# LFSC Model Notation

## Model Indices and Sets

NotationDescription
$z \in \mathcal{Z}$$z denotes a zone and \mathcal{Z} is the set of zones in the network t \in \mathcal{T}$$t$ denotes an time step and $\mathcal{T}$ is the set of time steps
$t \in \mathcal{T}^{start}$This set of time-coupling constraints wrap around to ensure the output in the first time step of each year (or each representative period)
$t \in \mathcal{T}^{interior}$This set of time-coupling constraints wrap around to ensure the output in the inner time step of each year (or each representative period)
$f \in \mathcal{F}$Index and set of all synthetic fuels resources
$b \in \mathcal{B}$Index and set of all synthetic fuels process byproducts

## Decision Variables

NotationDescription
$x_{f,t}^{\textrm{C,Syn}}$this term represents CO2 input by synthetic fuels resource $f$ at time period $t$
$x_{f,b,t}^{\textrm{By,Syn}}$this term represents the byproducts $b$ produced by synthetic fuels resource $f$ at time period $t$
$y_{f,t}^{\textrm{C,Syn}}$capacity of synthetic fuels resources in the liquid fuels supply chain
$x_{z,t}^{\textrm{Gasoline,Conv}}$this term represents conventional gasoline purchased by zone $z$ at time period $t$
$x_{z,t}^{\textrm{Jetfuel,Conv}}$this term represents conventional jetfuel purchased by zone $z$ at time period $t$
$x_{z,t}^{\textrm{Diesel,Conv}}$this term represents conventional diesel purchased by zone $z$ at time period $t$

## Parameters

NotationDescription
$\textrm{c}_{f}^{\textrm{Syn,INV}}$investment cost per tonne CO2 input of synthetic fuels resource
$\textrm{c}_{f}^{\textrm{Syn,FOM}}$fixed operation cost per tonne CO2 input of synthetic fuels resource
$\textrm{c}_{f}^{\textrm{Syn,VOM}}$variable operation cost per tonne of CO2 input by synthetic fuels resource
$\textrm{c}_{g}^{\textrm{Syn,FUEL}}$fuel cost per tonne of CO2 input by synthetic fuels resource
$\textrm{c}_{b}^{\textrm{By,Syn}}$selling price per mmbtu of byproduct by synthetic fuels resource (if any)
$\textrm{c}_{z}^{\textrm{Gasoline,Conv}}$purchase cost per mmbtu of conventional gasoline
$\textrm{c}_{z}^{\textrm{Jetfuel,Conv}}$purchase cost per mmbtu of conventional jetfuel
$\textrm{c}_{z}^{\textrm{Diesel,Conv}}$purchase cost per mmbtu of conventional diesel
$\overline{y}_{f}^{\textrm{\textrm{C,Syn}}}$upper bound of capacity is defined,then we impose constraints on maximum CO2 input capacity of synthetic fuels resource
$\underline{y}_{f}^{\textrm{\textrm{C,Syn}}}$lower bound of capacity is defined,then we impose constraints on minimum CO2 input capacity of synthetic fuels resource