A linear programming approach for designing a herbaceous biomass delivery system

There are a number of systems-related issues associated with the harvest, storage, and transport of herbaceous biomass from on-farm storage locations to a centrally located plant. This modeling effort is directed toward the design of a biomass delivery system that considers storage, scheduling, and transportation issues. A statement of the problem, along with its salient characteristics, is presented, and a linear programming model is constructed. Uncertainty in production levels due to weather is addressed by reformulating the linear program as a two-stage problem with recourse. A specific case-study of a plant located in a country in the Piedmont of Virginia is described. The data for this study includes 20 producers having four to seven storage locations each. The model was solved using this data set and appropriate sensitivity analyses were conducted to illustrate the range of decision-making options that are available. The model minimized delivered cost by scheduling shipments from the various on-farm storage locations to meet a 5600 dry Mg monthly demand. The total cost (ownership+operating+labor) was $500/day/truck, and the resultant average cost of transportation ranged from $8 to $10/dry Mg. The average travel distance (farm+secondary+primary roads) was found to be 22 km for delivering the 67 200 dry Mg required for a year-round operation.