415 Final.docx

# Dism ri 1ti u t2t1u1 possible validfor u1 b b2 wip u1

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:hiP\$.Dis\$M ****ri= 1/ti… u =t2/t1..u>1 possible; validfor u!=1.. b =B+2.. WIP =u/(1-u) -[(b+1)u^(b+1)] /[(1-u^b+1].. TH =[(1-u^b)/(1- u^(b+1))]r1.. FT = WIP /TH..(u=1) Tot FT =Tot WIP.. TotWIP =WIP+(TH*t1 ).. Tot FT =TotWIP/ TH..WIP=b/2..TH= (b/b+1) r1.. OrdC/yr =k*ord/yr(l/Q).. PropC =lc.. HC =hQ/2 ..#ords =l/Q*.. Tb/wO = Q*365/l.. Qamt =lt/T.. Q* = sqr(2kl/h).. reOint=T* =Q*/l..p!=inf/Inst.. avgInv =Q/2(1-l/p).. AnSet = k*l/Q.. propC= lc.. HC =hH/2.. Q*= sqr(2kl/h(1/1- l/p)).. TInvC =hQ(P-l)/2P.. TprodRun =Q*/P ****base stock ( Q =1, r =reO pt, R =basestockLvl=r+1, l =LT, θ =meanDinLT, =stdinl, p(x) = p Dduringl=x, G(x) =pDinl<x, h =unithc=ic, b =unitBOcost)… BalEQ:invpos(R)= onhandInv-BO+O …X=rand D for lead time t… E[X] = θ… StockOut if X>R… ExpServLevel:S(R) =P(X<R)=> if cont =G(R) if discrete = G(R-1)=G(R) …#O=X(Dduringlast(l)timeunits) so R- X =onhandinv-BO… BO =>ifx<R = 0 ifx > R =x-R… AvgBackorderlvl=B(R )= {x=R to inf}   (x-R)p(x)=θp(R)+(θ-R)[1-G(R)] E[BO]=B(R)… AvgOnhandInv = I(R) = R-θ+B(R )… SS =r-θ p(i)= [e^(-θ)*θ^(i) ]/i! => Poission(i, θ,False)… p D duringlead<x : G(x)= {i=0 to i=x} p(i) =>Poisson(I,θ,TRUE)… OptimalBaseStock: ObjFunc: Y(R)=hI(R)+bB(R) =h(R-θ+B(R)) +bB(R)=h(R-θ)+(h+b)B(R)...if G is cont G(R*) = b/(h+b) …If l is norm G(R*) = b/(h+b) <=>   ((R*-θ)/  )=z where   (z)=b/ (h+b) & R*= θ+z  so if z>0 R* incs in θ & inc in …( =D/yr, B =replenLT, X =randDinLT, K =cost/O, c =unitCost) Ords/yr= /Q, setup/OCosts =k /Q… S(Q,r)= 1/Q {x=r+1 to r+Q}   G(x-1)=1/Q[G(r)+...+G(r+Q-1)]...
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