Analyzing the Trade-Offs between Meeting Biorefinery Production Capacity and Feedstock Supply Cost: A Chance Constrained Approach

Commercial-scale switchgrass production for cellulosic biofuel remains absent in U.S. A well-recognized difficulty is the steady provision of high-quality feedstock to biorefineries. Switchgrass yield is random due to weather and growing conditions, with low yields during establishment years. Meeting biorefinery production capacity requirements 100% of the time or at any other frequency requires contracting sufficient amount of agricultural land areas to produce feedstock. Using chance-constrained programming, the trade-offs between the degree of certainty that refinery demand for feedstock and the cost of contracting production acreage is assessed. Varying the certainty from 60% to 95%, we find the costs of production, logistics and transportation ranged from 27% to 96% of the cost of 100% certainty. Investors and managers need to consider the cost of certainty of biomass acquisition when contracting for production acreage.

A Unified Mathematical Model for Stochastic Data Envelopment Analysis

Efficiency measurement is one aspect of organizational performance that managers are usually interested in determining. Data envelopment analysis (DEA) is a powerful quantitative tool that provides a means to obtain useful information about the efficiency and performance of organizations and all sorts of functionally similar, relatively autonomous operating units. DEA models are either with a constant rate of return (CRS) or variable return to scale (VRS). Furthermore, the models could be input-oriented or output-oriented. In many real-life applications, observations are usually random in nature; as a result, DEA efficiency measurement may be sensitive to such variations. The purpose of this study was to develop a unified stochastic DEA model that handles different natures of variables independently (random and deterministic) and can be adapted to model both input/output-oriented problems, whether it is CRS or VRS. The chance-constrained approach was adopted to handle the stochastic variables that exist in the model. The developed model is implemented through an illustrative example.