Preliminary Transportation Cost Model for OPLB

Transcription

1 Preliminary Transportation Cost Model for OPLB Prepared by R.I. Carreira, H.L. Goodwin, and K.B. Young November 11, 2004 Note: See attached MS Excel spreadsheet: GAMS Solution-concise.XLS

2 Introduction A mathematical programming model was developed to determine the minimum cost of transporting poultry litter outside of two watersheds located in the Northwest Arkansas/ Eastern Oklahoma regions: the Eucha-Spavinaw Watershed (ESW) and the Illinois River Watershed (IRW). Only raw broiler and turkey litter were considered in this initial model. The model was developed and solved using the General Algebraic Modeling System software, commonly known as GAMS. The present report describes the assumptions used in the model, parameters, different scenarios considered, and the preliminary solutions obtained. Model Construction Nutrients Considered As this time, the model considers nitrogen, phosphorus, potassium, and calcium in terms of litter content and crop requirements, although the only constraining nutrient is phosphorus. The nutrient content of litter by bird type assumed in the model is presented in Table 1. Table 1. Nutrient Content of Litter by Bird Type (Lbs/Ton) Assumed in Model 1 N P K C Broiler Turkey Source: VanDevender, K. (2000) Litter Sources In the ESW, it is estimated that there are 94,132 tons of broiler litter and 13,268 tons of turkey litter produced annually; in the IRW, broiler litter amounts to 164,696 tons and turkey litter amounts to 39,810 tons as reported in Deliverable 1 (MS Excel spreadsheet, sorted by source and type of poultry litter, that quantifies the amount of poultry litter produced in the watersheds mentioned above). The source towns for litter in the two watersheds considered are Jay, Decatur, Siloam Springs, and Prairie Grove. Geographic details regarding these town sources are reported on Table 2. The minimum amount of litter required to be transported out of each watershed was set exogenously and several scenarios were investigated. One of the constraints 1

3 in the model forced the amount of litter coming out of the ESW to be divided as one third coming out of Decatur and the remaining two thirds out of Jay. All costs considered in the model refer to the transport cost of moving the litter from these town sources. However, we assume that there is a minimum charge of $100 for transporting litter by truck (both for truck only shipments and truck-barge shipments), i.e., any trip where litter is transported by truck will cost at least $100 independently of its start and destination. Table 2. Sources of Poultry Litter Considered in Initial Transportation Model Town Source County State Watershed Siloam Springs Benton Arkansas IRW Prairie Grove Washington Arkansas IRW Jay Delaware Oklahoma ESW Decatur Benton Arkansas ESW Market Destinations Eight counties, as described in Table 3, were identified as potential initial market destinations for the litter, as determined in focus groups held in Arkansas, Missouri, and Oklahoma. For simplicity, it was assumed that the litter would be delivered to the county seat of the respective county market. Table 3. Markets for Poultry Litter Considered in Initial Transportation Model County Seat County State Lonoke Lonoke Arkansas Stuttgart Arkansas Arkansas Clarendon Monroe Arkansas Nevada Vernon Missouri Muskogee Muskogee Oklahoma Newport Jackson Arkansas Harrisburg Poinsett Arkansas Blytheville Mississippi Arkansas From the 1997 Census of Agriculture, data were collected referring to the acreage in each market county being harvested for corn, silage, soybean, rice, wheat, cotton, and sorghum. These data were combined with nutrient application rates (nutrients considered were nitrogen, phosphorus, potassium, and calcium) for each of these crops recommended by University of Arkansas Extension publications to produce a table that contains the amount of nutrients required at each 2

4 destination market (Deliverable 1). Part of this acreage was assumed to be cut land. The application rate of poultry litter to cut land was assumed to be 1 ton/acre, as advised by soil scientists. The availability of land in each market county by land type is reported in Table 4. Table 4. Available Acreage by Market and Land Type Considered in Model Market Cut Land 1 Non-Cut Land Lonoke 4, ,618 Arkansas ,570 Monroe 1, ,772 Vernon 0 128,746 Muskogee 0 38,357 Jackson 3, ,273 Poinsett 1, ,563 Mississippi 2, ,700 Note: 1. See Young, Goodwin, and Wailes, Transportation Methods Two alternative transportation methods were investigated: transportation by truck and a combination of truck and barge (initially it was intended for the model to include transportation by rail but attempts to gather the necessary information failed due to lack of cooperation on the part of the rail companies). It was assumed that the capacity of the trucks was 22 tons and barge capacity was 1496 tons (note that the actual capacity of the barge is 1500 tons; however, previous contacts with the trucking companies indicated that full loads were preferable to partial loads, thus we assumed the barge capacity is a multiple of the truck capacity). The outgoing and incoming ports for litter considered in barge transportation are reported in Table 5. Table 5. Ports Considered in Truck/Barge Transportation Combination Port River County State Outgoing Barge Ports Catoosa Verdigris Rogers Oklahoma Fort Smith Arkansas Crawford Arkansas Incoming Barge Ports Pendleton Arkansas Lincoln Arkansas Pine Bluff Arkansas Jefferson Arkansas Little Rock Arkansas Pulaski Arkansas Hickman Mississippi Mississippi Arkansas 3

5 Parameters Distances Distances between litter sources and markets as well as between litter sources and outgoing ports and incoming ports and markets were obtained through Mapquest. Barge distances between outgoing and incoming ports were obtained from the Corps of Engineers. Costs Transportation costs were obtained by contacting trucking companies and barge transportation companies. When shipping by truck, it was assumed that a short haul (less than 100 miles) was more expensive than a long haul on a per mile basis ($3 vs. $2.50 per loaded mile). This assumption is consistent with the information obtained from the companies contacted for a deadhead haul. Transportation costs by truck are reported in Table 6. Table 6. Cost per Ton of Transporting Litter by Truck Source \ Market Lonoke Arkansas Monroe Jackson Poinsett Mississippi Vernon Muskogee Siloam-Springs $26.85 $31.43 $31.90 $37.58 $34.26 $45.03 $15.29 $11.07 Prairie-Grove $23.64 $28.22 $28.69 $34.37 $31.05 $41.82 $17.40 $10.01 Jay $29.80 $34.38 $34.85 $40.52 $37.21 $47.97 $14.92 $11.47 Decatur $27.90 $32.47 $32.94 $38.62 $35.31 $46.07 $13.59 $12.94 Barge transportation cost included a combined loading/unloading charge for crane use of $5/ton of litter at both ports and a transportation charge of approximately $0.013/ton per mile along barge route. Barge-truck transportation costs are reported in Tables 7, 8, 9, and 10. The model does not include per ton costs related to unloading at demand points, storage of litter at barge loading points or truck unloading points, or additional cleaning of trucks after litter transport. Costs for unloading at demand points would be borne by the end-user. Note that these costs can be considered uniform across locations and do not change the optimal destinations selected by the model. Storage costs at barge loading sites would be dependent upon availability of storage facilities; estimates for construction of such facilities are approximately $120,000 for a one barge capacity structure. Additional truck cleaning costs after litter transport would depend upon 4

6 requirements of backhauls agents and recipients; backhauls are not considered in this initial modeling effort. Table 7. Cost of Transporting One Ton of Litter by Truck and Barge from Siloam Springs, AR Market: Lonoke Arkansas Monroe Jackson Poinsett Mississippi Vernon Muskogee In Port Out Port Catoosa Little-Rock $24.48 $26.33 $29.07 $31.93 $32.91 $40.67 $58.14 $46.57 Catoosa Pine-Bluff $29.73 $25.57 $28.28 $35.48 $38.46 $46.36 $62.81 $51.24 Catoosa Pendleton $33.95 $27.95 $30.56 $41.49 $38.94 $33.95 $68.82 $57.25 Catoosa Hickman $44.33 $44.69 $41.49 $40.52 $36.20 $29.07 $71.88 $72.09 Fort-Smith Little-Rock $21.35 $23.20 $25.94 $28.80 $29.78 $37.54 $55.01 $43.44 Fort-Smith Pine-Bluff $26.57 $22.41 $25.13 $32.32 $35.30 $43.20 $59.65 $48.08 Fort-Smith Pendleton $30.82 $24.82 $27.43 $38.36 $35.81 $42.61 $65.69 $54.12 Fort-Smith Hickman $41.20 $41.56 $38.36 $37.39 $33.07 $25.94 $68.75 $68.96 Table 8. Cost of Transporting One Ton of Litter by Truck and Barge from Prairie Grove, AR Market: Lonoke Arkansas Monroe Jackson Poinsett Mississippi Vernon Muskogee In Port Out Port Catoosa Little-Rock $25.79 $27.64 $30.37 $33.24 $34.22 $41.98 $59.45 $47.88 Catoosa Pine-Bluff $31.03 $26.87 $29.59 $36.79 $39.77 $47.67 $64.12 $52.55 Catoosa Pendleton $35.26 $29.26 $31.87 $42.80 $40.24 $35.26 $70.13 $58.56 Catoosa Hickman $45.64 $46.00 $42.80 $41.83 $37.50 $30.38 $73.19 $73.40 Fort-Smith Little-Rock $19.97 $21.82 $24.56 $27.42 $28.40 $36.16 $53.64 $42.06 Fort-Smith Pine-Bluff $25.19 $21.03 $23.75 $30.95 $33.93 $41.83 $58.28 $46.70 Fort-Smith Pendleton $29.44 $23.44 $26.05 $36.98 $34.43 $41.24 $64.31 $52.74 Fort-Smith Hickman $39.82 $40.18 $36.98 $36.01 $31.69 $24.56 $67.37 $67.58 Table 9. Cost of Transporting One Ton of Litter by Truck and Barge from Jay, OK Market: Lonoke Arkansas Monroe Jackson Poinsett Mississippi Vernon Muskogee In Port Out Port Catoosa Little-Rock $24.88 $26.73 $29.47 $32.33 $33.31 $41.07 $58.55 $46.98 Catoosa Pine-Bluff $30.13 $25.97 $28.69 $35.88 $38.86 $46.76 $63.21 $51.64 Catoosa Pendleton $34.35 $28.35 $30.96 $41.90 $39.34 $34.35 $69.22 $57.65 Catoosa Hickman $44.73 $45.09 $41.89 $40.93 $36.60 $29.47 $72.28 $72.50 Fort-Smith Little-Rock $23.39 $25.23 $27.97 $30.84 $31.82 $39.58 $57.05 $45.48 Fort-Smith Pine-Bluff $28.61 $24.45 $27.16 $34.36 $37.34 $45.24 $61.69 $50.12 Fort-Smith Pendleton $32.86 $26.85 $29.47 $40.40 $37.84 $44.65 $67.73 $56.16 Fort-Smith Hickman $43.24 $43.60 $40.40 $39.43 $35.10 $27.98 $70.79 $

7 Table 10. Cost of Transporting One Ton of Litter by Truck and Barge from Decatur, AR Market: Lonoke Arkansas Monroe Jackson Poinsett Mississippi Vernon Muskogee In Port Out Port Catoosa Little-Rock $26.35 $28.20 $30.94 $33.80 $34.78 $42.54 $60.02 $48.45 Catoosa Pine-Bluff $31.60 $27.44 $30.16 $37.35 $40.33 $48.23 $64.68 $53.11 Catoosa Pendleton $35.82 $29.82 $32.43 $43.37 $40.81 $35.82 $70.69 $59.12 Catoosa Hickman $46.20 $46.56 $43.36 $42.40 $38.07 $30.94 $73.75 $73.97 Fort-Smith Little-Rock $23.09 $24.94 $27.68 $30.54 $31.52 $39.28 $56.75 $45.18 Fort-Smith Pine-Bluff $28.31 $24.15 $26.87 $34.06 $37.04 $44.94 $61.39 $49.82 Fort-Smith Pendleton $32.56 $26.56 $29.17 $40.10 $37.55 $44.35 $67.43 $55.86 Fort-Smith Hickman $42.94 $43.30 $40.10 $39.13 $34.81 $27.68 $70.49 $70.70 Mathematical Model Objective Function As stated above, the objective of the model is to find the quantities of litter to export from each town source to each county market to minimize the total transportation costs subject to the model constraints as described below. At this point no market prices for litter were included in the model because this information is still being collected. Equations/Constraints 1. Minimum Removal Constraint The first constraint introduced in the model is related to the removal of litter from each watershed. This constraint assures that the total amount of litter removed from each watershed cannot be less than the minimum removal specified in the model. There are three different minimum removal levels for each watershed, thus nine different litter removal scenarios were investigated as stated in Table 11. The levels for the ESW watershed correspond to 30, 50 and 70 percent of the total litter produced in the watershed. The removal levels reported in Table 11 for the IRW were based upon voluntary levels specified by the integrators for targeted removal. 6

8 Table 11. Poultry Litter Removal Scenarios for Eucha-Spavinaw and Illinois River Watersheds (Tons) Scenario\Watershed ESW IRW i 35, ,000 ii 35, ,500 iii 35, ,000 iv 59,712 45,000 v 59,712 67,500 vi 59,712 90,000 vii 83, ,000 viii 83, ,500 ix 83, , Litter Supply Constraint The second constraint assures that the amount of litter removed from each watershed for each bird species does not exceed the total amount of litter produced in the watershed as specified in the Litter Sources section. 3. Litter Demand Constraint It was assumed that any county market destination could not receive more that 30,000 tons of poultry litter. 4. Cut Land Constraint Cut lands (laser leveled) in the Arkansas Delta comprise a majority of the existing markets for raw poultry litter, both in terms of quantity of litter and longevity of market exposure. For this reason, cut lands are considered an already developed market. This constraint has two distinct forms: the first is that cut land receives litter first, thus all cutland receives the maximum amount of litter possible at the rate of 1 ton/acre. In the second form, cut land was not assigned any priority in the application of litter. These two cut land scenarios combined with the nine watershed removal scenarios described above yield a total of 18 possible models. 5. Phosphorus Constraint With this constraint, litter cannot be applied to the soil such that the total phosphorus content exceeds the recommended phosphorus application rate for each crop in each market destination. 7

9 6. Eucha-Spavinaw Watershed Constraint With respect to the amount of litter removed from the Eucha-Spavinaw Watershed, one third must be transported out of Jay and the remaining out of Decatur. 7. Integer Constraints These constraints assure that litter must be transported in such a way that, for all the optimal routes, trucks and barges are always transported full. Mixed Integer Programming (MIP) Algorithm As stated earlier, the above model was solved using GAMS. Because we imposed integer conditions, i.e., barges and trucks had to be transported at full capacity, the problem is a mixed integer programming problem and not a linear programming one. This has several implications: firstly, the model becomes harder to solve in terms of finding a good solution the choice of the algorithm matters; secondly, it takes a lot longer to find a solution; thirdly, even if a solution is found it may not be the global optimal solution; and fourth, with MIP (mixed integer programming) the shadow prices 1 cannot be interpreted. Thus, and given the high number of scenarios, the best approach is to pick an algorithm and calibrate it such that it finds a good integer solution (not necessarily the global optimum, see Kalvelagen, 2004 for more details). GAMS/XA is a linear and mixed-integer programming solver which handles large scale MIP problems. It is a fairly robust solver and it allows the user to fine-tune the quality of the solution. The relative gap between the best identified solution and the best possible solution for this analysis was set at 7 percent, meaning that the obtained solution is either the best solution or it is within 7 percent of the best solution. 1 A shadow price is a marginal cost representing the change in the objective function, in this case transportation cost, due to a one-ton-increase in the quantity of litter demanded at the market site (Baker, 2000). 8

10 Model Results Concise solutions for the 18 models considered are contained in the Excel spreadsheet GAMS Solution-concise.XLS. The solutions track how much litter goes from each source to each destination, route, transportation method (by truck or by truck-barge-truck), type of litter (broiler or turkey), and what type of land it should be applied to (cut land or non-cut land). In addition, the solutions report the number of barges and trucks needed for its implementation. Please refer to the attached spreadsheet for the detailed concise solutions. This report contains only summary tables, which do not contain information regarding the specific routes. As stated earlier, the nature of the model requires the use of mixed integer programming which is difficult to solve for an optimal solution. The solutions presented may be the optima or are within 7 percent of the optima. Discussion of Findings The routes selected by the GAMS/XA algorithm are directly related to the transportation costs of litter which were presented in tables 6 to 10. The cheapest destination for transporting a ton of litter is Muskogee County (OK) by truck, independent of the source. The next cheapest option is Vernon County (MO), also by truck. These two options cost less than $20/ton (Table 6); the relatively low transportation cost is a direct consequence of their proximity to Northwest Arkansas. Within Arkansas, the cheapest destination by truck is Lonoke County with cost ranging between $24 and $28/ton followed by Arkansas and Monroe counties, with truck transportation cost ranging between $28 and $35/ton (Table 6). A cheaper option than truck in terms of cost would be to use a truck-barge combination within the state of Arkansas: for example, the per ton cost of moving from Prairie Grove to Lonoke is less than $20; roughly $21 will ship it from Prairie Grove to Arkansas County (Table 8). In the Illinois River Watershed, it is always cheaper to ship from Prairie Grove than it is from Siloam Springs (Table 6); thus, in all scenarios most of the litter is exported from Prairie Grove (Tables 12 to 15). Clearly, shipping litter to Muskogee and Vernon Counties via truck is comparatively more advantageous in terms of transportation cost. Therefore, these destinations were selected in all scenarios studied. Truck/barge combination was the selected transportation method to ship most 9

11 of the litter within Arkansas. In all scenarios, a small amount of litter was transported within Arkansas using only trucks despite the higher cost because the total amounts of litter were not sufficient to fill a barge and we imposed conditions that did not allow partial-barge transportation. Because in all scenarios we use a combination of truck/barge and truck-only transportation and because Vernon and Muskogee Counties are comparatively cheap destinations, the average transportation cost is much lower than if only one of the transportation methods was used. Thus, the cost of transporting one ton of litter varies between roughly $16 and $21 (Table 16). As we increase the total amount of litter to be shipped, the transportation cost increases as cheaper destinations are saturated and the litter must be transported farther. These results are consistent with previous work by Wimberly and Goodwin (2000). With respect to the cutland priority constraint, by forcing cut land to receive litter first the transportation cost is increased slightly (Table 16). For the scenarios tested, the value of this difference varies between around $8,000 and $90,000 in total transportation cost; on a per ton basis, this difference is less than $1. It makes sense for this to happen. More cut land is located in Eastern Arkansas and it is more costly to ship litter over there because of the greater distance. For example, without cut land priority, Poinsett County only receives litter in scenario ix, but with cut land priority it enters the solution in all scenarios. Note that the more binding constraints an optimization model contains, the worse is its solution. However, the phosphorus constraint was not binding given that we had imposed that no more than 30,000 tons of litter is shipped to any location. Conclusions The two main points that result from the analysis is that (a) combining cheap and expensive destinations reduces average transportation cost of transporting raw poultry litter, thus allowing for more litter to be transported farther and (b) by combining truck and truck/barge transportation we also reduce the average cost of transporting one ton of litter. Thus the selection of which markets to ship to and the transportation method used in each route is essential in minimizing total transportation cost. The significant increase in cost to ship litter to Eastern Arkansas 10

12 compared with shorter distance markets in Missouri and Oklahoma suggests that Eastern Arkansas farmers will have to pay substantially more to get litter or a major subsidy will be required to offset the increased transportation cost. The preliminary nature of this analysis yields insight as to potential results from future more complex modeling efforts. Future modeling efforts will attempt to: 1) introduce time and possible seasonal variations in litter deliveries based upon crop demand; 2) quantify potential backhaul opportunities; 3) incorporate differential costs for delivery of litter to centralized storage facilities at demand sites; 4) optimize the transportation model results utilizing actual market prices elicited from end-users in the various markets; and 5) consider shipping both pelleted litter and raw litter packaged in bales with plastic over-wraps. 11

13 Table 12. Tons of Litter Transported by Truck under Each Scenario by Source, Market, Bird Type, and Land Type with Cut Land Priority as Determined by the GAMS/XA Algorithm (See Table 12 for Truck/Barge Transportation for Each Model) Source Scenario Scenario i Scenario ii Scenario iii Scenario iv Scenario v Scenario vi Scenario vii Scenario viii Scenario ix Removal: Removal: Removal: Removal: Removal: Removal: Removal: Removal: Removal: ESW:35,827 ESW:35,827 ESW:35,827 ESW: 59,712 ESW:59,71 ESW: 59,712 ESW: 83,597 ESW: 83,597 ESW: IRW: 45,000 IRW: 67,500 IRW: 90,000 IRW: 45,000 2 IRW: 67,500 IRW: 90,000 IRW: 45,000 IRW: 67,500 83,597 IRW: 90,000 Siloam Springs Prairie Grove 10,362 10,318 10, Jay 12,430 10,736 10,604 14,762 16,192 16,170 16,214 16,214 16,192 Decatur 23,936 23,892 23,892 28,666 30,228 29,964 28,864 29,942 28, Market Vernon 29,986 28,820 29,986 28,666 29,260 29,964 28,886 29,964 28,776 Muskogee 16,192 16,170 14,850 14,740 16,170 16,170 16,170 16,170 16,192 Monroe Jackson Mississippi Lonoke Poinsett Arkansas Bird Turkey 13, ,266 10,494 1, Broiler 33,440 44,858 31,570 32,934 45,408 46,442 45,034 46,288 44,946 Land Non-Cut Land 46,696 44,990 44,836 43,406 45,430 46,508 45,078 46,398 44,968 Cut Land ,

14 Table 13. Tons of Litter Transported by Truck & Barge under Each Scenario by Source, Market, Bird Type, and Land Type with Cut Land Priority as Determined by the GAMS/XA Algorithm (See Table 11 for Truck Transportation for Each Model) Source Scenario Scenario i Scenario ii Scenario iii Scenario iv Scenario v Scenario vi Scenario vii Scenario viii Scenario ix Removal: Removal: Removal: Removal: Removal: Removal: Removal: Removal: Removal: ESW:35,827 ESW:35,827 ESW:35,827 ESW: 59,712 ESW:59,71 ESW: 59,712 ESW: 83,597 ESW: 83,597 ESW: IRW: 45,000 IRW: 67,500 IRW: 90,000 IRW: 45,000 2 IRW: 67,500 IRW: 90,000 IRW: 45,000 IRW: 67,500 83,597 IRW: 90,000 Siloam Springs , , Prairie Grove 34,606 56,848 79,640 45,034 67,474 88,176 46,728 67,254 89,980 Jay 22 1,210 1,342 5,148 3,718 3,740 11,660 11,660 11,682 Decatur ,154 9,592 9,856 26,884 25,806 26, Market Vernon Muskogee Monroe 968 2,024 14,542 1,012 14,872 29,568 17,556 29,502 29,986 Jackson 3,520 3,520 3,542 4,994 3,520 3,520 3,542 3,586 6,270 Mississippi 4,004 2,992 3,014 2,508 2,508 8,976 2,992 10,472 29,986 Lonoke 25,674 29,678 29,986 29,986 28,688 29,942 29,986 29,964 29,788 Poinsett 1,210 1,210 1,210 1,210 1,210 1,232 1,210 1,210 2,640 Arkansas ,920 29,986 21,626 29,986 29,986 29,986 29,986 29,986 Bird Turkey 10,472 8,976 14,960 31,416 16,456 49,368 14,960 19,448 52,360 Broiler 25,432 49,368 67,320 29,920 64,328 53,856 70,312 85,272 76,296 Land Non-Cut Land 23,158 45,566 69,480 48,558 69,018 90,424 72,472 91, ,856 Cut Land 12,746 12,778 12,800 12,778 11,766 12,800 12,800 12,778 12,800

15 Table 14. Tons of Litter Transported by Truck under Each Scenario by Source, Market, Bird Type, and Land Type without Cut Land Priority as Determined by the GAMS/XA Algorithm (See Table 14 for Truck/Barge Transportation for Each Model) Source Scenario Scenario i Scenario ii Scenario iii Scenario iv Scenario v Scenario vi Scenario vii Scenario viii Scenario ix Removal: Removal: Removal: Removal: Removal: Removal: Removal: Removal: Removal: ESW:35,827 ESW:35,827 ESW:35,827 ESW: 59,712 ESW:59,71 ESW: 59,712 ESW: 83,597 ESW: 83,597 ESW: IRW: 45,000 IRW: 67,500 IRW: 90,000 IRW: 45,000 2 IRW: 67,500 IRW: 90,000 IRW: 45,000 IRW: 67,500 83,597 IRW: 90,000 Siloam Springs Prairie Grove 9,130 10,340 10, Jay 11,902 10,758 9,812 16,236 14,960 16,192 16,236 16,214 16,214 Decatur 23,892 23,892 23,892 28,688 29,986 28,820 28,578 30,184 30, Market Vernon 28,732 28,820 27,918 28,710 29,986 28,820 28,622 29,986 29,986 Muskogee 16,170 16,192 16,170 16,170 14,960 16,170 16,192 16,170 16,192 Monroe Jackson Mississippi Lonoke Poinsett Arkansas Bird Turkey 13, , , ,176 3,674 Broiler 31,636 44,946 44,000 34,606 44,924 32,340 44,770 35,244 42,790 Land Non-Cut Land 44,946 45,012 44,088 44,880 44,968 44,990 44,814 46,354 46,222 Cut Land

16 Table 15. Tons of Litter Transported by Truck & Barge under Each Scenario by Source, Market, Bird Type, and Land Type without Cut Land Priority as Determined by the GAMS/XA Algorithm (See Table 13 for Truck Transportation for Each Model) Source Scenario Scenario i Scenario ii Scenario iii Scenario iv Scenario v Scenario vi Scenario vii Scenario viii Scenario ix Removal: Removal: Removal: Removal: Removal: Removal: Removal: Removal: Removal: ESW:35,827 ESW:35,827 ESW:35,827 ESW: 59,712 ESW:59,71 ESW: 59,712 ESW: 83,597 ESW: 83,597 ESW: IRW: 45,000 IRW: 67,500 IRW: 90,000 IRW: 45,000 2 IRW: 67,500 IRW: 90,000 IRW: 45,000 IRW: 67,500 83,597 IRW: 90,000 Siloam Springs Prairie Grove 35,860 56,870 80,146 45,012 67,496 89,980 44,968 67,496 89,980 Jay 44 1,188 2,134 3,674 4,950 3,718 11,638 11,660 11,660 Decatur ,132 9,834 11,000 27,170 25,564 25, Market Vernon Muskogee Monroe , ,308 29,788 23,804 29,766 29,964 Jackson ,452 8,756 Mississippi 0 1,496 1, , ,552 28,424 Lonoke 29,920 28,424 29,612 29,986 29,986 29,986 29,986 29,964 29,986 Poinsett Arkansas 5,984 28,424 29,986 29,854 29,986 29,986 29,986 29,986 29,986 Bird Turkey 34,408 25,432 41,888 2,992 43,384 40,392 40,392 41,888 49,368 Broiler 1,496 32,912 40,392 56,848 38,896 64,328 43,384 62,832 77,792 Land Non-Cut Land 31,304 53,722 76,162 55,240 76,680 96,620 78,198 95, ,266 Cut Land 4,600 4,622 6,118 4,600 5,600 8,100 5,578 9,508 10,894

17 Table 16. Summary Solution for the Litter Transportation Models as Determined by the GAMS/XA Algorithm Scenario Scenario i Scenario ii Scenario iii Scenario iv Scenario v Scenario vi Scenario vii Scenario viii Scenario ix Removal: Removal: Removal: Removal: Removal: Removal: Removal: Removal: Removal: ESW:35,827 ESW:35,827 ESW:35,827 ESW:59,712 ESW: 59,712 ESW: 59,712 ESW: 83,597 ESW: 83,597 ESW: 83,597 Variable IRW: 45,000 IRW: 67,500 IRW: 90,000 IRW: 45,000 IRW: 67,500 IRW: 9,000 IRW: 45,000 IRW: 67,500 IRW: 90,000 Solution for Models Where Cut Land Receives Litter First 16 Total cost $1,390,021 $1,819,853 $2,362,272 $1,946,606 $2,416,348 $2,940,781 $2,554,978 $3,042,241 $3,626,644 Tons of litter transported by truck 46,750 45,012 44,836 43,428 46,464 46,508 45,078 46,420 44,968 Tons of litter transported by truck/barge 35,904 58,344 82,280 61,336 80, ,224 85, , ,656 Total Tons of litter transported 82, , , , , , , , ,624 Average cost $16.82 $17.61 $18.58 $18.58 $18.99 $19.64 $19.60 $20.13 $20.89 Solution for Models Where Cut land Does Not Have Priority Receiving Litter Total cost $1,294,244 $1,775,437 $2,336,377 $1,852,637 $2,392,433 $2,930,516 $2,502,733 $3,033,796 $3,608,258 Tons of litter transported by truck 44,946 45,012 44,088 44,924 44,968 45,012 44,858 46,420 46,464 Tons of litter transported by truck/barge 35,904 58,344 82,280 59,840 82, ,720 83, , ,160 Total tons of litter transported 80, , , , , , , , ,624

18 17 Average Cost $16.01 $17.18 $18.49 $17.68 $18.80 $19.57 $19.46 $20.07 $20.78

19 References Baker, K Gaining Insight in Linear Programming from Patterns in Optimal Solutions. INFORMS Transactions on Education, 1(1). Kalvelagen, E Model Building with GAMS. Mapquest VanDevender, K University of Arkansas Cooperative Extension Service. Wimberly, J. and H.L. Goodwin Eucha/Spavinaw Watershed Raw Litter Marketing Plan. Report prepared for the Tulsa Metropolitan Utility Authority. Young, K.B. H.L. Goodwin, E.J. Wailes Economics of Poultry Litter Use on Cut Rice Fields. AAES Research Series 517, University of Arkansas. 18