415 Final.docx

# Grq 1 sqr 1 1qbr brq sqr gr stockoutsunderest sqr

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G(x-1)=1/Q[G(r)+...+G(r+Q-1)]... S(Q,r) =1-(1/Q)[B(r)- B(r+Q)] ... S(Q,r) G(r) => stockouts,underest S(Q,r)... SerLvl(typeII) S(Q,r) =1-B(r)/Q => neglects B(r,Q), underest S(Q,r)… B(Q,r) = 1/Q{x=r+1 to r+Q}   B(x)=(1/Q)[B(r+1)+…+B(r+Q)] …avg inv declines from Q+s to s+1 so I(Q,r) [ (Q+r) +(r+1)]/2 +B(Q,r) - θ =[(Q+1)/2]+s= [(Q+1)/2]+r- θ +B(Q,r) Q,r w/BO costs Obj= Y(Q,r)= (  /Q)K+bB(Q,r)+hI(Q,r) => Y~(Q,r )=(  /Q)K+bB(r)+h[((Q+1)/2)+r- θ +B(r)] Q* =  [(2K  )/h ]… G(r* )= b/(h+b) => r* = θ +z if G is normal( θ , ), where (z)=b/(h+b)... on-hand =(n<Q) r+Q-n BO =0 OnO =0 ****** ( ri =m(@stat)*PT, rb =BNrate, To= avgPTs).. To = LongtermPTavgofeach station… (CritWIP)Wo =To*rb… FT(BC) = ifw< Wo = To, otherwise =w/rb…maxTH for givenWIP: TH(best)= ifw< Wo=w/To, otherwise=rb… WIP(w) =TH*FT… TH(WC )=1/To… FT(WC) =wTo… PWC : FT(single) =(1+(w-1)/N)*t… FT(line) =Nt+(w-1)*t=To+(w-1)/rb… TH =WIP/FT=rb[w/ (w+Wo-1)] ****** EXP: MEAN = STD DEV mr=cr Ce = /te… SCV =Ce^2… MachDT:to =basePT, co =PTcoeffofvar= /te, ro =basecap=1/to, mf =meant2fail, mr =mean2repair, cr =coeffvar ofrepair( r/mr)… Aval=A = mf/(mf+mr )=UT/(UT+DT)… effP.rate=re =Aro,or, te =to/A… e^2 = ( o A ) 2 + mr 2 + r 2 ¿ ( 1 A ) ¿ ¿ A mr ce^2 e 2 te 2 ¿¿ ) = co 2 +(1+ c r 2 )A(1-A) m r t 0 SetupVar: N s =ts/tb/wfail, t s =avgset dur, s = set stddev , c s = s t s t e = t o + t s N s e 2 = o 2 + s 2 N s + N s 1 N s 2 t s 2 c e 2 = e 2 t e 2 multrun : tj =m*to
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