## 3 State-of-the-Art
### Biomass Supply Chains  
#### 3.4.1 Short Distance Supply Chains  
Short distance supply chains are those shorter than 50 km, or when, even if the distance is larger, only one transportation mode is used. The methodology of short distance supply chains is used for describing the process flowsheet from biomass harvesting to the stage of availability for conversion or recovery, eventually including the last stage of final consumption after conversion/recovery [119; 120; 121]. Several steps can be identified for a short distance supply chain for a biomass torrefaction unit, shown in Figure 2, where the different stages of the supply chain are listed, as well as the set of tasks associated with each stage.  
Figure 2: Definition of the different steps and options that may be present in a short distance supply chain.  
Based on the definition of the different steps and respective tasks, it is possible to calculate the costs associated with the entire operation, providing the sequence of options followed during the process, since the model allows the combination of all different options and tasks between them. The total costs associated with the supply chain are calculated using Equation (9).  
\[\text{TOC}=\text{HOC}+\text{TC}+\text{PPOC}+\text{TSC}+\text{FUOC}, \tag{9}\]  
where TOC are Total Operation Costs, HOC are Harvesting Operation Costs, TC are Transportation Costs, PPOC are Production Plant Operation Costs, TSC are Transportation and Storage Costs, and FUOC are Final Use Operation Costs.  
Each of the costs associated with each step are calculated using Equations (10)-(14).  
\[\text{HOC} = \text{Op}_{\text{n}}\,\text{Costs}\,\,(\sum_{i=1}^{\text{n}} \text{T}_{\text{n}}=\text{T}_{1}+\ldots+\text{T}_{\text{n}-1}+\,\text{T}_{ \text{n}}), \tag{10}\] \[\text{TC} = \text{Op}_{\text{n}}\,\text{Costs}\,\,(\sum_{i=1}^{\text{n}} \text{T}_{\text{n}}=\text{T}_{1}+\ldots+\text{T}_{\text{n}-1}+\,\text{T}_{ \text{n}}),\] (11) \[\text{PPOC} = \text{Op}_{\text{n}}\,\text{Costs}\,\,(\sum_{i=1}^{\text{n}} \text{T}_{\text{n}}=\text{T}_{1}+\ldots+\text{T}_{\text{n}-1}+\,\text{T}_{ \text{n}}),\] (12) \[\text{TSC} = \text{Op}_{\text{n}}\,\text{Costs}\,\,(\sum_{i=1}^{\text{n}} \text{T}_{\text{n}}=\text{T}_{1}+\ldots+\text{T}_{\text{n}-1}+\,\text{T}_{ \text{n}}),\] (13) \[\text{FUOC} = \text{Op}_{\text{n}}\,\text{Costs}\,\,(\sum_{i=1}^{\text{n}} \text{T}_{\text{n}}=\text{T}_{1}+\ldots+\text{T}_{\text{n}-1}+\,\text{T}_{ \text{n}}), \tag{14}\]  
where \(\text{Opn}\) costs are the costs associated with each of the five options and Tn corresponds to the sequence of the n tasks incorporated to pursue each option. This model includes all operations of a logistical nature, even those associated with the production process. In this way, the model intends to exhaustively describe all operations in the process, with the objective of optimizing the design and operation of the logistical process.  
The great difference between the model presented above in relation to other studies, namely those presented by [PERSON] et al. (2016), [PERSON] et al. (2017), [PERSON] et al. (2017) or [PERSON] et al. (2019), lies in the fact that these authors do not include the logistics components that occur inside the biomass recovery units in their analyses, dealing only with the logistical processes that occur outside of biomass recovery [122; 123; 124; 125]. However, it is understood that, similarly to the treatment that is given in, e.g., automotive industry, short-distance operations should be evaluated, aiming to eliminate unnecessary operations and to achieve cost reductions [126; 127; 128; 129].