Integrating MTS Commerce Data with Multimodal Freight Transportation Performance Measures to Support MTS Maintenance Investment Decision Making (2014)

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20 Overview Concurrently—and in coordination with—the activities described, the research team developed an operations research model for evaluating and prioritizing a set of possible proj- ects (specifically lock and dam projects and/or dredging proj- ects). The objective function was designed to maximize the expected total positive impact of selected potential projects on the freight transportation system as a whole. The operations research model is built on a network using network flow techniques. The network consists of links and nodes. For each port area, a network covering the area of inter- est is established. The network associated with each port area consists of four different types of links (see Figures 2 and 3): 1. Numbered port segments/waterway links ( ) for inland waterway ports or the port itself for coastal and Great Lakes ports. Locks and dams are also represented by links in the theoretical network model. 2. In the case of inland ports, waterway segments/links that connect a port to other ports ( ). 3. Highways that feed freight into this waterway network or remove it ( ). 4. Connected railroads for transporting freight out of or into the port ( ). It is assumed that each of these link types has a maximum capacity and a certain level of current utilization. The objec- tive of the model is to maximize the possible freight through- put served by the restored or increased system availability by identifying lock and non-lock waterway segments/links for maintenance. In the case of dredging, the model determines dredging location and depth; in the case of locks, it determines reductions in average delay and evaluates their associated combined effects on the system network including landside linkages. The freight network analysis is based on historic freight demand. Definition of Terminologies There are several terms used in the description of the model that need to be clearly defined to avoid confusion: • Link. A component of infrastructure that carries a mea- surable volume of tonnage with a capacity that can be improved through maintenance operations. Examples of a link include: river segment(s), lock(s), ports, segments of highways, and/or segments of rail lines. • Node. The connection point between two links. • Corridor. The path of a particular commodity flow between an origin and destination pair. This may include highway, rail, and/or water routes that together form a corridor. Data Needs The following data are needed to build a sufficiently robust model: 1. Origin-destination freight demand for the selected com- modity groups (in thousand tons). 2. Current utilization of highway and railroad routes and remaining throughput capacity before level of service becomes unacceptable (in tonnage). 3. A known total project budget cap. 4. Portfolios of alternative projects, each complete with bud- get and benefit. The benefit is the restored potential utili- zation at the location2 (in tonnage). 5. Current utilization of waterway segments/links (before/ without project, in tonnage).3 S E C T I O N 3 Proposed Metrics and Operations Research Methods 2 Assume multiple options of dredging or maintenance at each location are known. 3 Restored availability from project completion is added on top of this base availability.

21 6. Current level of lock utilization (in tonnage). 7. The additional tonnage throughput due to Corps proj- ects improvement (either waterway segments or locks, in tonnage). Underlying Assumptions There are two assumptions that are critical to the integrity of the model: 1. At each location (e.g., a river segment/link or a lock), only one maintenance project may be selected. 2. The lack of detail in the inland waterway trip data forces the assumption that any changes associated with a river segment will be distributed uniformly across that segment. Assumption 1 implies that one location cannot be dredged for two depths simultaneously, which represents a logical requirement. Inputs to the Model Two tables were developed that provided the needed infor- mation for the modeling runs. The first table (see Table 9) pro- vides a list of all segments that are part of selected corridor/ commodity flows. For each segment, the table provides the average utilization, remaining project depth cargo capacity, increase in potential tons/year per unit of improvement, and cost per unit of improvement. A unit of improvement (or maintenance activity) consists of 1 ft of dredging for a water- way segment or one-third of the increased capacity resulting from the targeted reduction in average delay at a lock. In order to determine a reasonable cost per unit of mainte- nance activity, the researchers compiled data on dredging and lock expenses at the ports and potentially constrained locks. These data were taken from the Corps’ online dredging infor- mation system (10). These data are entered by Corps District personnel directly into the central database. Reports are posted every other Monday. There are a number of dredging-related Highway Railroad Waterborne Input/Output Connecon Points Figure 3. Abstract network representation of coastal seaport. Segment 3 Segment 2 Segment 7 Segment 9 Segment 8 Segment 6Segment 5 Segment 4Segment 1 River Segment Highway Railroad Waterborne Input/Output Lock Connec€on Points Figure 2. Abstract network representation of inland waterway port flows.

Table 9. Segment attributes.

Some datasets published by the Corps begin numbering the Ohio River in Pittsburgh and progress downstream, while others begin at the junction with the Mississippi River and progress upstream. This table starts the numbering sequence in Pittsburgh. Blank cells indicate segments for which no maintenance activity is considered. Dotted background indicates the actual port as opposed to segments connected to the port. Table 9. (Continued).

24 reports available on the website: advertising schedule, dredg- ing contracts awarded, anticipated work schedule, Corps/ industry dredge fleet status, long-term dredging cost analysis, number of contracts and quantity dredged, and other reports with miscellaneous information. In any dredging or lock maintenance event, a certain amount of the expense is caused by mobilization and demo- bilization of the equipment, regardless of the actual amount of work involved. The researchers had no way to estimate what percentage of the cost of any given dredging event was due to mobilization or demobilization. Furthermore, the model is predicated on the ability to treat each foot or 10 percent reduction in delays as a modular function, where each unit of work costs the same as the next one. Although this is not the way contracts are actually executed, adding in a function to calculate the difference in each unit based on whether it is absorbing one-third, two-thirds, or all of the mobilization/ demobilization costs would add a high degree of complexity and would not change the final result in a meaningful way. In this research, each unit was treated as a standard unit, and the cost of an event was simply the number of units times the unit cost. The resulting increase in project depth cargo capacity resulting from a unit of dredging would simply be the 30 percent increase in project depth cargo divided by three (two in the case of Huntington). Finally, the public dataset only provides information on the quantity of cubic yards stipulated in the request for pro- posal; it does not provide the final quantity, nor does it indi- cate how that quantity was distributed across the dredged area. For instance, there is no indication of whether the quan- tity was a relatively deep section in a fairly small geographi- cal area or whether the quantity was a thin layer spread over a wide geographical area. Therefore, the data that are used below are simply an attempt to arrive at dollar amounts that would be reasonable given the history of dredging in the spe- cific area. Duluth Data for 5 years of dredging activity were compiled for each of the three ports that are relevant to the Duluth case study (see Table 10). The coal shipped from Duluth has the highest tonnage going to St. Clair River, Michigan. Table 11 shows its dredging history. The iron ore shipped from Duluth has the highest tonnage going to Burns Harbor, Indiana. Table 12 shows its dredging history. The researchers used the 2011 dredging event for Duluth as the standard. It seems to indicate that the cost of dredging rose significantly from 2008 to 2011. Given this rise in cost, the latest figure would be the one to use. Since this research assumes a dredging event of 3 ft, the cost of each foot of dredging would be $2,828,485 divided by 3, or $942,828. For St. Clair, the cost for the two dredging events was very similar. The researchers used the latest event, 2011, as the standard. This resulted in a unit cost of $879,200 divided by 3, or $293,067/ft. Finally, for Burns Harbor, the researchers used the 2009 event as the standard, yielding a unit cost of $2,025,629 divided by 3, or $675,210/ft. Hampton Roads Table 13 shows the dredging expense data for 2007 to 2011. The researchers needed to establish the cost of a dredg- ing event for the Norfolk Harbor Channel and the Newport News Channel. The 2007 event was considered to be the most representative and was selected as the standard for a potential dredging event in Norfolk Harbor. This yields a unit cost of $2,668,024 divided by 3, or $889,341/ft. Data specifically for Newport News Channel were not available. The researchers used 50 percent of the 2011 event as the potential cost of a FY Project Name Cubic Yards Winning Bid 2007 Duluth-Superior, MN&WI 100,000 $1,736,425 2008 Duluth-Superior, MN&WI 190,500 $1,497,890 2009 --- --- --- 2010 --- --- --- 2011 DULUTH-SUPERIOR HBR MN & WI 116,000 $2,828,485 Table 10. Port of Duluth dredging history (5 years). FY Project Name Cubic Yards Winning Bid 2007 --- --- --- 2008 --- --- --- 2009 --- --- --- 2010 Channels in Lake St Clair, MI 62,500 $887,375 2011 Channels in Lake St Clair, MI* 66,000 $879,200 *Work actually done in FY 12 Table 11. St. Clair River dredging history (5 years). FY Project Name Cubic Yards Winning Bid 2007 Burns Harbor NIPSCO* Dredging 200,000 $1,923,818 2007 Burns Waterway Dredging 131,500 $773,828 2008 --- --- --- 2009 Burns Harbor NIPSCO 150,000 $2,025,629 2010 --- --- --- 2011 --- --- --- *Northern Indiana Public Service Company Table 12. Burns Harbor dredging history (5 years).

25 dredging event for Newport News. This yields a unit cost of $562,359/ft. Huntington As mentioned earlier, Huntington was assumed to only need 2 ft of dredging. Unfortunately, there have been no recent dredging events anywhere on the Upper Ohio that would yield real world cost data for a Huntington case sce- nario. However, there was a dredging event on the Big Sandy River within the selected 5-year timeframe. It was chosen as the standard event. Table 14 shows the dredging history for the upper Ohio River and the Big Sandy River. The cost of the 2010 event on the Big Sandy River yields a unit cost of $1,508,872 divided by 2 or $754,436/ft. In order to add one degree of complexity, an additional river segment was selected as part of the potential dredging scenario for Huntington, and the same unit cost was assumed. Hunting- ton also has one lock, Emsworth, which could potentially pose a constraint on the system. Table 15 shows the mainte- nance expense history for Emsworth.4,5 Since 2010 appears to be the most extensive maintenance project performed at this lock, it was selected as the standard. It was assumed that this work could produce a reduction in delays of 60.9 percent on the average. This yields a unit cost (cost per one-third of the potential reduction) of $2,116,593 divided by 3, or $705,531. Plaquemines At Plaquemines, the only dredging work that would be relevant would be dredging downstream on the Mississippi River. The problem with analyzing Plaquemines based on the dredging activity in that segment is that a much larger com- munity of users is affected than just Plaquemines. Deep draft navigation occurs all the way up the Mississippi River to Baton Rouge, and all users up to that point are affected by dredg- ing that takes place downstream from Plaquemines. Shippers sending commodities by barge to the lower Mississippi River may choose an alternate route if a restriction on the size of oceangoing vessels causes freight rates to rise to an unaccept- able degree. In a real world situation, all of these ports would have to be treated as one entity for purposes of evaluating whether the dredging needs to be done. For purposes of test- ing the model in the present study, the assumption was made that any dredging that is done is done because Plaquemines needs it, even though it is a somewhat inaccurate assumption. Table 16 shows the dredging history for the Mississippi River downstream of Plaquemines. Table 13. Hampton Roads dredging history (5 years). FY Project Name Cubic Yards Winning Bid 2007 Norfolk Harbor 50-ft Channel 506,200 $2,668,024 2008 Norfolk Harbor Channel 567,900 $1,944,000 2009 Norfolk Harbor Thimble Shoal 473,700 $2,678,090 2009 Norfolk Harbor and CI Reach 600,300 $3,691,515 2010 --- --- --- 2011 Norfolk Harbor - Craney Island Reach 1,237,900 $3,374,153 4 From annual reports of the Secretary of the Army on civil works activities. 5 Includes Emsworth, L&D 52, and John Day. FY Project Name Cost 2006 Emsworth – maintenance costs $1,389,000 2007 Emsworth—nothing reported --- 2008 Emsworth—nothing reported --- 2009 Emsworth—nothing reported --- 2010 Emsworth – maintenance costs $2,116,593 2011 Emsworth – maintenance costs $157,800 Table 15. Emsworth lock and dam maintenance history (5 years). FY Project Name Cubic Yards Winning Bid 2007 Ohio River Open (2 of 4 opt)—Louisville 1,000,000 $4,356,146 2008 Ohio River Open (3 of 4 opt)—Louisville 1,000,000 $4,587,629 2008 Mississippi River Harbors—Memphis N/A $9,037,409 2009 Big Sandy Harbor 200,000 $1,297,510 2009 Ohio River Open Channel (Base )—Louisville 1,000,000 $4,770,604 2009 Mississippi River Harbors—Memphis N/A $12,753,760 2010 Big Sandy River Dredge 220,000 $1,508,872 2010 Ohio River Open Channel (Op 1)—Louisville 1,000,000 $4,994,389 2010 Mississippi River Harbors—Memphis N/A $9,663,200 2010 Baton Rouge Harbor CY 341,168 $1,590,000 2011 Ohio River Open Channel (Op 2) LRH 1,000,000 $5,254,328 2011 Ohio River Open Chanel (Op 2) 1,000,000 $5,254,328 Table 14. Ohio River and selected Mississippi River ports dredging history (5 years).

26 For the case study, the 5-year average was used as the stan- dard. This yields a unit cost of $54,632,891 divided by 3, or $18,210,963/ft. Portland-Coastal Table 17 shows the 5-year dredging expense history for the deep draft portion of the Columbia River. The totals for 2010 and 2011 are almost the same. The researchers chose 2011 as the standard, since it is the most recent. This yields a unit cost of $14,049,300 divided by 3, or $4,683,100/ft. Portland-Inland Table 18 shows the 5-year history for Portland-Inland. The only active dredging reach on the Columbia/Snake River shallow draft system is in the reach between Vancouver and The Dalles. The 5-year average cost for this reach is $600,605. This yields a unit cost of $600,605 divided by 3, or $200,202/ft. FY Project Name Cubic Yards Winning Bid 2007 MISS RIV SWP LSD HOP 1-2007 2,300,000 $2,429,100 2007 MISS RIV SWP LSD HOP 2-2007 2,300,000 $2,684,210 2007 MISS RIV SWP LSD HOP 3-2007 2,300,000 $3,233,100 2007 MISS RIV SWP LSD HOP 4-2007 2,300,000 $2,584,500 2007 MISS RIV SWP LSD HOP 6-2007 2,300,000 $2,659,976 2007 MISS RIV SWP LSD HOP 7-2007 2,300,000 $2,659,976 2007 MISS RIV SWP LSD HOP 8-2007 2,300,000 $2,181,935 2007 MISS RV PASS A LOUTRE CY CT 4,000,000 $8,850,000 2007 MISSISSIPPI RIV SOUTH PASS 7,000,000 $18,370,000 2007 Totals 27,100,000 $45,652,797 2008 MISS RIV SWP LSD HOP 1-2008 2,300,000 $3,075,800 2008 MISS RIV SWP LSD HOP 10-2008 2,300,000 $4,007,350 2008 MISS RIV SWP LSD HOP 11-2008 2,300,000 $5,093,120 2008 MISS RIV SWP LSD HOP 12-2008 2,300,000 $5,259,400 2008 MISS RIV SWP LSD HOP 2-2008 2,300,000 $3,500,000 2008 MISS RIV SWP LSD HOP 3-2008 2,300,000 $4,157,350 2008 MISS RIV SWP LSD HOP 4-2008 2,300,000 $4,246,900 2008 MISS RIV SWP LSD HOP 5-2008 2,300,000 $4,789,220 2008 MISS RIV SWP LSD HOP 6-2008 2,300,000 $4,585,000 2008 MISS RIV SWP LSD HOP 7-2008 2,300,000 $4,717,600 2008 MISS RIV SWP LSD HOP 8-2008 2,300,000 $3,261,000 2008 MISS RIV SWP LSD HOP 9-2008 2,300,000 $3,595,000 2008 MISS RV PASS ALOUTRE CY CT 4,000,000 $9,600,000 2008 Totals 31,600,000 $59,887,740 2009 MISS RIV SWP LSD HOP 2-2009 6,300,000 $10,278,400 2009 MISS RIV SWP LSD CUT 1-2008 3,000,000 $11,116,326 2009 MISS RIV SWP LSD HOP 3-2009 2,300,000 $4,071,260 2009 MISS RIV SWP LSD HOP 4-2009 2,300,000 $4,188,868 2009 MISS RIV SWP LSD HOP 6-2009 3,300,000 $5,659,000 2009 MISS RIV SWP LSD HOP 7-2009 2,300,000 $4,454,320 2009 MISS RIV SWP LSD HOP 9-2009 2,300,000 $4,997,600 2009 Totals 21,800,000 $44,765,774 2010 MISS RIV SWP LSD CUT 1-2009 2,745,396 $10,291,941 2010 MISS RIV SWP LSD HOP 1-2010 5,092,922 $12,799,420 2010 MISS RIV SWP LSD HOP 10-2010 1,308,197 $3,950,400 2010 MISS RIV SWP LSD HOP 11-2010 3,701,750 $10,340,500 2010 MISS RIV SWP LSD HOP 3-2010 1,871,098 $5,002,500 2010 MISS RIV SWP LSD HOP 4-2010 1,590,126 $6,130,825 2010 MISS RIV SWP LSD HOP 5-2010 1,428,619 $3,925,650 2010 SWP HEAD OF PASSES HDDA 8,000,000 $30,599,560 2010 Totals 25,738,108 $83,040,796 2011 MISS RIV SWP LSD CUT 1-2010 3,241,180 $8,850,651 2011 MISS RIV SWP LSD HOP 1-2011 1,800,000 $11,381,550 2011 MISS RIV SWP LSD HOP 2-2011 1,200,000 $5,574,100 2011 MISS RIV SWP LSD HOP 4-2011 2,300,000 $5,191,800 2011 MISS RIV SWP LSD HOP 7-2011 2,619,074 $5,929,000 2011 MISS RV NO HAR LSD CT 1-2011 1,000,000 $2,890,251 2011 Totals 12,160,254 $39,817,352 5-Yr Average 23,679,672 $54,632,891 Table 16. Plaquemines dredging history (5 years)—reaches at or downriver from Plaquemines.

27 Portland-Inland also has one lock, John Day, that could poten- tially pose a constraint on the system. Table 19 shows the main- tenance expense history for the John Day lock and dam. Since there has been so much maintenance activity at this site, the 5-year average was used as the standard. This yields a unit cost of $14,759,894 divided by 3 or $4,919,965 for each unit of reduction in delay. Segment Table A table was prepared to list all relevant segments for pur- poses of the modeling effort. These segments are grouped by mode and then by port within each mode. This table pro- vides the model with the information necessary to determine capacity and the unit cost to increase capacity. All origin- destination flows are defined by the segments included in the flow. By examining the segments in the flow, the model is able to incorporate any possible constraints and the unit cost of any proposed maintenance activity. Table 9 was used for the model’s segment input. The segments with a dotted fill in Table 9 indicate a segment containing a port complex or location where maintenance might be performed. Many of the segments have a capacity of 999,999,000 tons per year for waterway segments or 100,000,000 for truck segments. This was just a shorthand way of telling the model that these segments have unlimited capacity and do not need to be consid- ered as potential constraints to cargo flows. An examination of the Remaining Project Depth Cargo Capacity column will reveal which segments have the potential to constrain cargo flows. Origin-Destination Table An origin-destination table was prepared that contains each corridor to be analyzed. It essentially provides the seg- ments that compose each corridor along with some freight volume information. Table 20 was used in the modeling effort. A series of explanatory notes follows Table 20. Origin-Destination Explanatory Notes Duluth. A high percentage, but not all, of Duluth’s traf- fic uses the full channel depth when available. A 30 percent increase in Duluth’s project cargo tonnage would result in a 27.6 percent increase in total tonnage. Hampton Roads. Very little of Hampton Roads traffic uses the full project depth. In fact, the only cargo that uses this depth is export coal. For the other port case studies, the percentage increase in overall tonnage was used to predict the increase in corridor flows. In the case of Hampton Roads, since all of the affected tonnage is export coal and it is the only cargo that uses the full project depth, the full 30 percent increase was applied. Huntington. The segments that were analyzed for Huntington were based on the flow patterns of the top four commodities. However, they only represent a certain percentage of these flows. These flows had to be adjusted upward to represent the total tonnage related to these four Table 17. Portland-Coastal dredging history (5 years). FY Project Name Cubic Yards Winning Bid 2007 --- --- --- 2008 --- --- --- 2009 --- --- --- 2010 Dredge OREGON Rental 140,961 $925,130 2010 Dredge OREGON Rental 430,323 $2,096,962 2010 Dredge OREGON Rental 1,020,692 $2,246,004 2010 Dredge OREGON Rental 224,659 $512,452 2010 Dredge OREGON Rental 571,788 $1,115,336 2010 Dredge OREGON Rental 356,917 $2,364,222 2010 Dredge OREGON Rental 554,101 $1,012,846 2010 Dredge OREGON Rental 286,882 $409,961 2010 Dredge OREGON Rental 369,400 $2,302,546 Total OREGON 3,955,723 $12,985,459 2010 Lower Columbia River Clam 84,000 $646,124 2010 Lower Columbia River Clam 92,000 $786,686 2010 Totals 4,131,723 $14,418,269 2011 Dredge OREGON Rental 1,885,176 $11,720,900 2011 Portland Harbor Clamshell 64,000 $2,328,400 2011 Totals 1,949,176 $14,049,300 Table 18. Portland-Inland dredging history (5 years). FY Project Name Cubic Yards Winning Bid 2007 Columbia River Between Vancouver, WA and The Dalles, OR 90,533 $412,993 2008 Columbia River Between Vancouver, WA and The Dalles, OR 72,850 $448,007 2009 Columbia River Between Vancouver, WA and The Dalles, OR 156,643 $862,752 2010 Columbia River Between Vancouver, WA and The Dalles, OR 72,510 $657,818 2011 Columbia River Between Vancouver, WA and The Dalles, OR 80,444 $621,454 Average 94,596 $600,605 FY Project Name Cost 2007 John Day—maintenance cost $13,083,038 2008 John Day—maintenance cost $17,007,808 2009 John Day—maintenance cost $14,277,859 2010 John Day—maintenance cost $20,107,321 2011 John Day—maintenance cost $9,323,444 John Day Average $14,759,894 Table 19. John Day lock and dam maintenance history (5 years).

US Origin US Destination Segments (List of Numbers) along Connecng Route Original O D Flow Adjustment Factor to Reach Total Tonnage Adjusted O D Flow Percent Projected Increase from Project Increase from Project Total Demand (Current + Increase from Project) Huntington Segment 1 Segment 4 Emsworth, Segment 2 6.526 1.750570513 11.424 28.0496% 3.204 14.628 Segment 1 Segment 5 Emsworth, Segment 2, Segment 4 22.722 1.750570513 39.776 28.0496% 11.157 50.933 Segment 1 Segment 6 Emsworth, Segment 2, Segment 4 1,203.568 1.750570513 2,106.931 28.0496% 590.985 2,697.916 Segment 1 Segment 8 Emsworth, Segment 2, Segment 4, Segment 6 25.913 1.750570513 45.363 28.0496% 12.724 58.087 Segment 2 Segment 4 217.773 1.750570513 381.227 28.0496% 106.933 488.160 Segment 2 Segment 5 Segment 4 180.100 1.750570513 315.278 28.0496% 88.434 403.712 Segment 2 Segment 6 Segment 4 6,440.566 1.750570513 11,274.665 28.0496% 3,162.497 14,437.162 Segment 2 Segment 8 Segment 4, Segment 6 233.409 1.750570513 408.599 28.0496% 114.610 523.209 Segment 3 Segment 6 Segment 4 4,463.019 1.750570513 7,812.829 28.0496% 2,191.466 10,004.295 Segment 3 Segment 8 Segment 4, Segment 6 1,720.300 1.750570513 3,011.506 28.0496% 844.715 3,856.221 Segment 4 Segment 1 Segment 2, Emsworth 2,254.283 1.750570513 3,946.281 28.0496% 1,106.915 5,053.196 Segment 4 Segment 2 3,304.068 1.750570513 5,784.004 28.0496% 1,622.389 7,406.393 Segment 4 Segment 5 3.259 1.750570513 5.705 28.0496% 1.600 7.305 Segment 4 Segment 6 4,056.672 1.750570513 7,101.490 28.0496% 1,991.938 9,093.428 Segment 4 Segment 8 Segment 6 445.009 1.750570513 779.020 28.0496% 218.512 997.532 Segment 5 Segment 1 Segment 4, Segment 2, Emsworth 33.863 1.750570513 59.280 28.0496% 16.628 75.908 Segment 5 Segment 2 Segment 4 1,708.117 1.750570513 2,990.179 28.0496% 838.733 3,828.912 Segment 5 Segment 4 0.818 1.750570513 1.432 28.0496% 0.402 1.834 Segment 5 Segment 6 6,199.861 1.750570513 10,853.294 28.0496% 3,044.304 13,897.598 Segment 5 Segment 7 Segment 6 0.636 1.750570513 1.113 28.0496% 0.312 1.425 Segment 5 Segment 8 Segment 6 985.161 1.750570513 1,724.594 28.0496% 483.741 2,208.335 Segment 6 Segment 1 Segment 4, Segment 2, Emsworth 1,460.607 1.750570513 2,556.896 28.0496% 717.199 3,274.095 Segment 6 Segment 2 Segment 4 1,852.364 1.750570513 3,242.694 28.0496% 909.562 4,152.256 Segment 6 Segment 3 Segment 4 1,266.594 1.750570513 2,217.262 28.0496% 621.933 2,839.195 Segment 6 Segment 4 108.730 1.750570513 190.340 28.0496% 53.390 243.730 Segment 6 Segment 5 189.945 1.750570513 332.512 28.0496% 93.268 425.780 Segment 6 Segment 6 11.980 1.750570513 20.972 28.0496% 5.883 26.855 Segment 6 Segment 8 41.089 1.750570513 71.929 28.0496% 20.176 92.105 Segment 7 Segment 2 Segment 6, Segment 4 2,280.756 1.750570513 3,992.624 28.0496% 1,119.914 5,112.538 Segment 8 Segment 2 Segment 6, Segment 4 56.682 1.750570513 99.226 28.0496% 27.832 127.058 Segment 8 Segment 5 Segment 6 363.176 1.750570513 635.765 28.0496% 178.329 814.094 Hampton Roads HRR1 HR1 HR2 14,498 1 14,498 30.00% 814 15,312 HRR2 HR1 HR3 9,749 1 9,749 30.00% 955 10,704 Duluth DSR2 DS4 DS1, DS2, DS3 8,000 1 8,000 27.60% 2,208 10,208 DSR2 DSR2 Undefined, not port related 11,825 1 11,825 0 11,825 DSR1 DS6 DS1, DS2, DS5 3,675 1 3,675 27.60% 1,014 4,689 DSR1 DSR1 Undefined, not port related 34,625 1 34,625 0 34,625 DS1 DS99 (This is all other ports no constraints) 29,046 1 29,046 27.60% 8,017 37,063 Table 20. Origin-destination table.

US Origin US Destination Segments (List of Numbers) along Connecng Route Original O D Flow Adjustment Factor to Reach Total Tonnage Adjusted O D Flow Percent Projected Increase from Project Increase from Project Total Demand (Current + Increase from Project) Plaquemines PL1 PL3 PL2 31,402 1 31,402 3.10% 973 32,375 PL0 PL1 30,010 1 30,010 3.10% 930 30,940 Portland Deep Draft PO0 PO1 Moved by water. Not accounted for in our flows insignificant 754 1 754 10.80% 81 835 PO0 POR2 PO1 2,033 1 2,033 10.80% 220 2,253 PO0 POR3 PO1, POR2 276 1 276 10.80% 30 306 PO2 PO2 Undefined, not port related 330,936 1 330,936 0 330,936 PO0 POR1 PO1 6,342 1 6,342 10.80% 685 7,027 POR1 POR1 Undefined, not port related 98,316 1 98,316 0 98,316 PO0 LOMB PO1 5,357 1 5,357 10.80% 579 5,936 PO0 MAR PO1 774 1 774 10.80% 84 857 PO0 I5 PO1 6,130 1 6,130 10.80% 662 6,792 PO0 I84 PO1 3,245 1 3,245 10.80% 351 3,596 Portland Shallow Draft Segment 1 Segment 4 Segment 3, John Day 480.262 1.330134716 638.813 23.30% 149 788 Segment 1 Segment 5 Segment 3, John Day, Segment 4 1,144.146 1.330134716 1,521.868 23.30% 355 1,876 Segment 1 Segment 6 Segment 3, John Day, Segment 4 27.527 1.330134716 36.615 23.30% 9 45 Segment 2 Segment 4 Segment 3, John Day 216.586 1.330134716 288.089 23.30% 67 355 Segment 2 Segment 5 Segment 3, John Day, Segment 4 218.683 1.330134716 290.878 23.30% 68 359 Segment 3 Segment 4 John Day 312.951 1.330134716 416.267 23.30% 97 513 Segment 3 Segment 5 John Day, Segment 4 1,034.642 1.330134716 1,376.213 23.30% 321 1,697 Segment 3 Segment 6 John Day, Segment 4 112.630 1.330134716 149.813 23.30% 35 185 Segment 4 Segment 1 John Day, Segment 3 136.033 1.330134716 180.942 23.30% 42 223 Segment 4 Segment 2 John Day, Segment 3 45.562 1.330134716 60.604 23.30% 14 75 Segment 4 Segment 3 John Day 7.359 1.330134716 9.788 23.30% 2 12 Segment 4 Segment 4 369.007 1.330134716 490.829 23.30% 114 605 Segment 4 Segment 5 240.966 1.330134716 320.517 23.30% 75 395 Segment 4 Segment 6 465.027 1.330134716 618.549 23.30% 144 763 Segment 4 Segment 7 Segment 6 2.374 1.330134716 3.158 23.30% 1 4 Segment 5 Segment 1 Segment 4, John Day, Segment 3 999.428 1.330134716 1,329.374 23.30% 310 1,639 Segment 5 Segment 2 Segment 4, John Day, Segment 3 321.402 1.330134716 427.508 23.30% 100 527 Segment 5 Segment 3 Segment 4, John Day 275.665 1.330134716 366.672 23.30% 85 452 Segment 5 Segment 4 33.156 1.330134716 44.102 23.30% 10 54 Segment 6 Segment 4 583.785 1.330134716 776.513 23.30% 181 957 Segment 7 Segment 4 Segment 6 30.809 1.330134716 40.980 23.30% 10 51 Segment 8 Segment 4 Segment 6 12.370 1.330134716 16.454 23.30% 4 20 Table 20. (Continued).

30 commodities. One more adjustment was required to raise the total to the total for all commodities at Huntington. This resulted in an adjustment factor of 1.750571 being applied to the flows that were originally analyzed based on the selected segments. Not all of Huntington’s traffic requires the full project depth, although a high percentage does. A 30 percent increase in project depth cargo for Huntington is equivalent to a 28.0 percent increase in total tonnage. Plaquemines. Very little of the traffic at Plaquemines uses the full cargo depth. An increase of 30 percent in cargo depth tonnage is only a 3.1 percent increase overall. Portland-Coastal. Certain assumptions were made regarding rail traffic in the Portland area. Given historical freight patterns in this area, the researchers assumed an aver- age railcar payload of 65 tons. They further assumed an aver- age of 100 cars per train with 40.8 percent being empty (2). (Western railroads have historically had an empty return ratio of 1.69, which is equivalent to 40.8 percent of the cars running empty.) This means that the average train carries 65 × 100 × (1-0.408) = 3,848 tons. The data show that the Burlington Northern Santa Fe (BNSF) line out of Portland is already running above its the- oretical capacity. Compared to other ports, shipments at the Port of Portland use the full project depth less frequently. A 30 percent increase in project depth cargo is equivalent to a 10.8 percent increase overall for international shipments. Truck traffic for Portland was allocated to the main access arteries by using annual truck counts on those arteries. These particular routes are heavily influenced by port traffic, so the simplifying assumption was made that 100 percent of their traffic was port related. Portland-Inland. A 30 percent increase in project depth cargo for inland waterway traffic at the Port of Portland equates to a 23.3 percent increase in overall inland waterway tonnage at the port. Model Specifications Background Based on the networks shown in Figure 2 and Figure 3, commodities may need to pass through one or more locks or transit one or several segments/links of the waterway, depend- ing on the specific origin-destinations. Therefore, if an origin- destination commodity traverses several segments/links or locks, the needed availability, or utilization level, should be provided for all the locks and river segments/links involved. Availability reduction at one lock or on one waterway segment may be the limiting factor in availability over a number of connected waterway segments/links. This consideration for network effect is specifically addressed in the proposed multi- modal network flow model described in the mathematical model that follows. The flowchart shown in Figure 4 depicts how data are fed into the model and the outputs that result. Definitions of the model parameters and variables are provided below. Variables The variables that are used in the model are the following: • xkij: Total commodity tonnage flow after project implemen- tation on link (i,j) for commodity k (tons). • f kij: The tonnage accommodated on the network out of the total demand from origin i to destination j. • dij: The depth of dredging for a river segment/link between node i and j (feet). This depth is a non-negative real num- ber6 that is set to a value of zero if (i,j) is a rail/highway segment. • hij: The total increase in effective hours of lock operations due to a decrease in delays for the lock represented by link (i,j). This variable is a non-negative real number. Parameters The parameters used in the model are the following: • q: The amount of increase in waterway available capacity for project depth cargo resulting from one unit increase (tons/ft) in draft due to dredging. • r: The increase in waterway availability resulting from one unit of reduction in delay of lock operation (ton/h). • cij: Cost of a unit depth of dredging for waterway segment/ link between node i and j ($/ft). • gij: The capacity of link (i,j) that represents loading/ unloading capacity at a dock. Due to the lack of data, this parameter is set to infinity for this project. • lij: Current availability of link (i,j) that represents a lock before a maintenance project (tons). • sij: Current availability of segment from node i to j before a maintenance project (tons). • wij: Cost of one unit of reduction in delay in lock operation for the lock represented by link (i,j) in the network ($/h). • jij: The weight for origin-destination flow from i to j. This weight may represent the distance of that flow, so that the total mileage value is maximized, or value of the commod- ity flows, or other economic impacts that might be relevant to the analysis. • B: Total budget available for all maintenance projects each year ($). 6 This requirement can be relaxed in the model specification, but is included here for convenience of presentation.

31 • E: The set of links of the network including links for locks/ dams and links for river segments and road and railway sections. • L: Set of all links in the network model that represent load- ing and unloading operations at ports. • OD: Set of all origin and destination pairs. • Dkij: Demand of commodity k to be shipped from origin i to destination j (tons). • I(i, j): Set of all itineraries of freight that traverse link (i,j). The following paragraphs present the proposed model. Objective Function (0)Max fij ijk kji ∑∑∑ ϕ Subject To (s.t.) i , \ (1)x s d q i j E Eijk ij ij k l∑ ( )≤ + ∀ ∈ i , (2)x l h r i j Eijk ij ij k l∑ ( )≤ + ∀ ∈ Operations Research Model Monetary data ($): Dredging cost (cij) Lock improvement cost (wij) Available budget (B) Current availability data (tons): Segment (s ij) Lock/dams (l ij) Capacity increase for a unit of improvement (tons): Segment (q) Lock/dams (r) Commodity data (tons): O-D demand (Dijk ) Model parameter: Weighting factor (ϕ ij) Input Data Output Results Results: The depth of dredging (dij) The increased operational time of lock/dam (hij) The total flow of commodity k (xijk ) The total flow between each O-D pair (fijk ) Figure 4. Flowchart of proposed operations research model.

32 (3) :: , \ ∑∑∑ + ≤ ( ) ∈∈ c d w h Bij ij ij ij i Eji i j E E ll i i , (4)x g i j Lijk ij k ∑ ( )≤ ∀ ∈ , , (5) , x f i j OD kijk mnk mn I i j ∑ ( )= ∀ ∈ ( )∈ , , (6)f D i j OD kijk ijk ( )≤ ∀ ∈ , 0 , , (7)x f i j kijk ijk ≥ ∀ , : , , (8)d h Integer i j kij ij ∀ The objective function maximizes the overall system ben- efit, i.e., maximizes the total tons of all commodity transits between all origin-destination pairs by increasing the pos- sible flow (tonnage) between each origin-destination pair. Constraint (1) restricts the flow of all commodities over all origin-destination pairs to the availability (existing tonnage plus tonnage induced by improved conditions) for every seg- ment. It is quite possible that just one river segment/link or lock is the bottleneck in the whole system, and improving only that lock or segment/link will create a large increase in flow over the entire system. Therefore, increasing the amount of freight over the entire system does not necessarily mean performing maintenance on all locks or waterway segments/ links along the path. Constraint (1) satisfies this condition by considering the total traffic volume and the total availability of each link (whether a river segment or lock). As an exam- ple, if a tonnage increase on a path consisting of Segments/ Links 1 and 2 is needed and the existing depth of Segment/ Link 2 already provides enough availability to accommodate this increase, it does not need dredging; only Segment/Link 1 needs to be dredged to reach that availability over both segments/links. In this constraint, q represents the added availability to each waterway segment/link resulting from one unit of dredging (tons/ft). Based on this constraint, each waterway segment on the path should provide enough availability to accommodate the existing and the additional tonnage of commodities that transit the waterway segment/ link. For the landside links (e.g., highways and rail lines), there may also be a similar capacity constraint without the term for waterway maintenance. The proposed model applies to large multimodal networks that can automatically identify bottlenecks. Constraint (2) ensures capacity constraint from dams/ locks, similar to Constraint (1). It requires the total flow through a lock/dam to be within the capacity allowed by the lock’s/dam’s operating hours and historical operating param- eters. With this constraint, the model depicts the availability of the system not just as a function of waterway segment/link depth, but also as a function of the availability of locks/dams on the path connecting an origin to a destination. Constraint (3) ensures that the total operating and capital cost does not exceed the budget limit. Constraint (4) restricts the output and input tonnage at dock links to the available capacity for loading and unloading at the dock. Constraint (5) connects the link volume to the accommodated itinerary volumes that traverse that link by commodity. Constraint (6) defines the accommodated origin-destination volume not to exceed the total origin-destination demand. Constraint (7) and Constraint (8) require non-negativity and integrality of variables. The model is programmed and implemented in SAS™, calling an optimization function that has recently become available, a mixed integer linear solver of SAS. This solver uses a branch and cut algorithm to achieve the optimal solution. The formulations for the ports have 116 variables and 303 constraints, a very small-sized formulation compared with today’s computational technology. The computational time ranges from 0.03 to 0.30 seconds on a desktop computer. A similar model to this one that was as developed by Mitchell, Wang, and Khodakarami (6), when applied to a large inland waterway network with 7,344 river segments, has 34,625 variables and 69,934 constraints, which takes from seven to a couple of hundred seconds to solve on a computer, depend- ing on the required accuracy and other factors. Scenarios Evaluated by the Model The researchers created several scenarios designed to test various aspects of the model. Table 21 shows the potential maintenance projects that were included. The individual line items are explained in detail in the section titled “Inputs to the Model.” The researchers used various budgeting levels and various project combinations in order to analyze the effect of differ- ent variables on the modeling results. A budget level here rep- resents a percentage of the total requested budget that would be available to fund projects in a year. Table 22 shows the scenarios that were analyzed. Given the budget and time constraints of this project, it was not possible to do model runs for a large number of sce- narios. The researchers created representative scenarios that were based on their knowledge of the characteristics of each project and that they believed would show the model’s ability to produce a diversity of outcomes, thereby demonstrating its usefulness. A different set of scenarios might be just as valid. The scenarios run here are intended to highlight the model’s characteristics and robustness.

33 Projects Included Budget Amount (% of Total Possible Budget) All Projects $99,265,442 (100%) All Projects $79,412,354 (80%) All Projects $49,632,721 (50%) All Projects minus Duluth & Hampton Roads $49,632,721 (50%) All Projects minus Portland $79,412,354 (80%) All Projects minus Plaquemines $44,632,551 (total minus Plaquemines) Table 22. Scenarios analyzed. Location Unit Cost Total Cost Port of Huntington (Ohio River) $754,436/ft $1,508,872 Adjacent to Port of Huntington $754,436/ft $1,508,872 Emsworth Lock and Dam $705,531/20.3% delay reduction $2,116,593 Norfolk Harbor $889,341/ft $2,668,024 Newport News Channel $562,359/ft $1,687,077 Duluth Harbor $942,828/ft $2,828,485 St. Clair River $293,067/ft $879,200 Burns Harbor $675,210/ft $2,025,629 Mississippi River below Plaquemines $18,210,964/ft $54,632,891 John Day Lock and Dam $4,919,965/9.8% delay reduction $14,759,894 Shallow Draft above Portland (Portland-Inland) $200,202/ft $600,605 Portland-Deep Draft (Portland-Coastal) $4,683,106/ft $14,049,300 Total possible budget $99,265,442 Table 21. Potential case study maintenance projects.