ࡱ> than S: C - (1 - Q) * (P * ( 1 - PROB) - H * PROB) = 0; ! Setting to zero, gives; PROB = ( P - C/( 1 - Q))/( P + H); ! Now determine units to put into production, reservations to sell, etc.; ! Binomial; PROB = @PBN( Q, SB, SB - M); ! Poisson approximation; PROB = @PPS( Q * SP, SP - M); ! Normal approximation; PROB = @PSN(( SN - M + .5 - Q * SN)/ (( SN * Q * ( 1 - Q))^.5)); END MODEL: ! Safety lot size/ Over booking model; ! Compute S = number reservations to make; DATA: ! Capacity, e.g., seats available; M = 140; ! Prob{ unit is bad or no-show}; Q = .1; ! Cost per unit put in production; C = - 188; ! Penalty per good unit short of target; P = 0; ! Holding cost per good unit over target; H = 420; ENDDATA !----------------------------------------------; ! Model: Define PROB =; ! Prob{ Bads <= S - M} = Prob{ Goods >= M}; !The marginal cost of ordering S+1 rather Root EntryCONTENTS Root Entry*0_^`Rf Contents   to zero, gives;\cf2 \par PROB = ( P - C/( 1 - Q))/( P + H); \par \cf3 ! Now determine units to put into production, reservations to sell, etc.;\cf2 \par \cf3 ! Binomial;\cf2 \par PROB = \cf1 @PBN\cf2 ( Q, SB, SB - M); \par \cf3 ! Poisson approximation;\cf2 \par PROB = \cf1 @PPS\cf2 ( Q * SP, SP - M); \par \cf3 ! Normal approximation;\cf2 \par PROB = \par \cf1 @PSN\cf2 (( SN - M + .5 - Q * SN)/ \par (( SN * Q * ( 1 - Q))^.5)); \par \cf1 END\cf2 \par \par } {\rtf1\ansi\ansicpg1252\deff0\deflang1033{\fonttbl{\f0\fnil\fcharset0 Courier New;}} {\colortbl ;\red0\green0\blue255;\red0\green0\blue0;\red0\green175\blue0;} \viewkind4\uc1\pard\cf1\f0\fs20 MODEL\cf2 : \par \cf3 ! Safety lot size/ Over booking model;\cf2 \par \cf3 ! Compute S = number reservations to make;\cf2 \par \cf1 DATA\cf2 : \par \cf3 ! Capacity, e.g., seats available;\cf2 \par M = 140; \par \cf3 ! Prob\{ unit is bad or no-show\};\cf2 \par Q = .1; \par \cf3 ! Cost per unit put in production;\cf2 \par C = - 188; \par \cf3 ! Penalty per good unit short of target;\cf2 \par P = 0; \par \cf3 ! Holding cost per good unit over target;\cf2 \par H = 420; \par \cf1 ENDDATA\cf2 \par \cf3 !----------------------------------------------;\cf2 \par \cf3 ! Model: Define PROB =;\cf2 \par \cf3 ! Prob\{ Bads <= S - M\} = Prob\{ Goods >= M\};\cf2 \par \cf3 !The marginal cost of ordering S+1 rather than S: \par C - (1 - Q) * (P * ( 1 - PROB) - H * PROB) = 0;\cf2 \par \cf3 ! Setting