The notation used in the model is described below:
F, T, N, Y denote firm, technology, length of the planning horizon, and year,
respectively; δis the discount factor;
f cos tT is the fixed cost of installing technology T;
v cos tFT is the variable cost of installing technology T by firm F;
USEFTY is the utilization rate of technology T by firm F in year Y;
BUYFY and SELLFY , are the amounts of ERCs bought and sold by firm F in year Y;
SURPLUSFY is the amount of ERCs that cannot be sold (or expired) by firm F in
year Y;
emis limFY is the required reduction of NOx by firm F in year Y;
emisFT is the NOx reduction if technology T is used by firm F;
baselineF is the baseline emission level of firm F;
DFYT is a binary variable indicating whether or not technology T is adopted by firm
F in year T;
USEFTY , BUY FY , SELLFY and SURPLUSFY are all variable that are greater than or
equal to zero.
The objective function (1) represents the total cost of emission control. The
first term in the summation is the total variable cost resulting from the use of all
technologies adopted by the firms, while the second term represents the total fixed
cost of installing required equipments during the planning horizon. Variable costs are
defined as costs per ton of pollution reduction. It is determined by each firm’s
utilization rate of a given technology and depends on the efficiency of that technology
which may vary from firm to firm. Firms will incur no variable costs when LNB is
installed. The fixed cost involves annualized fixed costs assuming that most producers
would finance expensive equipments through bank loans and pay the total cost in
partial installments. Emission control equipments are durables and can be used
beyond the planning horizon. To reflect the cost and benefit situation during the
planning horizon, annual costs are incorporated in the model. Note, however, that
annualized fixed costs would be incurred throughout the entire planning horizon once
equipments are installed. The parameter emisFT measures the abatement efficiency
defined as the percentage emission reduction provided by technology T for firm F.
Equation (2) regulates the annual emission level for each firm. It means that at
the end of each year, in order to satisfy the EPA’s regulation, each firm must have
enough ERCs in hand to match its seasonal emission level. ERCs can be generated by
installing cleaner technology or by purchasing through market transactions. These two
sources on the left hand side of (2) constitute the supply side of ERCs. The permits
generated thereby can either be used to fulfill the required reduction, or sold to other