The Industria

Integrated Solu

Model: Math

Framew

Ravi K. Sriva

Air Pollution Prevention an

National Risk Management 

Office of Research & 

EPA

Elineth To

Office of Air Quality Plann

EPA

Samudra V

Sam Analy

March 18, 
ISIS Development Tea

• ORD – Ravi Srivastava, Will Ye

• OAQPS

Overall coordination: Elineth TorresISIS

‐Cement: Elineth Torres, Keith Bar

ISIS

‐Iron

& Steel: Matt Witosky, Donn

ISIS

‐Pulp

& Paper: Elizabeth Palma

Cost development: Tom Walton, Larry 

Charlie Fulcher

• Contractors

– Sam Analytics, Andover Technology P

Burtraw, RTI, Arcadis
Acknowledgements

• Dr. Dallas Burtraw et al., RFF• Dr. Richard Newell, Duke Univ• Dr. Elliott Lieberman, EPA/OA• Dr. Hendrik G. van Oss, USGS
ISIS: Broad Framework

• Objective – maximize total surplus over the 

interest, subject to:

– meeting the demand for the sector-specific com– satisfying any sector-specific emissions related 

• ISIS coded in the GAMS (General Algebra

System) language can dynamically evalua

– Multi-product industries operating with regional – Multi-pollutant policies– Short and long time horizons

• ISIS is a large dynamic linear programmin

– For example, a 10-year simulation of the U.S. c

required solving about 1.5 million variables with equations
Objective Function
Policies that can be Evaluated 

• Criteria pollutants (NO

x, SO

2, P

– emission limits and/or cap-and-tr

• Hazardous Air Pollutants (e.g., 

– emission limits

• CO

2

– cap-and-trade, emission taxes

• Long and short time horizons

– CO

2 (decades), Criteria/HAPs (a

• Regional or national requireme
Techno-economic Frame
Definitions: Indexes

• t is the set of years in the time horizon of interest;• i is the set of all units, including existing, replaceme

new units. Subsets of i described below define mor

populations of units;

– iE(i) is the set of existing units

– irepl(i) is the set of replacement units

– iExp(i) represents the set of expansion units– iNew(i) represents the set of new units

• f is the set of fuels applicable to the sector;

• m is the set of raw materials specific to the sector;

• j is the set of sector-specific pollutants of interest;

• k is the set of sector-specific controls relevant to th

policy of interest;

• ee is the set of energy efficiency measures; and

• r is the set of geographic regions where units are lo
Definitions: Mapping

• ri(i,r) is the mapping relating a unit i to its geographic loc

• poltikjee(t,i,k,j,ee) is the mapping relating availability, a

ability to change emissions of controls 

k and energy effic

unit i, pollutant j, and year 

t;

• poltik(t,i,k) is the mapping relating availability and applic

unit i and year 

t;

• poltiee(t,i,ee) is the mapping relating availability and ap

efficiency measures ee to unit i and year 

t;

• poltirk(t, ri(i,r),k) is the mapping relating availability and 

k to unit i located in geographic region r and year 

t; and

• poltiree(t, ri(i,r),ee) is the mapping relating availability a

energy efficiency measures ee to unit i located in geogra

t.
Objective Function

The area under the demand-price curves for all maNon-linear term – parameterization needed
Supply Constraints

∑ ),,(

+

∑ ),,(

≥

∑ 

i id d

prodnquant dcitity importedqu dcidtantity 

prodnquantity(t,i,dc) is the quantity supplied from the domestic production unit i timportedquantity(t,oi,id,dc) is the quantity of commodity received from the origin domestic import district id and supplied from that district to demand center dc in 

Importedquantity(t,id,dc) is the imported quantity supplied from import district id to 

Imports(t,oi,id,istep) is the imported quantity available at the import district id in yeof the imports curve for country oi.
Supply Related Cost

Production costsTransportation costsImports costs

Non-linear term - paramet
Demand Curves

dst

DP 

(

The above equation price-demand curvedemand centers. Hospecifications of onfunction in each timdc)}]. To determine the inelastic version exogenous D0(t, dcresulting shadow prequation (a) to geneall time periods and 
Objective Function
Cement Imports

• Two structurally different mode

– Mode 1: imports from Mexico and 

respond to the difference betweeproduction and demand

– Mode 2: imports from other coun

Thailand, Venezuela, South Koreand Rest-of-the-world) respond tprices and come in at an import dcountry- and district-specific cost
Cement Imports - Contin

• Mode 1 imports modeled as “kilns” opera

and Canada.

• Mode 2 imports – quantity and cost curve 

• Country- and district-specific quantity-cos

constructed using the algorithm employeconstructing the demand-price curves

Imports is the quantity arriving from oi at id with corresponding 

is the elasticity of imports relative to price

{Imports0, Iprice0} is a point on the applicable quantity-price cur
Emissions Constrain

Emissions constraint possibilities

• Emission limits -• Cap-and-trade -• Emission taxes -
Appendix
An Integrated View of Production, Air Pollution A

Multimedia Impacts

ISIS has being designed to include the above inte

Pollu

CO2, 

Industrial PlantsImprovements

Fuel(s)

Pollution Reduction Policy (Rate-based, cap-and-trade, emission taxes)

Product(s)

Product Substitution

Fuel Substitution/ Reduction (NOx, SO2, PM, CO2, ...)

Raw Materials 

Raw Material Substitution

Electricity

Change in use (Power 

plant emissions)

Water

Market(s)

Im(O
Calibration: Objective Fun
Calibration: Supply Const
Calibration: Supply Related Ac

Actual Production costsTransportation costsImports costs