(459b) Improving the Location Robustness of Spatially Distributed Variables for Biomass Supply Chains Under Supply Uncertainty

Due to climate change and other issues surrounding fossil fuels, finding alternative fuels and feedstocks is of vital importance. By expanding the role of the bioeconomy, biomass can be utilized as a substitute for both uses. Supply chain optimisation (SCO) is a method that can been used to help the biomass industry gain a foothold and expand while remaining economically viable. One issues is while supply chain network optimization offers a dependable method of searching a large solution space to find results that are feasible and maximized (or minimized) for the objective function, it does have a weakness in that small differences in initial conditions can cascade and result in non-negligible variations in the form of the optimized result. Frequently the actual value of the objective is similar for small differences in initial conditions, but the organization of the network that is recommended by the optimization can be measurably different. Spatially distributed variables can be noticeably different for different starting conditions.

Spatially distributed variables are variables in the biomass supply chain optimisation which may be distributed over the real map space, such as locations to build biochemical plants, locations for feedstock storage, or locations to grow biomass. These variables are decided in the process of optimising the supply chain for the objective variable – whether to place a plant in a specific location, or how much biomass to grow in each location. Each potential organisation is a solution which will have different values of the objective variable. These spatially distributed variables can be sensitive to changes in input values, as the supply chain optimises for the new starting conditions. The new optimal solution recommends placing refineries, storage facilities and growth sites in different locations depending on the starting conditions. Ideally these variables would be locationally robust.

Location robustness is the idea that there should be some consistency in the final design of the optimised supply chain for minor variation in the inputs. Input variation is bound to happen, and ideally these supply chain designs should be able to perform to a high level regardless of the variation in input. For some applications this is not a significant concern; for high investment situations, this may be problematic. A final supply chain design can be very expensive and time-consuming to implement, and a design which is optimal for the given input but is sensitive to variations in that input would be less useful than designs which can perform across a range of conditions. When a company is deciding where to locate refineries, where to grow crops or where to store products, the investment demands that a location be viable regardless if the input prices or yield rates vary slightly.

One major source of input variation for these supply chain systems is from uncertainty in the supply of biomass, such as year-to-year variation in biomass yield, or in land quality drift due to environment changes. It is also one that is particularly difficult to control – weather is still a factor in the productivity of farming. Biomass yield is a key input for biomass supply chains, which can have cascading impacts on the final biomass supply chain design. Understanding how uncertainty from this input in particular can be mitigated is key to designing supply chain frameworks and supply chains which are locationally robust.

This work seeks to develop a biomass supply chain optimization framework that considers location robustness as part of the framework. The work first seeks to identify the causes of this locational instability within some supply chain frameworks to understand how this arises. It then develops techniques that may be more locationally consistent due to the construction of the framework.

Biomass supply chain models often use the mean biomass yield of cellularised tracts of land to calculate yield for that cell. However, there can be large variety in the biomass yield within those tracts, losing useful information to aggregation and simplification. A biomass SCO framework has been developed which can incorporate some of this information about the quality of land available by piecewise linearly approximation of the biomass yield distribution, and incorporating this information into the optimisation. Using linear approximations of the biomass yield distributions allows the SCO model to make more accurate decisions about quantity and location of biomass growth operations, thereby affecting all downstream decisions as well. It is postulated that providing the optimisation with the option to focus on developing high yield land, that high quality land will be used more consistently. This would have the dual effects of being more reasonable from a development perspective – better to develop high quality land – and of potentially increasing the locational robustness. The good land will be used preferentially, reducing the number of new or different areas which may be developed for biomass growth under supply uncertainty.

A case study of the United Kingdom for potential biomass industry viability will be examined using the framework to illustrate the impact of retaining this biomass yield information in the optimisation. Initial results indicate that using the more accurate biomass yield estimates reduced the land overall usage. The framework results in a better use of the available land to meet available demands, reducing land use. Further, it allows for improved biomass output, which in turn increased the quantity of bioproducts which can be produced. All of this leads to an increase in the overall profit. The next step is to implement supply uncertainty and to examine the locational robustness of the framework with respect to these variations. This framework could be used with other optimisations with spatially distributed resources, where more detailed information could improve results, such as solar insolation or wind resource availability.