Designing a cost-time-quality-efficient grinding process using MODM methods

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1 Dgnng co-m-quly-cn grnng proc ung MODM mho Mym Mhjoob Dprmn o Inurl n Sym Engnrng, Foumn Fculy o Engnrng, Collg o Engnrng, Unvry o Thrn, Foumn, Irn Eml: mhjoob_m@u.c.r Abrc In h ppr mul-objcv mhmcl mol h bn u o opmz grnng prmr nclu orkpc p, ph o cu n hl p hch hghly c h nl urc quly. Th mhmcl mol o h opmzon problm con o hr conlc objcv uncon ubjc o hl r n proucon r conrn. Exc mho cn olv h NLP mol n con, hror ung M-hurc lgorhm hch prov nr opml oluon n no ubl. Conrng h, v Mul-Objcv Dcon Mkng mho hv bn u o olv h mul-objcv mhmcl mol ung GAMS or o chv h opml prmr o h grnng proc. Th Mul-Objcv Dcon Mkng mho prov rn cv oluon hr h con mkr cn choo ch oluon n rn uon. Drn crr hv bn conr o vlu h prormnc o h v Mul-Objcv Dcon Mkng mho. Alo, Tchnqu or Orr o Prrnc by Smlry o Il Soluon mho h bn u o obn h prory o ch mho n rmn hch Mul-Objcv Dcon Mkng mho prorm br conrng ll crr mulnouly. Th rul nc h Wgh Sum Mho n Gol progrmmng mho r h b Mul-Objcv Dcon Mkng mho. Th Wgh Sum Mho n Gol progrmmng prov oluon hch r compv o ch ohr. In on, h mho obn oluon hch hv mnmum grnng m, co n urc roughn mong ohr Mul-Objcv Dcon Mkng mho. Kyor: Mul-objcv; Grnng; MODM; TOPSIS; Mul-objcv Dcon Mkng 1

2 1. Inroucon To cr proucon co n mchnng m n o mprov h urc quly o mchn prouc, mporn o chv opml vlu o h grnng proc prmr nclu orkpc p, ph o cu n hl p (Khllpourzr n Khllpourzry 2018b, Khllpourzry l. 2011, Dvn l. 2012, Khllpourzry n Mhk 2014, Khllpourzry l. 2011, Zrh-Dr l. 2015, Khllpourzry l. 2011, Khllpourzry 2018, Khllpourzry n Pym For h purpo, mny rrch p non o opmzon problm o h grnng proc. Bkr l. (2004) propo n colony-b opmzon pproch o opmz o h grnng prmr ung mul-objcv mol h gh pproch unr hrml mg, hl r prmr, urc nh n ool n conrn. Thy compr h rul h Qurc progrmmng (QP) n Gnc Algorhm (GA) prn n prvou rrch. Thy ho h h n colony-b opmzon mho prorm br n olvng h grnng proc opmzon problm. Srvnn l. (2002) propo n Gnc Algorhm (GA) oluon mho o olv h gh objcv uncon o h grnng opmzon problm. Th rul clr h hr pproch robu n y mho comprng o h prvou rrch. Mor rrch n opmzon o h grnng proc nclu Mlkn l. (1980), Slok n Slok (2008), Krhn (2007), Rb l. (2015) Zhng l. (2014), Kk (2005), Khhl l. (2013), Kk n Km (2006), Yuup l. (2012), Bn Frj n Ammou (2006), Ln n L (2008), L l. (2011), Mukhrj n Ry (2008), Khllpourzr n Khllpourzr (2017), Khllpourzr n Khllpourzry (2016), Khllpourzr n Khllpourzry (2018). Dvr opmzon mho ugg o conr h c o h grnng prmr uch hl p, orkpc p, ph o rng, l o rng on h mnucur prouc. Gholm n Azz (2014) prn non-omn orng gnc lgorhm (NSGA II) o obn h opml vlu o orkpc p, hl p n ph o cu n h grnng proc. Thy prn rn Pro oluon or h mul objcv opmzon problm hch cn b lc by h con mkr n rn uon. 2

3 Almo ll o prvou rrch combn h objcv uncon o bul ngl gh objcv uncon o opmz h grnng prmr. Combnng h mulpl objcv uncon o cr ngl objcv uncon my l o gncn von n obnng h opml vlu o h con vrbl n h quly o h oluon. In on, h quly o h oluon rongly pn on h gh gn o ch objcv uncon, hr nng ubl gh or ch objcv uncon nohr complx con. Alo, xc mho cn olv h NLP mol o h grnng proc n con. Thror, ung M-hurc lgorhm hch prov nr opml oluon no ubl. Thr r mny ohr oluon mho hch hnl mul objcv opmzon problm uch mul-objcv con mkng (MODM) mho. A mnon bov, nng ubl gh or ch objcv uncon complx con. Gholm n Azz (2014) u NSGA-II lgorhm o olv h mul objcv mol o h grnng proc. Thy prn rn pro oluon hr h con mkr cn choo ch on n rn uon. Bu, mnon bov hr h problm no complx, h xc mho cn olv h problm n con. Thror, v mul-objcv con mkng (MODM) mho hv bn u o olv h mul objcv mhmcl mol o h problm ung GAMS or hch prov xc oluon or opmzon problm. Th oluon obn by ch mho n cv oluon o h opmzon problm n h con mkr cn choo ch MODM mho n rn uon. In on, MODM mho cn prov br oluon hn m-hurc lgorhm uch NSGA-II, MOPSO n c. A h n compr h prormnc o h MODM mho ung rn crr nclu objcv uncon vlu n CPU-Tm. Tchnqu or orr o Prrnc by Smlry o Il Soluon (TOPSIS) mho h bn u o rmn h b MODM mho n olvng h mul-objcv mhmcl mol o h grnng proc. 2. Mhmcl mol W u h mul objcv mhmcl mol o h grnng prmr propo by Gholm n Azz (2014). Th mhmcl mol o h problm nclu hr objcv uncon, non-lnr conrn n uppr n lor boun or h con vrbl. In h rrch h ollong noon h bn u: 3

4 M c : Co pr hour o lbor n mnron ($/h) p: Numbr o orkpc lo on h bl L : Lngh o orkpc (mm) L : Empy lngh o grnng (mm) b : Wh o orkpc (mm) b : Empy h o grnng (mm) b : Cro r (mm/p) : Tol hckn o cu (mm) p : Don o grnng (mm/p) S p : Numbr o prk ou grnng (p) : Dmr o hl (mm) b : Wh o hl (mm) G: Grnng ro S : Dnc o hl lng (mm) r : Sp o hl lng (mm/mn) : Tm o long n unlong orkpc (mn) ch : Tm o jung mchn ool (mn) N : Tol numbr o pc o b group urng h l o rng N : Bch z o orkpc 4

5 N : Tol numbr o orkpc o b group urng h l o rng C : Co o rng ($) C : Co o hl pr 3 3 mm ($/ mm ) C T : Proucon co ($) R : Surc roughn ( m ) Doc: Dph o rng (mm) L : L o rng (mm/rv) 3 WRP : Workpc rmovl prmr ( mm /mn N) WWP : Whl r prmr (mm3/mn N) T : Tol grnng m N p : Numbr o p m : Tm o mchnng (mn) : Tm o orkpc pproch (mn) : Whl p (m/mn) : Exr orkpc ph m (mn) : Work pc p (m/mn) A n Gholm n Azz (2014), h mhmcl mol o h problm cn b rprn : Mn R (1) 5

6 MnT N L L L p ch (2) MnC T M c L L ( 60p 1000 M c 60 N ch M c 1 60p N b )( b b Db 1000L )( p S p bl C ( pg bl M c S ) ( D b G 60p p Docb D pn r C ) ( pn ) ) 1 (3) Subjc o WRP ( Doc 1) L 3L D OL 43/ / ( ) R 5 / 38 g 3 /19 27 /19 c (4) Doc 27 /19 3/19 5/ /19 (1 ) L ( ) K p g Rc L WWP (1.2/ OL 43/ 304) 0.38 D OL 2Doc (1 ) 3L (5) G WRP / WWP (6) (7) (8) (9) Th m o quon (1-3) r o mnmz h proucon co, grnng m n urc roughn mulnouly. Inquly (6) rmn h hl r conrn n nqul (7-9) nc h uppr n lor boun o ch con vrbl. 3. Soluon mho Th mhmcl mol vlop n h prvou con conrn b-objcv mx ngr lnr progrmmng (MILP) mol. Th opml oluon o h vlop b-objcv mol n l oluon hch mnmz boh objcv uncon mulnouly. Snc, h 6

7 objcv uncon r n conlc uch oluon o no x (Khllpourzr l. (2018); Khllpourzr n Pnh 2018; Khllpourzr n Pnh 2016). In h c, h mul-objcv oluon mho houl b ulz o olv h mol. In h ppr v MODM mho prn by Hng n Mu (1979) ulz o olv h mul objcv opmzon mol o h grnng proc. A n Khllpourzr n Khmh (2017), Fzl- Khl l. (2017) n Pnh l. (2015) v MODM mho r n ollong: Invul opmzon mho Th mho conr ch objcv uncon prly, olv h opmzon problm n obn h opml oluon. Th mho b on h concp h h opml oluon o ch objcv uncon n cv oluon or h mul-objcv opmzon problm Lp-Mrc mho Th mho b on h concp o mnmzng h gron bn objcv uncon n hr l oluon obn by nvul opmzon mho. Equon (10) crb h Lp-Mrc mho. Mnmzon yp objcv uncon mu b convr o mxmzon yp. n MnD 1 * * r 1 r (10) Wgh um mho (WSM) Wgh um mho (WSM) mho, pov gh gn o ch objcv uncon. Th gn gh o objcv uncon mu y h 1 conrn. Th gol o mnmz h combn objcv uncon hch gh um o h objcv uncon ollong: n 1 MxU ( 1, 2,..., n ) n 1 (11) 7

8 3. 4. Mx-Mn mho Th purpo o Mx-Mn mho o mxmz h mnmum vlu o objcv uncon v o hr l oluon. Th quon (12) nc h mhmcl mol o h mho. Mx Mn 1,,..., * 1 2 * 2 n * n (12) Gol nmn mho Th Gol nmn mho m o n oluon or ch objcv uncon hch mnmz gh von o objcv uncon vlu h hr rl l oluon. Th gn gh o von n objcv uncon mu y h 1 conrn. Th mhmcl mol o h problm ollo: Mn Z..: Z * ; (13) Gol progrmmng mho In Gol Progrmmng mho h m o n oluon hch mnmz h pov or ngv von bn objcv uncon n hr rlvn l oluon. Equon (14) n h mhmcl mol o h Gol Progrmmng mho. Mn.. n 1 g 0, (, * ) ; 0 ; (14) 4. Exprmnl xmpl 8

9 Gholm n Azz (2014) u nn bll o h l h mm mnon o prorm h grnng proc. Th mrl o brv grnng hl h bn lc rom lumnum ox. In orr o r h grnng hl ngl pon mon rr h bn ulz. To opmz h grnng proc h vlu o h npu prmr hv bn lc Gholm n Azz (2014) n Tbl 1. M c p L L b Tbl 1: lu o h prmr b b G N mn mx * C T R c r ch N N N p C mn mx p b Doc L K vol g S C mn mx Fv MODM mho prn bov o opmz h grnng prmr hv bn ppl o chv h b nh urc, mnmum grnng co n m ung GAMS or. For h purpo, compur h 7 CPU n 8GB o rm h bn ulz. Drn crr hv bn conr o vlu h prormnc o h v MODM mho uch objcv uncon vlu n CPU-Tm (Khllpourzr n Mohmm 2016) Objcv uncon vlu Th hr objcv uncon vlu hv bn conr hr rn crr o compr h MODM mho n rm o bly o chv h b opml oluon (Khllpourzr n Pnh 2017; Khllpourzr n Khllpourzry 2017) CPU-Tm CPU-Tm crron nohr mporn cor o compr h MODM mho n rm o m n o olv h mul-objcv opmzon problm (Khllpourzr l. 2016; Pnh n Khllpourzr 2018; Mohmm n Khllpourzr 2017). Th rul o olvng h opmzon problm ung v MODM mho prn n Tbl 2. 9

10 Mho Tbl 2: Rul o MODM mho R T C T CPU- Tm Invul opmzon mho Lp-Mrc Mx-Mn Gol nmn WSM Gol progrmmng A n Tbl 2 ch oluon obn by ch MODM mho n cv oluon or h opmzon problm. Ech oluon cn b prrr by h con mkr n rn uon. For xmpl h mpornc o h urc quly hghr or h con mkr, h/h ll choo h Lp-Mrc mho hch obn oluon h h mnmum comprng o ohr mho. Fg. 1, 2 n 3 ho h objcv uncon vlu obn by ch MODM mho. Fg. 4 pc h CPU-Tm o h MODM mho. R Fg. 1: Mnmum urc roughn chv by MODM mho 10

11 Fg. 2: Mnmum proucon co obn ung ch MODM mho Fg. 3: Mnmum ol grnng m gn by MODM mho Fg. 4: CPU-Tm o ch MODM mho 11

12 5. Comprng MODM mho ung TOPSIS mho In orr o compr MODM mho, mu bul h con mrx Tbl 3. Mho Tbl 3: Dcon Mrx R T C T CPU-Tm Lp-Mrc Mx-Mn Gol nmn WSM Gol progrmmng TOPSIS mho Tchnqu or orr o Prrnc by Smlry o Il Soluon (TOPSIS) mho propo by Hng n Yoon (1981). Th concp o TOPSIS mho b on lcon o n lrnv hch h long (hor) nc rom h ngv (pov) l oluon. TOPSIS mho h bn ppl o rmn h b MODM mho n olvng h mul-objcv opmzon problm. A objcv uncon vlu r mor mporn o u hn CPU-Tm, lloc h 80% gh or objcv uncon crr n 20% gh or CPU-Tm crron. Th gh o ch crron gvn n Tbl 4. Tbl 4: Wgh o h crr Mho R T CT CPU-Tm Wgh j Fr n o normlz h con mrx ung Eucln Norm: n j r j 2 (37) r j Whr r h con mrx n n normlz con mrx ung Eucln Norm. h MODM mho n j h crron nx. Accorng o quon (38) o obn gh normlz con mrx, Wgh j houl mulply by normlz con mrx. 12

13 gh normlz mrx v j vj Wgh j nj mn, (38) Whr, Wgh j h gh o ch MODM mho. Thror, cn rmn h l pov oluon n h l ngv oluon ollong: loluon mx v j j v j j j :, mn j : (39) loluon mx v j j v j j j :, mn j : (40) Dnc rom h pov n ngv l oluon or ch MODM mho hv bn clcul ung blo ormul: n j1 ( v j loluon ) (41) n j1 ( v j loluon ) (42) Equon (43) prn h Smlry ro ormul. S (43) Th rul chv rom TOPSIS mho r prn n Tbl 5. Smlry ro Tbl 5: Rul o ung TOPSIS mho Gol Lp-Mrc Mx-Mn WSM nmn Gol progrmmng S

14 Th MODM mho h lrgr mlry ro prorm br n olvng h mhmcl mol o h mul-objcv opmzon problm o h grnng proc. Tbl 6 prn v MODM mho rnk ccorng o hr mlry ro. Tbl 6: MODM mho rnkng Mho Rnk Lp-Mrc 3 Mx-Mn 4 Gol nmn 5 WSM 1 Gol progrmmng 2 Th rul nc h h WSM h b oluon mho o h mul-objcv opmzon problm. Alo Gol progrmmng prorm gncnly br hn ohr MODM mho n olvng opmzon problm o h grnng proc. 6. Concluon In h ppr mul objcv mhmcl mol hv bn u o opmz h grnng prmr n n xprmnl c uy o chv b pobl grnng urc, mnmum proucon m n co. Combnng objcv uncon ung gh pproch my l o gncn von n obnng h opml vlu o h con vrbl n h quly o h oluon. To vo h, u v rn MODM mho o olv h mul objcv opmzon problm. Drn crr hv bn conr o compr h MODM mho uch objcv uncon vlu n CPU-Tm. Th rul nc h h oluon obn by ch MODM mho n cv oluon or h mul objcv mol n h con mkr cn choo ch MODM mho n rn uon. TOPSIS mho h bn ulz o rmn h b MODM mho conrng comprng crr mulnouly. Th rul nc h h WSM n Gol progrmmng mho r h b MODM mho n olvng mul objcv opmzon problm o h grnng proc. 14

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