The Industrial SectorsIntegrated Solutions (ISIS)Model: MathematicalFrameworkRavi K. SrivastavaAir Pollution Prevention and Controls DivisionNational Risk Management Research LaboratoryOffice of Research & DevelopmentEPAElineth TorresOffice of Air Quality Planning and StandardsEPASamudra VijaySam AnalyticsMarch 18, 20102ISIS Development Team•ORD– RaviSrivastava,WillYelverton•OAQPSOverallcoordination:ElinethTorresISIS‐Cement:ElinethTorres,KeithBarnettISIS‐Iron&Steel:MattWitosky,DonnaleeJonesISIS‐Pulp&Paper:ElizabethPalmaCostdevelopment:TomWalton,LarrySorrels,andCharlieFulcher•Contractors–SamAnalytics,AndoverTechnologyPartners,DallasBurtraw,RTI,Arcadis2Acknowledgements•Dr. Dallas Burtraw et al., RFF•Dr. Richard Newell, Duke University•Dr. Elliott Lieberman, EPA/OAP/CAMD•Dr. Hendrik G. van Oss, USGS3ISIS: Broad Framework•Objective – maximizetotal surplusover the time horizon ofinterest, subject to:–meeting the demand for the sector-specific commodities; and–satisfying any sector-specific emissions related requirements.•ISIS coded in the GAMS (General Algebraic ModelingSystem) language can dynamically evaluate–Multi-product industries operating with regional markets–Multi-pollutant policies–Short and long time horizons•ISIS is a large dynamic linear programming model–For example, a 10-year simulation of the U.S. cement industryrequired solving about 1.5 million variables with about 1 millionequations45Objective FunctionPolicies that can be Evaluated with ISIS•Criteria pollutants (NOx, SO2, PM, CO)–emission limits and/or cap-and-trade•Hazardous Air Pollutants (e.g., Hg, HCl)–emission limits•CO2–cap-and-trade, emission taxes•Long andshort time horizons–CO2(decades), Criteria/HAPs (annual)•Regional or national requirements6Techno-economic Framework7Definitions: Indexes•tis the set of years in the time horizon of interest;•iis the set of all units, including existing, replacement, expansion, andnew units. Subsets ofidescribed below define more-specificpopulations 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•fis the set of fuels applicable to the sector;•mis the set of raw materials specific to the sector;•jis the set of sector-specific pollutants of interest;•kis the set of sector-specific controls relevant to the emission reductionpolicy of interest;•eeis the set of energy efficiency measures; and•ris the set of geographic regions where units are located.8Definitions: Mappings•ri(i,r)is the mapping relating a unitito its geographic locationr;•poltikjee(t,i,k,j,ee)is the mapping relating availability, applicability, and theability to change emissions of controlskand energy efficiency measureseetouniti,pollutantj, and yeart;•poltik(t,i,k)is the mapping relating availability and applicability of controlsktounitiand yeart;•poltiee(t,i,ee)is the mapping relating availability and applicability of energyefficiency measureseeto unitiand yeart;•poltirk(t, ri(i,r),k)is the mapping relating availability and applicability of controlskto unitilocated in geographic regionrand yeart; and•poltiree(t, ri(i,r),ee)is the mapping relating availability and applicability ofenergy efficiency measureseeto unitilocated in geographic regionrand yeart.9Objective Function10The area under the demand-price curves for all markets dc.Non-linear term – parameterization neededSupply Constraints.),,(),,(),,(∑∑∑≥+dstepididstepdctdemanddcidtantityimportedqudcitityprodnquantprodnquantity(t,i,dc)is the quantity supplied from the domestic production unit i to demand center dc in year t,importedquantity(t,oi,id,dc)is the quantity of commodity received fromthe origin (country) of imports oi at thedomestic import district id and supplied from that district to demand center dc in year tImportedquantity(t,id,dc)is the imported quantity supplied from import district id to demand center dc in year t,Imports(t,oi,id,istep)is the imported quantity available at the import district id in year t at the istepthlevelof the imports curve for country oi.11Supply Related CostsProduction costs12Transportation costsImports costsNon-linear term - parameterizedDemand Curvesσ1dstepdstepD0DP0DP⎟⎟⎠⎞⎜⎜⎝⎛=)(The above equation (a) is used to generate theprice-demand curves for all time periods anddemand centers. However, this equation needsspecifications of one point on each demandfunction in each time period [i.e., {P0(t, dc), D0(t,dc)}]. To determine such points, a single run ofthe inelastic version of the ISIS model [withexogenous D0(t, dc)] is made and then theresulting shadow prices P0(t, dc) are used inequation (a) to generate price-demand curves forall time periods and demand centers.(a)13Objective Function14Cement Imports•Two structurally different modes–Mode 1: imports from Mexico and Canadarespond to the difference between domesticproduction and demand–Mode 2: imports from other countries (China,Thailand, Venezuela, South Korea, Greece,and Rest-of-the-world) respond to marketprices and come in at an import district atcountry- and district-specific costs15Cement Imports - Continued•Mode 1 imports modeled as “kilns” operating in Mexicoand Canada.•Mode 2 imports – quantity and cost curve given by16•Country- and district-specific quantity-cost curves areconstructed using the algorithm employed forconstructing the demand-price curvesImportsis the quantity arriving from oiat id with corresponding priceIprice(Imports)is the elasticity of imports relative to price{Imports0, Iprice0} is a point on the applicable quantity-price curve.Emissions ConstraintsEmissions constraint possibilities•Emission limits -•Cap-and-trade -•Emission taxes -17Appendix18An Integrated View of Production, Air Pollution Abatement, andMultimedia ImpactsISIS has being designed to include the above interactionsPollution Controls (NOx, SO2,PM,CO2, VOC, .. )IndustrialPlantsImprovementsFuel(s)Pollution Reduction Policy(Rate-based, cap-and-trade,emission taxes)Air emissionsProduct(s)Product SubstitutionFuel Substitution/Reduction (NOx, SO2, PM,CO2, ...)Raw MaterialsRaw Material SubstitutionElectricityChange in use (Powerplant emissions)WaterWasteMarket(s)Imports(Overseas emissions)19Calibration: Objective Function20Calibration: Supply Constraints21Calibration: Supply Related Actual CostsActual Production costs22Transportation costsImports costs