An optimization model using the Assignment Problem to manage the location of parts

Transcription

1 An optimization model using the Assignment Problem to manage the location of parts Master Thesis at the engine assembly at Scania CV AB Josefin Lundquist & Linnéa O Hara

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8 D12 D16 EOQ GAP LC LV P MCGAP WPL ABC analysis B1 cartons Basic engine line DE DELT F inal assembly line Inline engine K2 cartons Location Model Location strategy Material facades Mechanical fitter Process engineer V 8 engine

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11 k *m``2mi bi imb h?2 7QHHQrBM; b2+ibqm /2b+`B#2b i?2 QT2` ibqmb Q7 a+ MB Ƕb 2M;BM2 bb2k#hv r?2`2 i?2 bb2k#hv T`Q+2bb- bmtthv T`Q+2bb M/ i?2 p `BQmb HQ+ ibqm bi` i2;b2b `2 2tTH BM2/ KQ`2 T`Q7QmM/HvX h?2 b2+ibqm 2M/b rbi? M BMbB;?i BMiQ K M ;2K2Mi Q7 KQpBM; T `ib iq M2r HQ+ ibqmb M/ T `i BMi`Q/m+iBQMbX h?2 BM7Q`K ibqm BM i?bb b2+ibqm Bb +QHH2+i2/ 7`QK +QKKmMB+ ibqm rbi? 2KTHQv22b rq`fbm; i.1gh- i?2b` BMi2`M H /Q+mK2Mib M/ i?`qm;? T` +ib+2 BM HQ;BbiB+ i2 KbX kxr a+ MB Ƕb 2M;BM2 bb2k#hv h?2 2M;BM2 bb2k#hv- iq;2i?2` rbi? i2bibm; M/ T BMiBM;- Bb T`Q/m+iBQM mmbi rbi?bm a+ MB BM aƺ/2`i HD2 i? i ;Q2b mm/2` i?2 /2MQi ibqm.1x HH QT2` ibqmb i F2 TH +2 7Q`2KQbi BM i?2 #mbh/bm; R8y- r?2`2 i?2 +im H bb2k#hv i F2b T `i- rbi? bmttq`i 7`QK i?2 G* i? i +QMbBbib Q7 #mbh/bm; Rdd M/ R3k- b22 };m`2 RX h?2 G* Bb `2bTQMbB#H2 7Q` ;QQ/b `2+2BpBM;- BMp2MiQ`v +QMi`QH M/ /2HBp2`v Q7 T HH2ib- #Qt2b M/ b2[m2m+2 TB+F2/ GoS QM Q`/2` bb;m Hb 7`QK i?2 QT2` ibqmb Q7 #mbh/bm; R8yX 6B;m`2 R, M Qp2`pB2r Q7 i?2 #mbh/bm;b R8y- Rdd R3kX kxrxr P`; MBx ibqm.1 #` M+?2b Qmi iq MmK#2` p bm#/bpbbbqmb- BM+Hm/BM; i?2 HQ;BbiB+ /2T `ik2mi.1g BM@ +Q`TQ` ibm; i?2 /2T `ik2mi 7Q` T`Q+m`2K2Mi- K i2`b H TH MMBM;- T`Q/m+iBQM TH MMBM; M/ HQ;BbiB+ /2p2HQTK2MiX h?2 H bi M K2/ /2T `ik2mi- HQ;BbiB+ /2p2HQTK2Mi.1Gh- K M ;2b HQ;BbiB+ Bbbm2b rbi?bm 7Q` 2t KTH2 T +F ;BM;- ;QQ/b ~Qr- rq`f K2i?Q/b M/ HQ+ ibqm Q7 T `ib M/ iqqhb BM i?2 p `BQmb TH i7q`kbx kxk.2b+`btibqm Q7 T`Q/m+iBQM T`Q+2bb2b h?2 bb2k#hv Bb /BpB/2/ BMiQ i?`22 K BM bb2k#hv HBM2b, BMHBM2 # bb+ 2M;BM2c BMHBM2 }M H bb2k#hv M/ o3x AMi2`M HHv- i?2 BMHBM2 bb2k#hv HBM2- i? i Bb #Qi? i?2 # bb+ 2M;BM2 HBM2 M/ i?2 }M H bb2k#hv HBM2 Bb + HH2/.Rk M/ i?2 o3 bb2k#hv HBM2 Bb + HH2/.ReX HH 2M;BM2b T bb i?2 2M;BM2 i2bibm;- BM@ M/ Qmi~Qr M/ T BMiBM; #27Q`2 i?2 2M;BM2b `2 `2 /v iq #2 i` MbTQ`i2/ QM iq i?2 }M H bb2k#hv Q7 i?2 p2?b+h2 Q` TTHB+ ibqmx j

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17 TC = PD+ DK Q + hq 2

18 c ij x ij i I j J a ij x ij b j, j J i I x ij =1, i I j J x ij {0, 1}, i I,j J c ij a ij b j x ij p ij x ij i I j J a ijk x ij b jk, j J, k K i I

19 x ij

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22 c ij b jk a ijk x ij {0, 1}, i I,j J x ij x ij x ij =1, i I j J a ijk x ij b jk, j J, k K i I i I c ij x ij j J c ij = d (1)i c (1)j + d (2)i c (2)j + h j r i + p i d (1)i c (1)j d (2)i c (2)j h j r i p i

23 c ij x ij i I j J x ij =1, i I j J a ijk x ij b jk, i I x ij {0, 1}, j J,k K i I,j J p ij p ij c ij p ij = c in c ij, i I = {1,...,m},j J = {1,...,n} c ij p ij p ij x ij i I j J p ij x ij i I j J x ij =1, i I j J a ijk x ij b jk, i I x ij {0, 1}, j J,k K i I,j J p ij = c in c ij, i I = {1,...,m},j J = {1,...,n} x ij x ij

24 a ijk c ij x ij i I j J x ij =1, i I j J a ijk x ij b jk, i I x ij 0, j J,k K i I,j J b jk a ijk

25 p ij

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27 WPL i WPL i 1 i i i (package i + filledcapacity) < maximumcapacity filledcapacity filledcapacity + package i recommendedlocation i Line recommendedlocation i recommendedlocation i recommendedlocation i (package i <> pallet) i i recommendedlocation i Line filledcapacity package i recommendedlocation i recommendedlocation i

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32 a ijk a ijk

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