars, assuming 120,000 l capacity tank cars. The refineries served by BNSF are located in six states; California, Illinois, Louisiana, Minnesota, Montana and Texas. Other than in Texas, the delivered single car rates and unit train rates charged by BNSF did not vary for refineries in the state. Therefore, in all cases but Texas (where the demand is represented by two refineries reflecting the differential train rates in those locations), refinery demand for ethanol was agglomerated into state totals. Assuming ethanol makes up 10% of the total gasoline output of the refineries, the ethanol requirements for the refineries in each state are listed in Table 2. The Liters per day column in Table 2 represents the liters of oil input to the refineries represented in this study by state (EIA, 2008). From that we estimated the liters of gasoline produced (Gasoline Prod. Liter/day) by multiplying the percentage of the weekly totals of refinery gasoline production by Petroleum Administrative Defense District (PADD) (EIA, 2008a). Assuming 10% ethanol by volume, we obtained the ethanol demand for each refinery in liters and, then converted demand into 120,000 l tank cars. Because we only used a subset of ethanol plants, we reduced the amount of refinery demand per state to reflect this reduction in supply partially by just using those refineries in a state that are located on the BNSF. The refinery demands used in the model are also shown in Table 2. The potential unit train agglomeration sites, ethanol plants and refineries used for this example were chosen to be representative of the problem and to demonstrate the types of results that are possible using R-INSLA. Demurrage is the charge assessed by a railroad for the amount of time necessary to load or unload a tank car. Demurrage also includes the charges for storing empty cars assigned to customers. We assumed a demurrage charge of $525 per week ($75 per day) based on BNSF Railway published demurrage charges (Engstrom,
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Fig. 2. The study area.
Table 1 Location and output of ethanol plants used in study.
at 10% interest: amounting to $50 per tank car length over the 14 day model cycle.
Ethanol plant location
Supply millions liters/yr
Tank cars/yr
Unit trains/yr
CHARLES CITY, IA MERRILL, IA SHENANDOAH, IA SAINT ANSGAR, IA CEDAR RAPIDS, IA CORNING, IA COUNCIL BLUFFS, IA DEXTER, IA GRINNELL, IA HARTLEY, IA FERGUS FALLS, MN JANESVILLE, MN HANKINSON, ND ADAMS, NE O’NEILL, NE ALBION, NE ATKINSON, NE CAMBRIDGE, NE FAIRMONT, NE MADRID, NE NORFOLK, NE MARION, SD MECKLING, SD MINA, SD REDFIELD, SD
440 200 200 400 160 240 440 400 400 440 230 400 400 200 400 400 160 176 400 176 200 400 240 400 200
3666.7 1666.7 1666.7 3333.3 1333.3 2000.0 3666.7 3333.3 3333.3 3666.7 1916.7 3333.3 3333.3 1666.7 3333.3 3333.3 1333.3 1466.7 3333.3 1466.7 1666.7 3333.3 2000.0 3333.3 1666.7
36.7 16.7 16.7 33.3 13.3 20.0 36.7 33.3 33.3 36.7 19.2 33.3 33.3 16.7 33.3 33.3 13.3 14.7 33.3 14.7 16.7 33.3 20.0 33.3 16.7
Total number of tank cars per day
Tank cars/day 10.0 4.6 4.6 9.1 3.7 5.5 10.0 9.1 9.1 10.0 5.3 9.1 9.1 4.6 9.1 9.1 3.7 4.0 9.1 4.0 4.6 9.1 5.5 9.1 4.6 176
2000 and BNSF, 2005). Typical costs for building a railroad siding are presented in Table 3. We assume one turnout and one bumper is required. To obtain the investment cost per tank car per model cycle at each storage node, we amortized the cost over 30 years
4.2. Results The R-INSLA model was run with the input data described above, for seven time periods, with each time period representing two operating days; the length of the dynamic cycle is 14 days. Demurrage charges of $75 per tank car per day ($150 per time period) were used at each of the 25 ethanol producing plants. We did not assess demurrage charges for the four BNSF agglomeration nodes because we assume that is part of the gain from BNSF assembling unit trains. (A small charge of $5 per tank car per day was used in the model to minimize the resident time for tank cars at the agglomeration nodes.) We did not assess an opportunity cost for the storage of ethanol. Supply at each ethanol plant was rounded up to the nearest integer number of tank cars. The total output of the 25 plants in the study was approximately two-thirds of the total demand, the amount demanded at each of the seven refineries was, therefore, scaled by 69% to equate supply and demand over the 14 day cycle. The total supply and demand in the system was 2461 tank cars over the cycle. Demand at each refinery was not indexed by time, but the total 14 day demand at each refinery had to be met sometime over the cycle. Four different scenarios were run with these data. Table 4 provides a summary of the scenarios and the optimal transportation and total costs associated with each obtained in the R-INSLA model solutions. In Scenario 1 no storage or unit trains were permitted. Ethanol from the twenty five plants was shipped to the refineries exclusively by individual carload trains providing baseline costs for esti-
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Table 2 Refinery ethanol requirements. State
Liters/day
Gasoline liters/day
Ethanol liters/day
Tank cars/day
CALIFORNIA ILLINOIS LOUISIANA MINNESOTA MONTANA TEXAS 1 TEXAS 2
60,177,768 91,392,000 102,816,000 11,760,000 19,824,000 372,288,000 20,160,000
28,885,328 45,696,000 39,518,640 5,880,000 9,119,040 166,934,878 10,684,799
2,888,533 4,569,600 3,951,864 588,000 911,904 16,693,488 1,068,480
96 152 132 20 30 556 36
mating the savings that potentially could be achieved using unit trains, storage, and agglomeration terminals. The total cost for meeting the 14 day demand at the refineries was over $10 million dollars. The California refinery was supplied by ethanol plants in Nebraska; the Illinois refinery by plants in Iowa and Minnesota; the Louisiana refinery by plants in North Dakota; the Minnesota refinery by plants in Iowa; the Montana refinery was supplied by a plant in North Dakota; and the large Texas refinery (Texas 1) by ethanol plants in Iowa, North and South Dakota and Nebraska, and the smaller Texas refinery (Texas 2) was supplied by a plant in Iowa. None of the four agglomeration terminals were used. Without the availability of unit trains, there was no cost advantage to utilizing these terminals. The costs for Scenario 2 represent the savings over the baseline costs, obtained in Scenario 1, resulting from the use of storage at ethanol plants and the utilization of unit trains; the four potential BNSF agglomeration terminals were not considered in this scenario. Thirteen of the 25 supply nodes invest in new rail sidings to accommodate enough tank cars to construct a unit train (Table 5). Each of these thirteen plants ships one unit train over the 14 day cycle, system wide transporting slightly over half the total demand (1300 tank cars) via unit trains. The Charles City, IA plant ships via unit train to the refinery in California, while the other twelve ship to the Texas 1 refinery. The remainder of the demand is met by individual carload shipments from some of these plants that ship by unit train and from the other ethanol plants. The total transportation costs are reduced by almost 19% through the use of unit trains. Total system costs are reduced by slightly more than 12%, with the savings in transportation costs offset by new investment costs for siding capacity of $53,000 (the two-week period amortized fixed costs for building the siding) and total demurrage charges of $594,000 over the cycle (Table 4). As an example of the dynamic INSLA storage and shipment patterns that are generated by the model, the transactions for the eth-
Table 3 Siding construction costs: from Shafer (1998). Siding components (car length assumed to be 18.5 m)
Costs
Track (rails and ties) Turnout (allows rail cars to switch tracks) Bumper (end of track) Site development per rail car length
$25.00/m $25,000 $5,000 $1,500
anol plant at Janesville, MN are shown in Fig. 3. Storage starts at Janesville in the fourth period of the seven period cycle. In this period 10 of the 18 tank cars of supply is stored, and 8 are shipped via individual carload train to the refinery in Illinois. In the next four periods (5, 6, 7 and 1), the 18 tank car supply is stored accumulating to the maximum storage capacity of 82 tank cars in period 1. The 18 tank car supply in period 2 is then used with the 82 stored tank cars to assemble the 100 tank car unit train that is shipped to the Texas 1 refinery. In period 3, the 18 unit supply is sent again via carload train to the Illinois refinery. Each of the thirteen ethanol plants that utilize storage has their own dynamic INSLA transaction pattern. In scenario 3 no storage was permitted, but the four potential BNSF agglomeration terminals could be utilized. Transportation and total system costs for this scenario are lower than both the baseline scenario 1, and scenario 2. Fourteen unit trains are used, two unit trains per period, all of which are constructed at the agglomeration terminal at Lincoln, NE; none of the other potential agglomeration terminals are used. The unit trains assembled at Lincoln are used to meet demand at the Texas 1 and Louisiana refineries. The other refinery demands are met by direct shipments from ethanol plants via carload trains. Storage is allowed at any of the ethanol plants and at the four potential BNSF agglomeration terminals in Scenario 4. Transportation costs show the greatest decline in this scenario, of more than 27% and total system costs decline by more than 24%, when compared with the costs in baseline scenario 1. Storage is used at five Table 5 Storage capacity and unit train shipments at ethanol plants. Ethanol plant
Storage capacity (tank cars)
Unit train to:
CHARLES CITY, IA SAINT ANSGAR, IA COUNCIL BLUFFS, IA DEXTER, IA GRINNELL, IA HARTLEY,IA JANESVILLE, MN HANKINSON, ND O’NEILL,NE ALBION, NE FAIRMONT, NE MARION, SD MINA, SD
80 82 80 82 82 80 82 82 82 82 82 82 82
California Texas 1 Texas 1 Texas 1 Texas 1 Texas 1 Texas 1 Texas 1 Texas 1 Texas 1 Texas 1 Texas 1 Texas 1
Table 4 Results of Rail-INSLA scenarios for case. Rail-INSLA scenarios
Total transportation costs
Siding investment costs
Total demurrage charges
Total system costs
Scenario 1: No unit trains, no storage Scenario 2: No agglomeration terminals Scenario 3: Unit Trains, no storage and agglomeration terminals allowed Scenario 4: Unit trains, storage and agglomeration terminals allowed
$10,497,950 $8,510,550 $8,395,850
$0 $53,000 $0
$0 $594,000 $0
$10,497,950 $9,157,550 $8,395,850
$7,653,050
$20,400
$231,460
$7,904,910
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120
Tank Cars of Ethanol
100 80 60 40 20 0 Supply Storage Unit Train Carload
1
2
3
4
5
6
7
18 82 0
18 0 100
18 0 0
18 10 0
18 28 0
18 46 0
18 64 0
0
0
18
8
0
0
0
Time Period (2 Days) Fig. 3. INSLA pattern for Janesville, MN ethanol plant for the seven, two day periods.
Fig. 4. Projected optimal ethanol flows to refineries.
of the ethanol plants, Council Bluffs, IA, Hankinson, ND, Fairmont, NE, and Marion, SD and Mina, SD, with storage capacities shown in Table 4 for those plants. Eighteen unit trains are utilized, five from the five ethanol plants and thirteen through the BNSF agglomeration terminal at Lincoln, NE – due to its advantageous location with respect to ethanol plants and refineries. The terminal at Lincoln needed to handle an additional of 74 tank cars to meet this schedule. As in scenario 3, none of the other three potential
agglomeration terminals are used. Ten of the thirteen unit trains originating at the Lincoln terminal serve the Texas 1 refinery, along with unit trains (one each) from the ethanol plants at Council Bluffs, Marion, and Mina. Two of the unit trains originating at Lincoln serve the California refinery, and one serves the refinery in Louisiana, supplemented with unit trains from Hankinson and Fairmont. All other demand is supplied by carload trains directly from the ethanol plants. Almost three quarters of the total demand is
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supplied using unit trains in this scenario. The optimal flows of ethanol for this scenario are shown in Fig. 4. The results of these scenario runs suggest that utilization of storage and agglomeration terminals can reduce transportation costs significantly. 5. Solution experience The INSLA model, as formulated for the case study, had 4047 constraints and 7121 variables, of which 1421 are integer. We ran the model on a laptop computer with a 2 GHz Intel Pentium M processor and 2 GB Ram, using the CPLEX solver in AIMMS version 3.8 (AIMMS, 2008). Solution times varied, from 0.54 s for scenario 1, in which no storage or unit trains were allowed; to a solution that we terminated after 1700 s (at a solution gap of 1.7%) for scenario 4 where all options were available. For scenario 4 the integer solution reported in the paper was found within 15 s, however, the remaining time was spent pruning the branch and bound tree attempting to find a better integer solution. Our experience with other example problems suggests solution times can vary greatly with the input parameters used for models with the same structure and size (Ratick and Osleeb, 2008). 6. Summary and conclusions Increasing demands for biofuels will have an effect on the nationwide transportation system, particularly train transportation. In this paper, we developed an Interperiod Network Storage Location–Allocation (INSLA) model, Rail-INSLA, to evaluate rail transportation cost efficiencies that may be realized through the use of storage on the network to agglomerate unit train sized shipments. In order to test the model, we developed a case study on a part of the BNSF Railway system using existing ethanol plants, potential BNSF unit train assembly terminals, and refineries that blend ethanol into gasoline. Through the evaluation of four scenarios, which concatenate the use of storage, unit trains and the agglomeration terminals in the system, we demonstrate that the optimal location and scheduling of storage and agglomeration terminals can reduce transportation costs significantly. As we and other researchers have shown, transportation logistics has spatial and temporal dimensions, as exemplified by the distribution problems associated with the use of ethanol described in this paper. In this case, the spatial dimension describes the distribution of ethanol from relatively small and geographically dispersed plants, to refineries where it is blended with gasoline. The temporal dimension deals with the time necessary to produce the ethanol, to fill the tank cars and perhaps store them to assemble unit trains to deliver ethanol to refineries. Each of these components has its own set of costs that must be factored into allocation and modal choice decisions, whether to ship ethanol as individual tank car loads or in unit trains. The Rail-INSLA model results track well with other studies of ethanol transportation rates. The results of scenario 4, where storage, unit trains and agglomeration terminals were available, provide an overall average transportation rate of approximately 2.7 cents per liter of ethanol transported in 120,000 l tank cars for an average distance of approximately 1100 miles. Both the US EPA and the American Petroleum Institute (API) (US EPA, 2007) reported the estimated cost per liter of ethanol – here the estimates were also for 120,000 l tank cars – from Chicago to Philadelphia, an 800 mile trip. EPA estimates were 2.3 cents per liter, and the API estimates of 4.25–5.5 cents per liter for individual tank cars, and 3.75–5 cents per liter by unit train. The cost savings we obtained from the use of storage and agglomeration nodes on the network, allowing for the utilization
of unit trains are a function of, and are likely to vary with, the choices of the size and location of ethanol supply plants and refineries, the structure of the transportation network, and of other model parameters, such as the time period, cycle length and size of unit trains. These results, however, are suggestive of the types of transportation cost efficiencies that may be realized through careful and systematic transportation planning using models such as the Rail-INSLA model developed in this paper. Acknowledgements The authors are grateful for the comments received from two anonymous referees who made numerous suggestions from which this paper benefited greatly. In addition, we would like to thank Dr. Michael Kuby for his comments on this paper and for his previous collaboration on the INSLA model. References AIMMS, 2008. AIMMS Version 3.8, Paragon Decision Technology B.V. Haarlem, The Netherlands. Akinci, B., Kassebaum, P., Fitch, J., Thompson, R., 2008. The role of bio-fuels in satisfying us transportation fuel demands. Energy Policy. Al-Khayyal, F., Hwang, S., 2007. Inventory constrained maritime routing and scheduling for multi-commodity liquid bulk, Part I: Applications and model. European Journal of Operations Research 176, 106–130. Ayoub, N., Martins, R., Wang, K., Seki, H., Naka, Y., 2007. Two levels decision system for efficient planning and implementation of bioenergy production. Energy Conversion and Management 48, 709–723. Black, W., 2001. An unpopular essay on transportation. Transportation Geography 9, 1–11. BNSF Railway Company, 2005. BNSF demurrage charts.. BNSF Railway Company, 2008a. . BNSF Railway Company, 2008b. . Cummings, A., 2007. Ethanol rail boom or bust?: confidence and uncertainty marking railroading’s 200-proof growth spurt. Train Magazine, 30–39. Demirbas, A., 2007. Progress and recent trends in biofuels. Progress in Energy and Combustion Science 33, 1–18. Energy Information Administration, 2008. US refineries operable capacity: atmospheric crude oil distillation capacity. US Department of Energy, Washington, DC. . Energy Information Administration, 2008a. This week in petroleum. US Department of Energy, Washington, DC. . Engstrom, J.C., 2000. BNSF Demurrage Book 6004-A. BNSF Railway Company, Fort Worth. Hill, J., Nelson, E., Tilman, D., Polasky, S., Tiffany, D., 2006. Environmental, economic, and energetic costs and benefits of biodiesel and ethanol biofuels. Proceedings of the National Academy of Science 103 (30), 1206–1210. Hinojosa, Y., Kalcsics, J., Nickel, S., Puerto, J., Velten, S., 2008. Dynamic supply chain design with inventory. Computers and Operations Research 35, 373–391. Kumar, A., Sokhansanj, A., 2007. Switchgrass (Panicum vigratum, L.) delivery to biorefinery using integrated biomass supply analysis and logistics (IBSAL) model. Biosource Technology 98, 1033–1044. Kumar, A., Cameron, J.B., Flynn, P.C., 2005. Pipeline transport and simultaneous saccharification of corn stover. Bioresource Technology 96, 819–829. Orden, A., 1956. The transshipment problem. Management Science 2, 276–285. Osleeb, J. Ratick, S., 1985. Synergistic gains from storage on a network: development of an interperiod storage location–allocation model. Final Report to the Geography and Regional Science Program. National Science Foundation, Washington, DC. Osleeb, J., Ratick, S., 1990. A dynamic location–allocation model for evaluating the spatial impacts for just-in-time planning. Geographical Analysis 22 (1), 50–69. Petrolia, D.R., 2008. The economics of harvesting and transporting corn stover for conversion to fuel ethanol: a case study of Minnesota. Biomass and Bioenergy 32, 603–612. Ratick, S. Osleeb, J., 2008. Development of an interperiod network storage location– allocation (INSLA) model for the distribution ethanol biofuels. Presentation to Interdisciplinary Transportation Colloquia/Seminar Program, University of Connecticut. Ratick, S., Osleeb, J., Kuby, M., Lee, K., 1987. Interperiod network storage location– allocation (INSLA) models. In: Ghosh, A., Rushton, G. (Eds.), Spatial Analysis and Location–Allocation Models. Van Nostrand Reinhold, Co., New York, pp. 269– 301. Shafer, J., 1998. Rail Haul Analysis. Centre County Solid Waste Authority, Bellefonte, PA. . US Congress, 2005. Energy Policy Act of 2005, Public Law 109-58, August 8.
J.P. Osleeb, S.J. Ratick / Journal of Transport Geography 18 (2010) 729–737 US Congress, 2008. Amendment to the Energy Policy Act of 2005. US Environmental Protection Agency, 2007. Regulation of Fuels and Fuel Additives: Renewable Fuel Standard Program, Chapter 6 Costs. Washington, DC (pp. 6-7–6-9). von Blottnitz, H., Curran, M., 2007. A review of assessments conducted on bioethanol as a transportation fuel from a net energy, greenhouse gas, and environmental life cycle perspective. Journal of Cleaner Production 15, 607–619.
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Contents lists available at ScienceDirect
Journal of Transport Geography journal homepage: www.elsevier.com/locate/jtrangeo
An Interperiod Network Storage Location–Allocation (INSLA) model for rail distribution of ethanol biofuels Jeffrey P. Osleeb a,*, Samuel J. Ratick b a b
Department of Geography, University of Connecticut, Storrs, CT 06269, United States Department of Geography and George Perkins Marsh Research Institute, Clark University, Worcester, MA 01610, United States
a r t i c l e
i n f o
Keywords: Ethanol logistics Unit train Multi-period optimization models
a b s t r a c t In response to the US federal renewable fuels standards, new ethanol plants of varying sizes are being established in the US. The transportation challenge is to decide on how best to move raw materials to these existing and new ethanol plants, and to ship the fuel from the ethanol plants to markets around the country. In this paper, we extend the Interperiod Network Storage Location–Allocation (INSLA) model formulation into a Rail-INSLA model to address the transportation/transshipment issues associated with the rail distribution of ethanol biofuels that include: transporting less than unit train quantities from each plant, developing new sidings at ethanol plants to accommodate a unit train, and determining the optimal number and locations for carrier operated terminals for the agglomeration of less than unit train size shipments into unit train shipments. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Increasing concerns for energy security in light of increasing oil imports, increasing costs, and oil supplies from increasingly unstable regions, has prompted the United States government to mandate that 30 billion liters of ethanol biofuels be produced domestically by 2009 (Energy Policy Act of 2005) and144 billion liters by 2022 (Amendment to the Energy Policy Act of 2005, 2008) and be added to gasoline in order to reduce our dependence on foreign sources. In response to these policies, new ethanol plants of varying sizes are being sited throughout the US, and particularly in the Midwest (the ‘‘Corn Belt”), to take advantage of the corn crop, currently the primary input in US-produced ethanol. Since ethanol is produced at geographically dispersed local ethanol plants, it must then be shipped to refineries where it is blended into gasoline. The transportation geography challenge in this growing market is to decide how best to transport raw materials to existing and proposed ethanol plants, and then how to ship the ethanol from these plants to refineries around the country. Currently, railroads represent the only means by which such large quantities of ethanol can be shipped efficiently.1 Depending on the size of the railroad tank car in which the ethanol is to be shipped, the 36 billion liters of ethanol mandated for 2008–2009 may require * Corresponding author. Tel.: +1 860 486 3656; fax: +1 860 486 1348. E-mail address: [email protected] (J.P. Osleeb). 1 A pipeline network to transport ethanol does not currently exist and it is doubtful, because of railroad right-of-way considerations. That they will be built in the future; there are also technical difficulties for pipeline shipments of this corrosive liquid. Barge transportation systems are currently at full capacity. 0966-6923/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jtrangeo.2009.09.011
between 300,000 and 900,000 tank car shipments from ethanol plants to refineries. While unit trains, which are composed of between 95 and 125 tank cars, provide the least transportation costs (lowest rates per tank car) for shipping ethanol, the size of many existing and proposed ethanol plants individually do not generate sufficient product to fill a unit train, and therefore, their shipments do not qualify for unit train rates. In response those shippers (ethanol plants) that are unable to generate sufficient volumes for unit trains can pay individual tank car rates (carload rates); invest in new rail sidings to store tank cars, or coordinate with other ethanol producers to agglomerate their output into unit train size shipments; or work with carriers to create unit train size shipments at central terminals. The significantly lower unit train rates would make them the preferred means of shipment. However, there are a number of other costs besides train rates that need to be factored into the decision. These costs include holding, demurrage and capital costs. Holding represents the opportunity cost of the ethanol, demurrage is the daily cost associated with a rail car that is either empty or waiting to be filled or filled and waiting to be transported; capital costs are associated with developing the proper length of rail sidings to store the tank cars until the unit train is assembled.2 In this paper, we develop a mixed-integer mathematical programming model to address the dynamic planning issues involved in the transportation/transshipment (Orden 1956) of biofuels from 2 Although tank storage of ethanol at supply nodes may be used to reduce demurrage costs it was not considered in this paper.
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plants to refineries. Our model is derived from the class of mathematical programming-based dynamic location–allocation models, termed ‘‘Interperiod Network Storage Location–Allocation models” (INSLA), designed to address the use of storage and agglomeration facilities to alleviate congestion on transportation networks, to allow for the realization of economies of scale in transportation, and to address the issues of cyclical supplies and demands (Ratick et al. (1987) and Osleeb and Ratick (1985, 1990)). We extend the INSLA model to determine the least cost transportation pattern for shipping ethanol on the Burlington Northern Santa Fe Railway (BNSF) from ethanol plants in the US Midwest to refineries in California, Illinois, Louisiana, Montana and Texas. The extended INSLA model formulation, Rail-INSLA, specifically addresses the location decisions and the costs and efficiency trade-offs involved in rail transportation of ethanol that include: transporting less than unit train quantities from each plant as is, developing new sidings at ethanol plants to accommodate a unit train, and determining the optimal number and locations for carrier operated terminals for the agglomeration of less than unit train size shipments into unit train shipments.
2. Background Adding ethanol to supplement petroleum in the production of gasoline in the US has spurred numerous debates concerning the unintended consequences for food production, world food prices, the environment, the chemical compatibility of ethanol with existing motors and fuel tanks (Hill et al., 2006) and the manner by which feedstock will be transported to ethanol plants. There is a long tradition in operations research and transportation geography that addresses many of the issues raised in the transportation of ethanol. We review some of these to highlight the issues raised and the manner by which they are addressed. Akinci et al. (2008) raise the issue of the sustainability of the entire ethanol enterprise, and conclude that ethanol production will be unable to sustain current US petroleum consumption patterns. Similarly von Blottnitz and Curran (2007) are concerned that human and ecological toxicology and acidification issues associated with ethanol production will outweigh the benefits derived from reducing green house gases. Black (2001) agrees with both studies arguing that the US cannot produce enough feedstock for ethanol to replace fossil fuels and that ethanol emissions are probably carcinogenic. Demirbas (2007) argues that the primary advantage of biomass fuels is the reduction of greenhouse gases and not necessarily a supplement to fossil fuels. A number of papers have addressed the issue of transporting feedstock to individual ethanol plants. Petrolia (2008) evaluates the input requirements for a typical ethanol facility in Minnesota that would produce ethanol from corn stover (cobs, stalks and leaves) and concludes that in most cases local farmers would be able to supply enough feedstock to prevent input costs from increasing significantly with the size of the ethanol plant. Kumar and Sokhansanj (2007) develop a model to evaluate different delivery systems for transporting switchgrass (another type of feedstock) to ethanol plants. Kumar et al. (2005) consider pipelines for the delivery of corn stover to ethanol plants and conclude they are cheaper than trucks and do not cause congestion, implying that ethanol plants can be larger in size than those previously served by trucks. Zhan et al. (2005) develop a GIS-based system to determine the procurements costs of switchgrass at potential ethanol locations, and conclude that there can be significant variations in procurement cost depending upon the locations of the ethanol plants. Ayoub et al. (2007) develop a decision support system to estimate biomass potential that includes the biomass supply chain, comprised of biomass resource suppliers, transportation and con-
version. They assume that transportation will occur in one type and size of vehicle. While this paper focuses on the transportation issues of supplying ethanol plants with feedstock, the transportation problems associated with distributing the ethanol to oil refineries is not addressed. Few studies have focused on the transportation logistics attendant upon shipping billions of liters of ethanol by rail from ethanol plants to oil refineries. To adequately address the problem of the distribution of ethanol, a logistics model that takes into account both time and space is required. It takes time to accumulate tank cars to make unit trains all the while incurring demurrage costs; and the tank cars must be moved over space from the ethanol plants to the refineries. Osleeb and Ratick (1985) and Ratick et al. (1987) developed a logistics modeling framework, Interperiod Network Storage Location–Allocation (INSLA), which simultaneously accounts for distribution and storage costs (inventory). Employing a similar approach, Hinojosa et al. (2008) suggests that customer demands can be dynamic and therefore the supply chain must change within a specified period of time to reflect the demand changes. This often requires the opening and closing of facilities over the planning horizon. Given the high costs associated with opening and closing facilities, their model prevents these adjustments from occurring over short time periods. A number of other papers have been published that address the space–time logistics problem. Yu et al. (2008) consider the inventory routing problem under a vehicle fleet size constraint. Their model addresses the availability of transport facilities and the tradeoff between delivering the product in the appropriate time period and transporting product in low demand periods when transport facilities are available but at the expense of carrying inventory. Another concern is the availability of capacity for multi-commodity transport. Al-Khayyal and Hwang (2007) consider the problem of shipping commodities between ports given commodity supplies, commodity demands, storage constraints at ports and the existing shipping capacity. They develop an efficient specially structured equivalent mixed-integer linear program formulation to solve this problem.
3. Model development The Rail-INSLA (R-INSLA) model developed in this paper is designed to find the least cost transportation pattern for shipping ethanol from supply plants to refineries, potentially utilizing storage at sidings and aggregation terminals to consolidate individual tank car shipments to unit train sizes. INSLA type models are designed over a closed dynamic cycle; that is, conditions in the last time period of a cycle form the initial conditions for the first period. For the transportation of ethanol, this might represent a typical week, month or year. R-INSLA can, however, be run under different scenarios in which the planning cycle – and network, supply and demand characteristics – are varied. The results of these scenario runs will allow users to determine which situation is most likely to occur and to plan according to that result. In our application presented later in this paper, the time unit (period) considered is two days, over a cycle of seven time periods, representing a typical two weeks in the operation of ethanol plants and refineries. The conditions at the end of the cycle, time period seven represents the initial conditions for next time period one. There are three types of nodes in our ethanol transportation network: (1) ethanol supply plants, (2) potential aggregation terminals run by the railroad to create unit trains, and (3) the refineries (final demand nodes). The considerations for investing to expand rail sidings to store ethanol-filled tank cars until unit train sizes are achieved can be modeled as a ‘‘logical sub-network” at supply nodes or agglomeration terminals (nodes), within this
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Fig. 1. Logical sub-network at a supply node.
overall transportation network (Osleeb and Ratick, 1990). Fig. 1 is an example of the logical sub-network at a supply node (to see examples of how logical sub-networks are embedded into the overall transportation/transshipment network see Ratick et al., 1987). Available supply in time period t can be shipped through the clearinghouse node to other nodes in the network (agglomeration terminals or final demand refineries) via carload trains, or stored in a rail siding at the ethanol plant. If storage is utilized, the accumulated ethanol-filled tank cars from previous time periods (Sjt) may be shipped, again through the clearinghouse node, to other nodes in the network via unit trains, taking advantage of the lower rates. If storage is utilized, a fixed investment cost is assessed, once for the cycle. Depending on the largest number of tank cars that need to be stored, Bj, this cost is indexed by location and not by time. Demurrage costs are also incurred and assessed each time period that a filled tank car is in storage. Logical sub-networks for railroad-operated agglomeration terminals on the network would be similar to the operation of a sub-network at a supply node (shown in Fig. 1) with the supply replaced by incoming flows of ethanol tank cars from ethanol production nodes in the network, and outgoing shipments only by unit train.3 Our extension of the original INSLA model framework consists of adding new variables and constraints that deal specifically with the agglomeration of carload trains to produce unit trains, which offer economies of scale in transportation. The formulation for the R-INSLA mixed-integer optimization model is given below: The total cost objective function (1) is comprised of five types of costs (the sum of expressions (i) through (v) below): Minimize:
i:
X X X ðC ijt X ijt þ C ijt X ijt Þþ t
i
ð1Þ
ji
Total transportation costs for unit train and less than unit train
ii:
X
SC j Bj þ
j2J
Total fixed costs for establishing sidings at storage nodes
iii:
XX j2J
Ajt X ijt
þ
t
3 We have in other applications allowed for supply nodes in the network to also be potential agglomeration nodes; in that case the input to the clearinghouse node would be both that node’s own supply and the amounts shipped from other supply nodes to that node.
Total initial demurrage costs for ethanol tank cars at storage nodes
iv:
XX
Ojt Sjt þ
t
j2J
Total sum of opportunity costs for storing ethanol and demurrage costs for tank cars at storage nodes
v:
XX j2J
djt Y jkt
t
The demurrage costs for unit trains at ethanol supply nodes Subject to the following constraints:
X
X ijt Eit
8i 2 E; t
ð2Þ
8j 2 DEM; t
ð3Þ
j2Mi
X
X ijt ¼ Djt
i2Nj
Sjt ¼ Sj;t1 þ
X
X X X ijt ½ X jkt þ X jkt 8j 2 J; t
i2Nj
Sj1 ¼ Sj;T þ
X
X ij1 ½
i2Nj
Sjt Bj
k2Uj
X
X jkl þ
k2Uj
8j; t
ð4Þ
k2CARj
X
X jk1 88j 2 J
ð5Þ
k2CARj
ð6Þ
X jkt ¼ CapUnit Y jkt
8j; k; t
ð7Þ
X jkt ; Sjt ; Bj 0 Y jt 2 fintg where: Decision variables Xijt = the number of tank cars of ethanol transported from node i to node j in time period t Sjt = the number of tank cars in storage node j in time period t Yjkt = the number of unit trains used to ship from node j to node k in time period t Bj = the maximum number of tank cars at storage node j in any time period. Parameters = C ijt C ijt
=
Eit
=
the cost per tank car for carload trains of ethanol shipped from node i to node j in time period t the cost per tank car in a unit train for ethanol shipped from node i to node j in time period t the maximum number of tank cars of ethanol that can be supplied from supply node i (ethanol plant) in time period t
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Djt
=
CapUnit
=
SCj
=
Ojt
=
Ajt
=
djt
=
Sets E
=
DEM J T Nj Uj
= = = = =
CARj
=
the number of tank cars of ethanol demanded at refinery j in time period t the number of tank cars of ethanol needed to make up a unit train the fixed cost per tank car slot for building a rail siding at storage node j the opportunity and demurrage costs for storing ethanol in tank cars at storage node j in time period t the initial demurrage cost/tank car at storage node j in time period t the demurrage charge per unit train at storage node j in time period t the set of all nodes i that can produce (supply) ethanol the set of all nodes j that have a demand for ethanol the set of all storage nodes j in the network the number of discrete time periods for the problem the set of all nodes i for which arc {i,j} is defined the set of all nodes k that can be reached from j via unit train the set of all nodes k that can be reached from j by carload trains
The constraints in (2) assure that the amount supplied from any ethanol plant i, in time period t, does not exceed that plant’s capacity in that time period in the cycle. There is one constraint for every plant in the network and for every time period – this would allow for a variable production schedule for ethanol. The constraints in (3) assure that the demands at nodes j (the refineries) are met in every time period; there is one constraint of this type for each demand node and for each time period. Constraints (4) and (5) are the continuity constraints for the INSLA time cycle. In (4) the amount in storage at the end of time period t (Sjt) is equal to the amount that was in storage in the previous time period, plus the amount shipped into storage node j in time period t, less the amount shipped out by unit and carload trains; one constraint of this type is needed for each storage node j and each time period t. Constraint (5) links the last period T to the first period in the cycle for all storage nodes (j in J). There is a storage node j associated with each ethanol plant node i, or as a free-standing agglomeration terminal in the network, at which tank cars of ethanol can be stored to produce unit size trains. Constraints (6) assures that the variable Bj – the size of the rail siding required at any storage node j – is at least as large as the maximum number of tank cars of ethanol stored at j in any time period. One constraint of this type is needed for each storage node j and each time period t. (Note that the variable Bj is not indexed by time.) The cyclic formulation in constraints (4) and (5) represents modal or average operating characteristics for ethanol production and distribution to refineries over the time horizon. The new ethanol tank car storage capacity at any node, Bj,4 would then be available at any time period in the cycle; this distinguishes the formulation of INSLAtype cyclical dynamic models from those associated with trends (Ratick et al., 1987 and Osleeb and Ratick, 1985, 1990).The constraints in (7) assure that each unit train is comprised of exactly the CapUnit number of tank cars, and that only full unit trains are transported from node j. This constraint along with constraints (4) and (5) assure
4 For the ethanol supply plants Bj represents the maximum number of tank cars from storage that needs to be added to that period’s supply to make a unit train. This assumes that the ethanol plants already have a large enough siding to accommodate one period’s supply.
that all ethanol shipped out of a storage node will be on either unit trains or carload trains (with less than CapUnit tank cars).
4. Case study application 4.1. Data The data required to undertake the analysis presented in this paper are varied and come from a number of disparate sources. Rail rate data for both single car and unit train movements were required as were data on the location and capacity of ethanol production and the location and refinery demand for ethanol. Since rail rate data for the Burlington Northern Santa Fe Railway (BNSF) were readily available on the internet (BNSF, 2008a), the BNSF Railway rail rates were used, as were ethanol plants and oil refineries that are accessible via the BNSF Railway. In some cases ethanol plants that could access the BNSF Railway via short lines were also used in the analysis. The BNSF Railway operates over 32,000 miles of main-line and haulage right agreements with Union Pacific (BNSF (2008b)). Fig. 2 is a map of the study area showing the primary routes of the BNSF Railway. For this study we are assuming that the BNSF Railway may agglomerate car loads from individual ethanol plants into unit trains at four yard locations: Council Bluffs, IA; Des Moines, IA; Lincoln, NE; and Minneapolis, MN. The ethanol plant data used in this analysis is a subset of the 76 ethanol plants that were listed as being in production or will be ready for production by the spring 2008 for the study area (Cummings, 2007). Of the 76 plants listed, this analysis included 25 of those plants that are located in Iowa, Minnesota, Nebraska, North Dakota and South Dakota. The daily ethanol output for each of those plants is given in Table 1. Their total daily output is approximately 176 tank cars, assuming 120,000 l capacity tank cars. The refineries served by BNSF are located in six states; California, Illinois, Louisiana, Minnesota, Montana and Texas. Other than in Texas, the delivered single car rates and unit train rates charged by BNSF did not vary for refineries in the state. Therefore, in all cases but Texas (where the demand is represented by two refineries reflecting the differential train rates in those locations), refinery demand for ethanol was agglomerated into state totals. Assuming ethanol makes up 10% of the total gasoline output of the refineries, the ethanol requirements for the refineries in each state are listed in Table 2. The Liters per day column in Table 2 represents the liters of oil input to the refineries represented in this study by state (EIA, 2008). From that we estimated the liters of gasoline produced (Gasoline Prod. Liter/day) by multiplying the percentage of the weekly totals of refinery gasoline production by Petroleum Administrative Defense District (PADD) (EIA, 2008a). Assuming 10% ethanol by volume, we obtained the ethanol demand for each refinery in liters and, then converted demand into 120,000 l tank cars. Because we only used a subset of ethanol plants, we reduced the amount of refinery demand per state to reflect this reduction in supply partially by just using those refineries in a state that are located on the BNSF. The refinery demands used in the model are also shown in Table 2. The potential unit train agglomeration sites, ethanol plants and refineries used for this example were chosen to be representative of the problem and to demonstrate the types of results that are possible using R-INSLA. Demurrage is the charge assessed by a railroad for the amount of time necessary to load or unload a tank car. Demurrage also includes the charges for storing empty cars assigned to customers. We assumed a demurrage charge of $525 per week ($75 per day) based on BNSF Railway published demurrage charges (Engstrom,
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733
Fig. 2. The study area.
Table 1 Location and output of ethanol plants used in study.
at 10% interest: amounting to $50 per tank car length over the 14 day model cycle.
Ethanol plant location
Supply millions liters/yr
Tank cars/yr
Unit trains/yr
CHARLES CITY, IA MERRILL, IA SHENANDOAH, IA SAINT ANSGAR, IA CEDAR RAPIDS, IA CORNING, IA COUNCIL BLUFFS, IA DEXTER, IA GRINNELL, IA HARTLEY, IA FERGUS FALLS, MN JANESVILLE, MN HANKINSON, ND ADAMS, NE O’NEILL, NE ALBION, NE ATKINSON, NE CAMBRIDGE, NE FAIRMONT, NE MADRID, NE NORFOLK, NE MARION, SD MECKLING, SD MINA, SD REDFIELD, SD
440 200 200 400 160 240 440 400 400 440 230 400 400 200 400 400 160 176 400 176 200 400 240 400 200
3666.7 1666.7 1666.7 3333.3 1333.3 2000.0 3666.7 3333.3 3333.3 3666.7 1916.7 3333.3 3333.3 1666.7 3333.3 3333.3 1333.3 1466.7 3333.3 1466.7 1666.7 3333.3 2000.0 3333.3 1666.7
36.7 16.7 16.7 33.3 13.3 20.0 36.7 33.3 33.3 36.7 19.2 33.3 33.3 16.7 33.3 33.3 13.3 14.7 33.3 14.7 16.7 33.3 20.0 33.3 16.7
Total number of tank cars per day
Tank cars/day 10.0 4.6 4.6 9.1 3.7 5.5 10.0 9.1 9.1 10.0 5.3 9.1 9.1 4.6 9.1 9.1 3.7 4.0 9.1 4.0 4.6 9.1 5.5 9.1 4.6 176
2000 and BNSF, 2005). Typical costs for building a railroad siding are presented in Table 3. We assume one turnout and one bumper is required. To obtain the investment cost per tank car per model cycle at each storage node, we amortized the cost over 30 years
4.2. Results The R-INSLA model was run with the input data described above, for seven time periods, with each time period representing two operating days; the length of the dynamic cycle is 14 days. Demurrage charges of $75 per tank car per day ($150 per time period) were used at each of the 25 ethanol producing plants. We did not assess demurrage charges for the four BNSF agglomeration nodes because we assume that is part of the gain from BNSF assembling unit trains. (A small charge of $5 per tank car per day was used in the model to minimize the resident time for tank cars at the agglomeration nodes.) We did not assess an opportunity cost for the storage of ethanol. Supply at each ethanol plant was rounded up to the nearest integer number of tank cars. The total output of the 25 plants in the study was approximately two-thirds of the total demand, the amount demanded at each of the seven refineries was, therefore, scaled by 69% to equate supply and demand over the 14 day cycle. The total supply and demand in the system was 2461 tank cars over the cycle. Demand at each refinery was not indexed by time, but the total 14 day demand at each refinery had to be met sometime over the cycle. Four different scenarios were run with these data. Table 4 provides a summary of the scenarios and the optimal transportation and total costs associated with each obtained in the R-INSLA model solutions. In Scenario 1 no storage or unit trains were permitted. Ethanol from the twenty five plants was shipped to the refineries exclusively by individual carload trains providing baseline costs for esti-
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Table 2 Refinery ethanol requirements. State
Liters/day
Gasoline liters/day
Ethanol liters/day
Tank cars/day
CALIFORNIA ILLINOIS LOUISIANA MINNESOTA MONTANA TEXAS 1 TEXAS 2
60,177,768 91,392,000 102,816,000 11,760,000 19,824,000 372,288,000 20,160,000
28,885,328 45,696,000 39,518,640 5,880,000 9,119,040 166,934,878 10,684,799
2,888,533 4,569,600 3,951,864 588,000 911,904 16,693,488 1,068,480
96 152 132 20 30 556 36
mating the savings that potentially could be achieved using unit trains, storage, and agglomeration terminals. The total cost for meeting the 14 day demand at the refineries was over $10 million dollars. The California refinery was supplied by ethanol plants in Nebraska; the Illinois refinery by plants in Iowa and Minnesota; the Louisiana refinery by plants in North Dakota; the Minnesota refinery by plants in Iowa; the Montana refinery was supplied by a plant in North Dakota; and the large Texas refinery (Texas 1) by ethanol plants in Iowa, North and South Dakota and Nebraska, and the smaller Texas refinery (Texas 2) was supplied by a plant in Iowa. None of the four agglomeration terminals were used. Without the availability of unit trains, there was no cost advantage to utilizing these terminals. The costs for Scenario 2 represent the savings over the baseline costs, obtained in Scenario 1, resulting from the use of storage at ethanol plants and the utilization of unit trains; the four potential BNSF agglomeration terminals were not considered in this scenario. Thirteen of the 25 supply nodes invest in new rail sidings to accommodate enough tank cars to construct a unit train (Table 5). Each of these thirteen plants ships one unit train over the 14 day cycle, system wide transporting slightly over half the total demand (1300 tank cars) via unit trains. The Charles City, IA plant ships via unit train to the refinery in California, while the other twelve ship to the Texas 1 refinery. The remainder of the demand is met by individual carload shipments from some of these plants that ship by unit train and from the other ethanol plants. The total transportation costs are reduced by almost 19% through the use of unit trains. Total system costs are reduced by slightly more than 12%, with the savings in transportation costs offset by new investment costs for siding capacity of $53,000 (the two-week period amortized fixed costs for building the siding) and total demurrage charges of $594,000 over the cycle (Table 4). As an example of the dynamic INSLA storage and shipment patterns that are generated by the model, the transactions for the eth-
Table 3 Siding construction costs: from Shafer (1998). Siding components (car length assumed to be 18.5 m)
Costs
Track (rails and ties) Turnout (allows rail cars to switch tracks) Bumper (end of track) Site development per rail car length
$25.00/m $25,000 $5,000 $1,500
anol plant at Janesville, MN are shown in Fig. 3. Storage starts at Janesville in the fourth period of the seven period cycle. In this period 10 of the 18 tank cars of supply is stored, and 8 are shipped via individual carload train to the refinery in Illinois. In the next four periods (5, 6, 7 and 1), the 18 tank car supply is stored accumulating to the maximum storage capacity of 82 tank cars in period 1. The 18 tank car supply in period 2 is then used with the 82 stored tank cars to assemble the 100 tank car unit train that is shipped to the Texas 1 refinery. In period 3, the 18 unit supply is sent again via carload train to the Illinois refinery. Each of the thirteen ethanol plants that utilize storage has their own dynamic INSLA transaction pattern. In scenario 3 no storage was permitted, but the four potential BNSF agglomeration terminals could be utilized. Transportation and total system costs for this scenario are lower than both the baseline scenario 1, and scenario 2. Fourteen unit trains are used, two unit trains per period, all of which are constructed at the agglomeration terminal at Lincoln, NE; none of the other potential agglomeration terminals are used. The unit trains assembled at Lincoln are used to meet demand at the Texas 1 and Louisiana refineries. The other refinery demands are met by direct shipments from ethanol plants via carload trains. Storage is allowed at any of the ethanol plants and at the four potential BNSF agglomeration terminals in Scenario 4. Transportation costs show the greatest decline in this scenario, of more than 27% and total system costs decline by more than 24%, when compared with the costs in baseline scenario 1. Storage is used at five Table 5 Storage capacity and unit train shipments at ethanol plants. Ethanol plant
Storage capacity (tank cars)
Unit train to:
CHARLES CITY, IA SAINT ANSGAR, IA COUNCIL BLUFFS, IA DEXTER, IA GRINNELL, IA HARTLEY,IA JANESVILLE, MN HANKINSON, ND O’NEILL,NE ALBION, NE FAIRMONT, NE MARION, SD MINA, SD
80 82 80 82 82 80 82 82 82 82 82 82 82
California Texas 1 Texas 1 Texas 1 Texas 1 Texas 1 Texas 1 Texas 1 Texas 1 Texas 1 Texas 1 Texas 1 Texas 1
Table 4 Results of Rail-INSLA scenarios for case. Rail-INSLA scenarios
Total transportation costs
Siding investment costs
Total demurrage charges
Total system costs
Scenario 1: No unit trains, no storage Scenario 2: No agglomeration terminals Scenario 3: Unit Trains, no storage and agglomeration terminals allowed Scenario 4: Unit trains, storage and agglomeration terminals allowed
$10,497,950 $8,510,550 $8,395,850
$0 $53,000 $0
$0 $594,000 $0
$10,497,950 $9,157,550 $8,395,850
$7,653,050
$20,400
$231,460
$7,904,910
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120
Tank Cars of Ethanol
100 80 60 40 20 0 Supply Storage Unit Train Carload
1
2
3
4
5
6
7
18 82 0
18 0 100
18 0 0
18 10 0
18 28 0
18 46 0
18 64 0
0
0
18
8
0
0
0
Time Period (2 Days) Fig. 3. INSLA pattern for Janesville, MN ethanol plant for the seven, two day periods.
Fig. 4. Projected optimal ethanol flows to refineries.
of the ethanol plants, Council Bluffs, IA, Hankinson, ND, Fairmont, NE, and Marion, SD and Mina, SD, with storage capacities shown in Table 4 for those plants. Eighteen unit trains are utilized, five from the five ethanol plants and thirteen through the BNSF agglomeration terminal at Lincoln, NE – due to its advantageous location with respect to ethanol plants and refineries. The terminal at Lincoln needed to handle an additional of 74 tank cars to meet this schedule. As in scenario 3, none of the other three potential
agglomeration terminals are used. Ten of the thirteen unit trains originating at the Lincoln terminal serve the Texas 1 refinery, along with unit trains (one each) from the ethanol plants at Council Bluffs, Marion, and Mina. Two of the unit trains originating at Lincoln serve the California refinery, and one serves the refinery in Louisiana, supplemented with unit trains from Hankinson and Fairmont. All other demand is supplied by carload trains directly from the ethanol plants. Almost three quarters of the total demand is
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supplied using unit trains in this scenario. The optimal flows of ethanol for this scenario are shown in Fig. 4. The results of these scenario runs suggest that utilization of storage and agglomeration terminals can reduce transportation costs significantly. 5. Solution experience The INSLA model, as formulated for the case study, had 4047 constraints and 7121 variables, of which 1421 are integer. We ran the model on a laptop computer with a 2 GHz Intel Pentium M processor and 2 GB Ram, using the CPLEX solver in AIMMS version 3.8 (AIMMS, 2008). Solution times varied, from 0.54 s for scenario 1, in which no storage or unit trains were allowed; to a solution that we terminated after 1700 s (at a solution gap of 1.7%) for scenario 4 where all options were available. For scenario 4 the integer solution reported in the paper was found within 15 s, however, the remaining time was spent pruning the branch and bound tree attempting to find a better integer solution. Our experience with other example problems suggests solution times can vary greatly with the input parameters used for models with the same structure and size (Ratick and Osleeb, 2008). 6. Summary and conclusions Increasing demands for biofuels will have an effect on the nationwide transportation system, particularly train transportation. In this paper, we developed an Interperiod Network Storage Location–Allocation (INSLA) model, Rail-INSLA, to evaluate rail transportation cost efficiencies that may be realized through the use of storage on the network to agglomerate unit train sized shipments. In order to test the model, we developed a case study on a part of the BNSF Railway system using existing ethanol plants, potential BNSF unit train assembly terminals, and refineries that blend ethanol into gasoline. Through the evaluation of four scenarios, which concatenate the use of storage, unit trains and the agglomeration terminals in the system, we demonstrate that the optimal location and scheduling of storage and agglomeration terminals can reduce transportation costs significantly. As we and other researchers have shown, transportation logistics has spatial and temporal dimensions, as exemplified by the distribution problems associated with the use of ethanol described in this paper. In this case, the spatial dimension describes the distribution of ethanol from relatively small and geographically dispersed plants, to refineries where it is blended with gasoline. The temporal dimension deals with the time necessary to produce the ethanol, to fill the tank cars and perhaps store them to assemble unit trains to deliver ethanol to refineries. Each of these components has its own set of costs that must be factored into allocation and modal choice decisions, whether to ship ethanol as individual tank car loads or in unit trains. The Rail-INSLA model results track well with other studies of ethanol transportation rates. The results of scenario 4, where storage, unit trains and agglomeration terminals were available, provide an overall average transportation rate of approximately 2.7 cents per liter of ethanol transported in 120,000 l tank cars for an average distance of approximately 1100 miles. Both the US EPA and the American Petroleum Institute (API) (US EPA, 2007) reported the estimated cost per liter of ethanol – here the estimates were also for 120,000 l tank cars – from Chicago to Philadelphia, an 800 mile trip. EPA estimates were 2.3 cents per liter, and the API estimates of 4.25–5.5 cents per liter for individual tank cars, and 3.75–5 cents per liter by unit train. The cost savings we obtained from the use of storage and agglomeration nodes on the network, allowing for the utilization
of unit trains are a function of, and are likely to vary with, the choices of the size and location of ethanol supply plants and refineries, the structure of the transportation network, and of other model parameters, such as the time period, cycle length and size of unit trains. These results, however, are suggestive of the types of transportation cost efficiencies that may be realized through careful and systematic transportation planning using models such as the Rail-INSLA model developed in this paper. Acknowledgements The authors are grateful for the comments received from two anonymous referees who made numerous suggestions from which this paper benefited greatly. In addition, we would like to thank Dr. Michael Kuby for his comments on this paper and for his previous collaboration on the INSLA model. References AIMMS, 2008. AIMMS Version 3.8, Paragon Decision Technology B.V. Haarlem, The Netherlands. Akinci, B., Kassebaum, P., Fitch, J., Thompson, R., 2008. The role of bio-fuels in satisfying us transportation fuel demands. Energy Policy. Al-Khayyal, F., Hwang, S., 2007. Inventory constrained maritime routing and scheduling for multi-commodity liquid bulk, Part I: Applications and model. European Journal of Operations Research 176, 106–130. Ayoub, N., Martins, R., Wang, K., Seki, H., Naka, Y., 2007. Two levels decision system for efficient planning and implementation of bioenergy production. Energy Conversion and Management 48, 709–723. Black, W., 2001. An unpopular essay on transportation. Transportation Geography 9, 1–11. BNSF Railway Company, 2005. BNSF demurrage charts.
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