Exam Supply Chain Management January 17, 2008

Transcription

1 Exam Supply Cha Maageme Jauary 7, 008 IMPORTANT GUIELINES: The exam s closed book. Sudes may use a calculaor. The formularum s aached a he back of he assgme budle. Please wre your aswers o he blak pages provded wh hs budle. Cross ou hose secos ha do o eed o be correced (e.g. draf soluos o he exercses), such ha I ca clearly see whch par of your work eeds o be correced. Please provde FORMULAS ad CALCULATIONS for he exercses. Provdg oly he fal soluo s worhless. SUCCESS!!!

2 Exam Supply Cha Maageme Jauary 7, 008 ueso Cosder a wo-sage supply cha, cossg of a maufacurer ad a realer. The produc produced hs cha s he revoluoary UPod, for whch hs cha holds a moopoly. Marke research has esmaed ha yearly demad for he UPod () depeds o he u prce (p): p. ( s us, p s $). The cos o maufacure a UPod amous o 35$ per u. escrbe he coordao problem ha arses hs supply cha. Wha aco(s) ca be ake order o esure ha he overall supply cha prof s maxmzed, despe he fac ha boh players focus o opmzg her ow prof? (f here s more ha oe possble aco, ls hem all ad jus choose oe o llusrae wh he ecessary calculaos).

3 Exam Supply Cha Maageme Jauary 7, 008 ueso Cosder ol compaes, Shell ad Toal. Ther curre ol drllg ses (wh respecve aual produco capaces housads of barrels, aual fxed operag coss assocaed wh rug a facory of hs sze, ad varable produco cos per housad barrels) are show Table. The markes o whch hey sell (wh respecve aual demads housads of barrels) are show Table. The coss of rasporao ( $) for movg 000 barrels from a parcular drllg se o a gve marke are gve Table 3. Boh compaes have decded o merge. Cosequely, hey are recosderg he demad ad capacy allocao of he exsg ses he maufacurg ework. For he capacy allocao decso, he followg opos exs: - shug dow a exsg se: ha case, he aual fxed operag cos ca be saved. - expadg he capacy of a exsg se: he curre produco capacy of each of he plas s oly 50% of wha s possble, gve he ol resources avalable. So he compay has he opo o double he capacy of each se. Carryg ou such a expaso causes a oe-me cos (vesme), as gve he las colum of Table. Moreover, causes he aual fxed operag coss for ha parcular se o crease by 50%. - No erveo. I ha case, plas keep her curre produco capaces ad aual fxed operag coss are curred regardless of wheher he pla s used or o. The oal budge avalable for facg he oe-me coss of he capacy expasos amous o 6 mllo $. Ths budge cao be exceeded. Compay Se Aual produco capacy ( 000 barrels) Shell Toal USA (Houso) Caada (Vacouver) Afrca (Ngera) Mddle Eas (Abu hab) Aual fxed operag coss ( 000 $) Varable produco cos ( $ per 000 barrels) Cos for doublg produco capacy ( 000$) Table : Curre produco ses, wh () respecve aual produco capaces, () aual fxed coss, ad (3) varable produco cos per 000 barrels. 3

4 Exam Supply Cha Maageme Jauary 7, 008 Compay Marke Aual demad ( 000 barrels) Shell USA 3000 Europe 000 Toal USA 000 Asa 4000 Table : Aual demads Compay USA Europe Asa Shell USA (Houso) Caada (Vacouver) Toal Afrca (Ngera) Mddle Eas (Abu hab) Table 3: Coss of rasporao ( $) for movg 000 barrels from a parcular drllg se o a gve marke evelop a mahemacal model allowg he merged compay o deerme he demad ad capacy allocao decsos, order o mmze he oal sum of fxed coss, capacy expaso coss, ad produco ad rasporao coss. To avod wrg ou a very leghy objecve fuco ad/or very legh cosras, please use symbolc oao ad expla wha each symbol sads for your oao. 4

5 Exam Supply Cha Maageme Jauary 7, 008 ueso 3 Cosder he followg saemes. Would you agree? Movae your opo. Wherever possble, use heorecal argumes, graphs, ec. If you beleve ha here s o heorecal argume, you may subsaae your po wh examples from he cases ha you solved durg he year, he arcles you read, couerexamples,. ) Assume ha you have a produc ha exhbs a red as well as seasoaly s demad. Assumg ha we use he mxed model formulao (whch akes o accou red as well as seasoaly effecs), he forecass geeraed by Wer s model wll always be superor o hose geeraed by he sac model. ) I aggregae plag, he use of he level sraegy s always o be preferred vew of maxmzg profs. 3) I ca be prove mahemacally ha he use of commo compoes, combao wh pospoeme, always allows o oba he same produc avalably wh less safey sock. Cosequely, frms should ry o explo hs prcple as much as possble (.e., apply preferably across all producs her porfolo). 5

6 Exam Supply Cha Maageme Jauary 7, 008 Formularum (oly hs docume may be used o he exam!) Chaper 7 Basc formula mxed model Forecas for k perods o he fuure : ( L kt ) S F + k S seaso o whch perod belogs eseasoalzg demad p eve: p + p + + p p + p j + j p odd: p + p j p j + Compug seasoal facors S S r j 0 S r jp+ Movg average forecasg Smple expoeal smoohg L ( N+ ) / N L + a + + (- a)l L - a(e + ) 6

7 Exam Supply Cha Maageme Jauary 7, 008 Hol s model L + a + + (- a)(l + T ) a + + (- a)f + F + -ae + T + β(l + - L ) + (- β)t Wer s model L + a( + /S + ) + (- a)(l +T ) T + β(l + - L ) + (- β)t S +p+ γ( + /L + ) + (- γ)s + Measures of forecas error E F A E MSE E MA MAPE A E 00 bas E bas TS MA Chaper 0 Model Basc EO model Aggregao (combg M TC( ) C + S + hc S * hc Talored aggregao: Sep : Formulas 7

8 Exam Supply Cha Maageme Jauary 7, shpmes) Sep : Sep 3: { } s S hc max, ) ( +,, m m m s hc k k m m s S hc m +,

9 Exam Supply Cha Maageme Jauary 7, 008 Chaper (r,) model wh backorders E( ) E( ) TC ( r, ) S + H ( r E( X ) + ) + b ( r) + ( r (r) x r) f ( x) dx X E( )( S + b( r*)) * H H * FX ( r*) be( ) Smplfed verso: E( )( S) * H H * FX ( r*) be( ) Reorder po for arge CSL (assumpo: ormally dsrbued demad): r E( X ) + σ z y X Varably repleshme lead mes: σ X E( L) σ + E( ) σ L E( X ) E( L) E( ) (R,S) perodc revew model wh backorders Impac of aggregao o radom compoe of demad Suppose R s fxed: S E X ') + ( σ ) ( z y X ' (assumpo: ormally dsrbued demad) E( X ') ( R + L) E( ) σ ( L)σ X ' R + Aggregao over k regos, k produc ypes, : σ C k σ ) + > j ( ρ σ σ j j 9

10 Exam Supply Cha Maageme Jauary 7, 008 Chaper Newsboy model wh dscree demad Expeced prof P() [ x*(p-c)-(-x)*(c-s) ] p( x) + *(p c)p( x) x 0 x + P( X cu ) c + c u o Expeced oversock Expeced udersock [ (-x)] x 0 [ (x-)] x + p( x) p( x) Newsboy model wh couous demad Expeced prof P() [ x*(p-c)-(-x)*(c-s) ] f X(x)dx + 0 F X cu ( *) c + c u o *(p c)f X (x)dx Expeced oversock [ (-x)] 0 Expeced udersock f(x)dx [(x ) ]f(x)dx 0