KEY EQUATIONS. ES = max (EF times of all activities immediately preceding activity)

Transcription

1 KEY EQUATIONS CHATER : Oeraos as a Comeve Weao. roduvy s he rao of ouu o u, or roduv y Ouu Iu SULEMENT A: Deso Makg. Break-eve volume: Q F. Evaluag roess, make-or-buy dfferee quay: Q F m b F b m CHATER 3: roje Maageme. Sar ad fsh mes: ES ma (EF mes of all aves mmedaely reedg avy) EF ES + LS LF LF m (LS mes of all aves mmedaely followg avy). Avy slak: S LS ES or S LF EF 3. roje oss: Cos o rash er u of me 4. Avy me sass: Crash os Normal os Normal me Crash me CC NC NT CT

2 e σ a + 4m + b 6 b a 6 (Eeed avy me) (Varae) 5. z-rasformao formula: where T z T E σ T due dae for he roje T E (eeed avy mes o he ral ah) mea of ormal dsrbuo σ Σ(varaes of aves o he ral ah) CHATER 6: roess erformae ad Qualy. Mea:. Sadard devao of a samle: ( ( ) σ or σ 3. Corol lms for varable roess orol hars a. R-har, rage of samle: b. -har, samle mea: ) Uer orol lm Lower orol lm UCL LCL + A R A R. Whe he sadard devao of he roess dsrbuo, σ, s kow:

3 Uer orol lm Lower orol lm UCL LCL + zσ zσ where σ σ 4. Corol lms for arbue roess orol hars a. -har, rooro defeve: Uer orol lm Lower orol lm UCL LCL + zσ zσ where σ ( ) b. -har, umber of defes: Uer orol lm Lower orol lm UCL LCL + z z 5. roess aably rao: C 6. roess aably de: Uer sefao Lower sefao 6σ C k Mmum of Lower sefao Uer sefao, 3σ 3σ CHATER 7: Cosra Maageme. Ulzao, eressed as a ere: Average ouu rae Ulzao 00% Mamum aay. Caay usho, C, eressed as a ere: 3

4 C 00% Ulzao rae (%) 3. a. Caay requreme for oe serve or rodu: M D N[ ( C 00)] b. Caay requreme for mulle serves or rodus: M {[ D + ( D Q) s] rodu + [ D + D Q) s] rodu + + [ D + ( D Q) s] } N[ ( C 00)] rodu SULEMENT C: Wag Les. Cusomer arrval osso dsrbuo: ( T )! λ λt e. Serve-me eoeal dsrbuo: [ T ] e µ T SINGLE-SERVER MODEL MULTILE-SERVER MODEL FINITE-SOURCE MODEL λ ρ Average ulzao of he sysem µ ρ λ sµ ρ 0 robably ha usomers are he sysem ( ρ) ρ ( λ µ )! ( λ µ ) s s! s < < s s robably ha zero usomers are he serve sysem 0 ρ 0 s 0 ( λ µ )! ( λ µ ) + s! s ρ 0 N N! λ ( N )! µ 0 Average umber of usomers he serve sysem λ L µ λ L λw µ L N ( 0 ) λ 4

5 Average umber of usomers he wag le s 0 Lq L q N ( ) L q ρl ( λ µ ) ρ s!( ρ) λ + µ λ Average me se he sysem, ludg serve W µ λ W q + µ W W L[ ( N L) λ] Average wag me le W q ρw W q L q λ W q [( N L) ] L λ q CHATER 8: roess Layou. Euldea dsae: d AB ( A B ) + ( y A yb ). Relear dsae: d AB A B + y A yb 3. Cyle me: r 4. Theoreal mmum umber of worksaos: 5. Idle me ( seods): Σ Σ 6. Effey (%): (00) 7. Balae delay (%): 00 Effey CHATER 9: Lea Sysems. Number of oaers: κ d ( ω + ρ )( + α) Σ TM Average demad durg lead me + Safey sok Number of us er oaer 5

6 CHATER 0: Suly Cha Sraegy.. Weeks of suly Iveory urover Average aggregae veory value Weekly sales (a os) Aual sales (a os) Average aggregae veory value CHATER : Loao. Load dsae sore: ld l d. Ceer of gravy: l l ad y l l y CHATER : Iveory Maageme. Q Cyle veory. ele veory dl 3. Toal aual os Aual holdg os + Q C ( H ) + D Q ( S) Aual orderg or seu os 4. Eoom order quay: EOQ DS H 5. Tme bewee orders, eressed weeks: TBO EOQ EOQ (5 weeks/year) D 6. Iveory oso O-had veory + Sheduled rees Bakorders I OH + SR BO 7. Couous revew sysem: 6

7 Reorder o(r) Average demad durg he roeo erval + Safey sok dl + zσ L roeo erval Lead me (L) Sadard devao of demad durg he lead me σ Order quay EOQ σ L L Releshme rule: Order EOQ us whe I R. Q D Toal Q sysem os: C ( H ) + ( S) + Hzσ L Q 8. erod revew sysem: Targe veory level (T) Average demad durg he roeo erval + Safey sok d( + L) + zσ +L roeo erval Tme bewee orders + Lead me + L Revew erval Tme bewee orders Sadard devao of demad durg he roeo erval σ + L σ + L Order quay Targe veory level Iveory oso T I Releshme rule: Every me erods order T I us. Toal sysem os: d D C ( H ) + ( S) + Hzσ d + L SULEMENT D: Seal Iveory Maageme. Nosaaeous releshme: Mamum veory: I ma d Q 7

8 Eoom roduo lo sze: ELS DS H d Toal aual os Aual holdg oss + Aual orderg or seu os Q d ( ) ( ) D C H + S Q Tme bewee orders, eressed years:. Quay dsous: ELS TBO ELS D Toal aual os Aual holdg os + Aual seu os + Aual os of maeral 3. Oe-erod desos: Q D C ( H ) + ( S) + D Q Q ayoff mar : ayoff D I( Q D) f Q D f Q > D CHATER 3: Foreasg. Lear regresso: Y a + bx. Nave foreasg: Foreas 3. Smle movg average: D F + D + D + D + + D + 4. Weghed movg average: F + Wegh ( D ) + Wegh ( D ) + Wegh 3 ( D ) + + Wegh ( D + ) 5. Eoeal smoohg: F D + ( ) F + α α 6. Tred-adjused eoeal smoohg: 8

9 A T α + α + F A + T + D ( β ( A A )( A T ) + ( β ) T ) 7. Foreas error: E D F CFE E E MSE σ CFE E ( E E MAD ( E MAE E ) / D )(00%) 8. Eoeally smoohed error: MAD α E + ( α)mad 9. Trakg sgal: CFE MAD or CFE MAD CHATER 5: Resoure lag Maser roduo Shedulg. rojeed O-Had Iveory rojeed o - had O - had MS quay rojeed veory a he ed veory a he + due a he sar requremes of las week of hs week hs week of hs week ed. Avalable o romse a. week 9

10 b. week Avalable- o - O - had Orders booked u MS quay romse quay + o week S whe he week week week e MS arrves Avalable- o - Orders booked u MS quay romse o week S whe he week week e MS arrves CHATER 6: Shedulg. erformae measures: Job flow me me of omleo Tme job was avalable for frs roessg oerao Makesa Tme of omleo of las job Sarg me of frs job Average WI veory Average veory Sum of flow mes Makesa Sum of me sysem Makesa Toal veory Sheduled rees for all ems + O-had veores of all ems Ulzao roduve work me Toal work me avalable. Cral rao: Due dae Today's dae CR Toal sho me avalable 3. Slak er remag oeraos: (Due dae Today's dae) Toal me remag S RO Number of oeraos remag 0

11 CD-ROM SULEMENTS SULEMENT G: Learg Curve Aalyss Learg urve: k k b log r b log SULEMENT H: Measurg Ouu Raes. Requred samle sze a me sudy: z σ. Normal me for a work eleme: NT ( F )( RF) 3. Normal me for he yle: NTC ΣNT 4. Sadard me: ST NTC( + A) z e 5. Requred samle sze a work samlg sudy: ( ) SULEMENT I: Aeae Samlg. Average ougog qualy: ( )( - ) AOQ a N N SULEMENT J: Faal Aalyss. Fuure value of a vesme a he ed of erods F ( l+ r). rese value of a fuure amou F + ( r) 3. rese value of a auy

12 A A A j / af A ( ) ( ( r) + ( + r) ( + r ) + r A ) + j 4. Sragh-le dereao D I S