s upper limit on SO x emission [Nm 3 /yr] s upper limit on GHG emission [kg/yr]
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1 Parameters η boiler efficiency [kj/kg] cc calorific vale of the fel a consmption parameter for HP generation b fixed consmption constant for HP generation s SOx SO x emission parameter [Nm 3 /ton of fel] s GHG GHG emission parameter [kg/ton of fel] c cost of nit amont of fel [$/ton] e coefficient of Electricity generation vs. HP steam inpt g coefficient of Electricity generation vs. MP-LP steam and condensate generation cpt storage capacity of a fel tank [ton] ssf safety stock parameter (defined as a fraction of cpt) p L,p U lower and pper limits on fel prchase [ton/order] cpo fixed cost of prchasing fel [$/order] h nit holding cost of fel [$/ton of fel] d demand of a certain prodct [kwh/hr or ton/hr] n length of a period [hors] U s pper limit on SO x emission [Nm 3 /yr] SOx U s pper limit on GHG emission [kg/yr] GHG β cost coefficient the exchange investment α constant of the fixed cost of exchange investment [$] ce price of nit Electricity [$ / kwh] cr SOx penalty cost of SO x release [$/Nm 3 ]
2 List of Tables Table 1. Operating characteristics for the energy system in the 2-company problem. Table 2. Energy demand in the 2-company problem. Table 3. Model and soltion statistics for the 2-company problem. Table 4. Smmary of the reslts for the non-integrated soltion in the 2-company problem. Table 5. Smmary of the reslts for the integrated soltion in the 2-company problem. Table 6. Comparison of the reslts for the 2-company problem. Table 7. Operating characteristics for the energy system in the 3-company problem. Table 8. Energy demand in the 3-company problem. Table 9. Model and soltion statistics for the 3-company problem. Table 10. Smmary of the reslts for the non-integrated soltion in the 3-company problem. Table 11. Smmary of the reslts for the integrated soltion in the 3-company problem. Table 12. Comparison of the reslts for the 3-company problem.
3 Table 1. Operating characteristics for the energy system in the 2-company problem. Company 1 Company 2 Fel 1 Fel 2 Fel 1 Fel 2 cc k I ijkt cpt s SOxk s GHGk c k Boiler 1 Boiler 2 Boiler 1 Boiler 2 η ijk fel1 η ijk fel2 a ijk MP a ijk EL X ijkhplgen b ijk HP b ijk EL Trbine 1 Trbine 2 Trbine 1 Trbine 2 e ijk HP e ijk MP e ijk LP X ijkellgen X ijkhplin X ijkmplgen X ijklplgen HP MP LP α jj' β jj'
4 Table 2. Energy demand in the 2-company problem. Company 1 Period 1 Period 2 Period 3 Electricity HP Steam MP Steam LP Steam Company 2 Period 1 Period 2 Period 3 Electricity HP Steam MP Steam LP Steam Table 3. Model and soltion statistics for the 2-company problem. Nonintegrated Integrated Nmber of constraints Nmber of variables Nmber of nodes in the branch and bond tree 0 0 Nmber of iterations CPU time (*sec) * On a PC with Pentim GHz Processor and 512 MB memory.
5 Table 4. Smmary of the reslts for the non-integrated soltion in the 2-company problem. Company Unit Company Unit Period Vale Company1 HP Company1 MP Company1 HP Company1 MP Company2 HP Company2 MP Company2 MP Company2 LP CompanyU Electricity Company1 Electricity CompanyU Electricity Company1 Electricity CompanyU Electricity Company1 Electricity CompanyU Electricity Company2 Electricity CompanyU Electricity Company2 Electricity CompanyU Electricity Company2 Electricity Table 5. Smmary of the reslts for the integrated soltion in the 2-company problem. Company Unit Company Unit Period Vale Company1 LP Company2 LP Company1 LP Company2 LP Company2 HP Company2 MP Company2 MP Company1 MP Company2 MP Company1 MP Company2 MP Company1 MP Company2 MP Company2 LP CompanyU Electricity Company1 Electricity CompanyU Electricity Company1 Electricity CompanyU Electricity Company1 Electricity CompanyU Electricity Company2 Electricity CompanyU Electricity Company2 Electricity CompanyU Electricity Company2 Electricity
6 Table 6. Comparison of the reslts for the 2-company problem. Non-Integrated Integrated Improvement (%) Total Cost 49, , SO x Release 2,619, ,346, GHG Release 6,534, ,939,
7 Table 7. Operating characteristics for the energy system in the 3-company problem. Company 1 Company 2 Company 2 Fel 1 Fel 2 Fel 1 Fel 2 Fel 1 Fel 2 cc k I ijkt cpt s SOxk s GHGk c k Boiler 1 Boiler 2 Boiler 1 Boiler 2 Boiler 1 Boiler 2 η ijk fel1 η ijk fel2 a ijk MP a ijk EL X ijkhplgen b ijk HP b ijk EL Trbine 1 Trbine 2 Trbine 1 Trbine 2 Trbine 1 Trbine 2 e ijk HP e ijk MP e ijk LP X ijkellgen X ijkhplin X ijkmplgen X ijklplgen HP MP LP α jj' β jj'
8 Table 8. Energy demand in the 3-company problem. Company 1 Period 1 Period 2 Period 3 Electricity HP Steam MP Steam LP Steam Company 2 Period 1 Period 2 Period 3 Electricity HP Steam MP Steam LP Steam Company 3 Period 1 Period 2 Period 3 Electricity HP Steam MP Steam LP Steam Table 9. Model and soltion statistics for the 3-company problem. Non-Integrated Integrated Nmber of constraints Nmber of variables 1,042 1,042 Nmber of nodes in the branch and tree 0 0 Nmber of iterations CPU time (*sec) * On a PC with Pentim GHz Processor and 512 MB memory.
9 Table 10. Smmary of the reslts for the non-integrated soltion in the 3-company problem. Company Unit Company Unit Period Vale Company1 HP Company1 MP Company1 HP Company1 MP Company2 MP Company2 LP CompanyU Electricity Company1 Electricity CompanyU Electricity Company1 Electricity CompanyU Electricity Company1 Electricity CompanyU Electricity Company2 Electricity CompanyU Electricity Company2 Electricity CompanyU Electricity Company2 Electricity CompanyU Electricity Company3 Electricity CompanyU Electricity Company3 Electricity CompanyU Electricity Company3 Electricity Table 11. Smmary of the reslts for the integrated soltion in the 3-company problem. Company Unit Company Unit Period Vale Company2 HP Company1 HP Company2 HP Company1 HP Company2 HP Company1 HP Company2 MP Company2 LP Company2 LP Company1 LP Company3 HP Company3 MP Company3 MP Company1 MP Company3 MP Company1 MP Company3 MP Company1 MP Company3 MP Company3 LP Company3 LP Company1 LP Company3 LP Company1 LP Company3 LP Company2 LP Company3 LP Company2 LP CompanyU Electricity Company1 Electricity CompanyU Electricity Company1 Electricity CompanyU Electricity Company1 Electricity CompanyU Electricity Company2 Electricity CompanyU Electricity Company2 Electricity CompanyU Electricity Company2 Electricity CompanyU Electricity Company3 Electricity CompanyU Electricity Company3 Electricity CompanyU Electricity Company3 Electricity
10 Table 12. Comparison of the reslts for the 3-company problem. Non-Integrated Integrated Improvement (%) Total Cost 73, , SO x Release 4,100, ,527, GHG Release 10,435, ,434,
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