The modeling exercise is predicated on the following assumptions: (1) An economically competitive technology for converting switchgrass biomass to some type of biofuel (if not cellulosic ethanol, perhaps a drop-in fuel) will be forthcoming; (2) A biorefinery will require a flow of feedstock throughout the year; (3) Switchgrass is the exclusive feedstock; (4) In the U. S. Southern Plains, the switchgrass harvest window extends from July through March; (5) Expected switchgrass biomass yield and fertilizer requirements differ by harvest month; (6) Land use services could be acquired in long term leases; (7) The biorefinery will require material to be delivered in standardized 1.22 m x 1.22 m x 2.44 m bales with no more than 15 percent moisture; (8) Harvest crews may be centrally managed; (9) The biorefinery is assumed to operate 350 days per year and require 3,630 Mg/day of switchgrass biomass. The model is based on an extension of models previously formulated by Tembo et al. (2003), Mapemba et al. (2007), Hwang (2007), Mapemba et al. (2008), Haque (2010), and Haque and Epplin (2012). It is a multi-region, multi-period, monthly time-step, mixed integer mathematical programming model and can be used to determine the cost to deliver a flow of biomass to a biorefinery.

The model was formulated to include all 77 Oklahoma counties as potential production regions and two land classes, cropland and improved pasture land. The model limits switchgrass production to no more than 10 percent of a county’s cropland and no more than 10 percent of a county’s improved pasture land based on data from the Census of Agriculture (USDA 2010). The assumption is made that cropland could be acquired for a long-term lease rate above average U. S. CRP rental rates (Data. gov 2010). The lease rate for cropland for each county was calculated by adding $49/ ha to the average CRP rental rate for that county as determined by Fewell et al. (2011). Long-term lease rates for improved pasture land are derived by adding $76/ha to the 2010 average county pasture rental rate (USDA 2010; Fewell et al. 2011). The modeled rental rates are designed to cover the opportunity costs of alternative production options and to account for increased land-lease rates that may occur in response to an entrant in the market for 10 percent of the county’s land, and to compensate for the lost option value from engaging in long term leases (Song et al. 2011).

Switchgrass biomass yield estimates for each production region were obtained from estimates produced by Oak Ridge National Laboratory (Jager et al. 2010). Yields for cropland and improved pasture land are not differentiated (U. S. Department of Energy 2011). Hwang (2007) used weather data to determine probability distributions for the number of suitable field work days per month for harvesting switchgrass for each Oklahoma county. The 95 percent probability level from the harvest day distributions is selected so that the number of harvest days per month is set to be equal to the number of days that would be suitable for harvest in 19 of 20 years. For most months, the number of mowing days exceeds the number of safe baling days.

The model simultaneously determines how many hectares from which county and which land class are optimal to harvest for each month; how much harvested biomass should be put in field storage each month; how much should be shipped to the biorefinery each month; how much should be put in biorefinery storage each month; and how much should be processed each month. The model accounts for differences in nitrogen and phosphorus fertilizer requirements depending on the month of harvest. An integer variable is included to determine the optimal number of mowing units (windrowers), and another integer variable is included to determine the optimal number of harvest units (rakes, balers, tractors, and stackers) (Table 8, 9). Thus, the model endogenously determines the number of harvest machines. Shipment and processing of biomass can be done in any of the 12 discrete periods (months of the year). In months when biomass is harvested, it may be placed in storage or transported directly from the field to the biorefinery. The harvest season extends from July through March of the following year.

The modified Wang (2009) transportation cost equation used for the budget reported in Table 5 is also used in the modeling exercise. Transportation costs depend on the distance the feedstock will be shipped from the fields to the biorefinery. The distance between any biomass supplying county and any plant location is estimated by the distance from the county’s central point to the plant location. Storage losses at the biorefinery and in the field are assumed to be one percent per month (Hwang 2007). Another assumption is that bales stored in the field would be covered with a plastic tarp. The cost of field storage is estimated to be $1.79/Mg regardless of the number of months the material is in storage (Hwang 2007).