*Columbirb. prn Table inflow(hydro-u,K) 1 2 3 .**. 43 44 4s hydrA 52 66 81 . . . . 57 66 85 A.2 Hydro-Eletric Generation Planning Mode1 2 (HEGP2) written by J.R. Birge and C. Supatgiat, O. Michigan, 1998, Lasc modified H. Jin Park Sinclude "columbia.datN VARIABLES COST ; POSITIVE VARIABLES ~therm~en(therm,u,modes,periodç,senarios) therm production in each mode in each month (MWh1 Ngen~flow(hydro,u,rnodes,periodç,çenarios~ hydro water release for generation in each mode in each month (m3) Llevel(hydro,u,periods,senarios) water level ac the end <strong>of</strong> period (Mm31 Nspil~Flow(hydro,u,modes,periods,senarios~ * water spi11 over the period due to over capacity (m3) Nexchange(areas,areas,modes,periods,senarios~ amount power transfer from (1st) to (2nd) in each mode , each node (Mhlh) Nrat~~low(hydro,u,rnodes,perioas,senarios1: slack in minimum flow constraints. Ic gets penalty in the objective function EQUÀTIONS OBJECTIVE NexpCapa(areas,mcdes,periods,senarios) Nimp~capa(areas,modes,periods,senarios1 ~lmeet,load(areas,nodes,periods,ser,arias) Nwat9al(hydro~u,perFoas,senariost NhydraMinC(hy~o~u,modes.petlods,senarios) Lnon&zt(hydro,u,periods,senario~l Lno~ttl(hydro,u,periods,senarios1 Lnomt22 i hltdro-u, periods , senarias 1 LnoxAnt3 1 (hydre-u, periods , senarias t , LnonAnt32 (hydre-u, periods , senarias 1 LanIInc33 ihydro-u, periods , senarios 1 , Lnor~t34 (hydre-u, periods, senarios 1 OP-CTXVE .. COST =E= - (SUM(senarios, probtsenarios)*~~~(periods, ST;TMtmodes,duration(mdes,periods)* çUM(therm,u, unitCost(themrmu) Nthermgen(theni~u,des,periods,send2:iosl~~ 1 ) 116
NwatBal(hydro,u,pericds,senarios1 .. -(initial(hydro,u)S(ord(periods) EQ 1) + Llevel(hydro,u,periods-1, senarios) S (ord (periods 1 GT 11 + (~(hydro,ul, links (hydro-ul hydre-u) ' SUM(modes, (Ngen,f1ow(hydro~u~,modes,periads,senarios) + Nspillflow(hydro,u~,mc~es,periods,ssnarios1 / 1000000.01) + inflow(hydro,u,periods,senarios) (num,hour(periods,senarios) 3600.0 / 1000000.0) - SüM(modes, (~gen,flow(hybro,u,modes,periods,senarios~ t NspillFlow(hydro,u,modes,periods,.senarios) 1 / 1000000.0) =L= - Llevel(hydro,u,periods,senarios); Llevel(hydro,u,peri3,sen3) =1= Lievel (hydre-u, peri3, sen3++ll ; Llevel(hydro_u,peri3,sen4) =1= Llevel(hydro,u,peri3,sen4++1); Llevel(hydro,u,peri3,sen5) =1= Llevel(hydro-u,peri3,sen5++1); L~eve~(hydrc~u,peri3,sen6) =1= LlevelIhydro-~,peri3,sen6++11 ;
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A PARALLEL PRIMAL-DUAL DECOMPOSITIO
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The University of Waterloo requires
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WATPAR, and in each of the tests, t
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To Soyoung and Katherine Eugene Par
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3.5 Sumary and Observations on the
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Table 4 . I Table 5.1 Table 5.2 Tab
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Chapter 1 Introduction 1.1 Brief Hi
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1.2 Motivation and Objectives of th
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2. Pmve and dernonstrate the conver
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Chapter 2 Literature Review This ch
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Benders komposition Method In the B
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in this algorithm, both subproblems
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SIMD vs MIMD Panllel computers cm b
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apan. In mmy LAN's, communication i
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angular linear programs by fixing t
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Chapter 3 Paralle1 Decomposition of
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ound constraints. The two parts are
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constnicted in the sarne way by res
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1T 17 t-IT T nlk*'T )' and &'-' = (
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a proposal is passed back to the fi
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END - solve ; if it is infeasible o
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l, and Theorem 3. lb mles out the p
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nonlinking constraints and upper bo
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(The "only if* part) If P is infeas
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. - Thmm 3.6 Suppose (-ri. )Jik, VI
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the optimal value has ken reached.
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spfl, we have have k .J< k PI -1 -
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zi - $' 5 z+ - &J-[, and by Theorem
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Chapter 4 Paraiiel Decomposition of
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upper bound constraints and nonnega
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type subproblem. The lower bound su
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An algorithm could be defined to ex
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Figure 43 9-stage decomposition pri
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combinations of known solutions of
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lower bound subproblem (parts 1 and
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&.',* and CI::;, are a 1 x (i - 1)
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from the same aggregated subproblem
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problems is discussed. Various prop
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- Page 99 and 100: Chapter 5 Preliminary Implementatio
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- Page 153 and 154: short SolveProb(C3XEWptr env, CP.XL
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- Page 169 and 170: BIBLIOGRAPHY Aardal. K. And A. An.
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