EVALUATION OF PERFORMANCE MEASURES OF FMS Bottleneck Model. Part mix Mix of the various part or product styles produced by the system

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1 Natoal Ittute of Techology Calcut Deartmet of Mechacal Egeerg EVALUATION OF PERFORMANCE MEASURES OF FMS Bottleeck Model Provde tartg etmate of FMS deg arameter uch a roducto rate ad umber of worktato Bottleeck refer to the fact that the outut of the roducto ytem ha a uer lmt for a gve roduct mx The model ca be aled to ay roducto ytem that oe th bottleeck feature maually oerated maufacturg cell, job ho, etc Termology ad Symbol Part mx Mx of the varou art or roduct tyle roduced by the ytem j - The fracto of the total ytem outut that of tyle j P j= j = where P the total umber of dfferet art tyle made the FMS durg the tme erod of teret Worktato ad Server - Number of dtct worktato - Number of erver at worktato, =,, Proce routg Proce routg clude the loadg oerato at the begg of roceg o the FMS ad the uloadg oerato at the ed of roceg It aumed that every art tyle ha uque roce la t jk - Proceg tme at tato for art j for t kth oerato Work hadlg ytem Codered a (+) th worktato + - Number of carrer the FMS hadlg ytem (eg:- Number of coveyer cart, AGV, Mooral vehcle, etc) t + - Mea traort tme requred to move a art from oe worktato to the ext tato the roceg routg Oerato frequecy Exected umber of tme a gve oerato the roce routg erformed Performace meaure of FMS 7 March 0

2 Natoal Ittute of Techology Calcut Deartmet of Mechacal Egeerg f jk - Oerato frequecy for oerato k roce la j at tato FMS Oerato arameter Average workload for a gve tato the mea total tme et at the tato er art coderg all the art roceed the worktato - Average workload at tato = j k t jk f jk j Average workload of hadlg ytem the mea traort tme multled by the average umber of traort requred to comlete the roceg of a workart Average umber of traort equal to the mea umber of oerato the roce routg mu oe t - Mea umber of traort t = j f jk j k k f jk t + = t + determe average umber of oerato for art j Sytem erformace meaure Producto rate of all art Producto rate of each art tyle Utlzato of dfferet worktato Number of buy erver at worktato Above erformace meaure are calculated uder the aumto that the FMS roducg at t maxmum oble rate Producto rate cotraed by the bottleeck tato Workload er erver = Bottleeck tato = max R - Maxmum roducto rate of all art tyle roduced by the ytem Performace meaure of FMS 7 March 0

3 Natoal Ittute of Techology Calcut Deartmet of Mechacal Egeerg Bottleeck tato arameter are rereeted wth a Producto rate Producto rate the umber of ut roduced er ut tme It the roduct of the roducto rate of a erver ad umber of erver at the bottleeck tato R = R j = j ( R) = Utlzato j Mea utlzato of each worktato the roorto of tme that the erver at the tato are workg ad ot dle It aumed that the bottleeck tato ha 00% utlzato U - Utlzato of tato ( R ) U = = U - Average tato utlzato the average utlzato of all tato + U = U = + Overall FMS utlzato ca be obtaed ug a weghted average, where the weght baed o the umber of erver at each tato for the regular tato the ytem The traort ytem omtted, a roceg tato utlzato mortat FMS U - Overall FMS utlzato U = = = S U S Number of buy erver Aume that erver at bottleeck tato are buy at the maxmum roducto rate BS - Number of buy erver o average at tato Performace meaure of FMS 7 March 0

4 Natoal Ittute of Techology Calcut Deartmet of Mechacal Egeerg Number of erver buy at bottleeck tato durg the tme Number of erver buy at tato BS Note = = R The roducto rate of the ytem ca be creaed by creag the rate of the tem, whch are ot roceed the bottleeck tato If exce caacty ext other tato Exteded Bottleeck Model Some aumto of the bottleeck model are Suffcet umber of art the ytem to avod tarvg of worktato There o delay due to queue Exteded bottleeck aroach ca overcome ome of the aumto Aume a cloed queug etwork wth fxed umber of art the FMS Whe oe art comleted ad ext the FMS, a ew raw workart mmedately eter the ytem Let N be the umber of art the ytem N lay a crtcal role the oerato of the ytem If N maller tha the umber of worktato, the ome of the tato wll be dle due to tarvg eve the bottleeck tato If N large, the the ytem wll be fully loaded wth queue of art watg frot of the tato R wll rovde good etmato of the roducto caacty Log maufacturg lead tme A er Lttle law WIP = Throughut Maufacturg Lead Tme (MLT) N = R (MLT ) MLT = + + = + T w Tw - Mea watg tme exereced by a art due to queue at the tato Baed o the value of N (mall or hgh) ad Lttle law, the ytem arameter (roducto rate ad MLT) ca be calculated Performace meaure of FMS 75 March 0

5 Natoal Ittute of Techology Calcut Deartmet of Mechacal Egeerg Cae (mall N) Bottleeck tato ot fully utlzed Producto rate ot R T w of a ut theoretcally zero The MLT ca be calculated ad the roducto rate ca be calculated ug Lttle law MLT = + + = MLT - MLT for cae R = N MLT R = j j R Cae (Large N) Producto rate cotraed by bottleeck tato R = MLT ca be calculated ug Lttle law MLT = N R T w = MLT + + = The dvdg le betwee cae ad cae deedg o the crtcal value of N Let N be the crtcal value of N N = R = + + = R ( MLT ) Grahcal Rereetato of exteded bottleeck model Performace meaure of FMS 76 March 0

6 Natoal Ittute of Techology Calcut Deartmet of Mechacal Egeerg MLT R MLT R 0 N (a) N 0 N (b) N Geeral behavor of the exteded bottleeck model (a) MLT a a fucto of N ad (b) Producto rate a a fucto of N Valdty of the Model The author (Mejab) of the model comared the reult wth the reult obtaed from Queug model (Ca-Q) for everal thouad roblem A adequacy factor uggeted whch decrbe the dcreace of th model from queug model Adequacy factor (AF) N AF = U + = Atcated dcreace betwee the exteded bottleeck model ad CAN-Q model a a fucto of the adequacy factor. Adequacy Factor Atcated dcreace wth Ca-Q AF < 0.9 Dcreace < 5% are lkely 0.9 AF.5 Dcreace 5% are lkely AF >.5 Dcreace < 5% are lkely Performace meaure of FMS 77 March 0

7 Natoal Ittute of Techology Calcut Deartmet of Mechacal Egeerg Szg of FMS Determato of umber of erver requred at each worktato to acheve a ecfed roducto rate Iformato eeded Part mx, roce routg ad roceg tme S = mmum teger R ( ) S - Number of erver at tato R - Secfed roducto rate of all art to be roduced by the ytem - Workload at tato A erformace evaluato roblem: A FMS ued to roduce four art. The FMS cot of oe load/uload tato ad two automated roceg tato (rocee X ad Y). The umber of erver for each tato tye to be determed. The FMS alo clude a automated coveyor ytem wth dvdual cart to traort art betwee erver. The cart move the art from oe erver to the ext, dro them off, ad roceed to the ext delvery tak. Average tme requred er trafer.5 m. The followg table ummarze the FMS: Stato Load ad uload Stato Proce X Stato Proce Y Stato Traort ytem Number of huma erver (worker) to be determed Number of automated erver to be determed Number of automated erver to be determed Number of cart to be determed All art follow the ame routg, whch Aume that each oerato carred out oly oce for a tem. The roduct mx ad roceg tme at each tato are reeted the table below: Product Product mx Stato (m) Stato (m) Stato (m) Stato (m) A B C D Requred roducto art/hr whch dtrbuted accordg to the roduct mx dcated. Ue the bottleeck model to determe: () the mmum umber of erver at each tato ad the mmum umber of cart the traort ytem thoe are requred to atfy roducto demad ad () the utlato of each tato for the awer above. Ue arorate model to determe: () the crtcal value of work--roce vetory (v) the maufacturg lead tme f there are 8 tem the ytem? Performace meaure of FMS 78 March 0

8 Natoal Ittute of Techology Calcut Deartmet of Mechacal Egeerg Soluto For =,, (L/U tato, Proce tato X ad Y) = j k t jk Whe = (Materal hadlg ytem) t + = t + f jk j f jk t = j k = (+)0.+5x0.+5x0.+5x0. = 5 m. j = 5x0.+0x0.+0x0.+0x0. = 7.5 m. = 5x0.+0x0.+0x0.+5x0. =.5 m. For = t = [Every roduct ha ame umber of trafer] = x.5 = 0.5 m. Bottleeck tato tato (Aumg oe erver er tato) Requred Producto rate = art er hour Number of erver requred at each tato S = mmum teger R ( ) R = art er hr. = 0. art er m. For tato,,, ad R value are, 5.5,.7 ad. reectvely. Therefore, umber of erver at tato,,, ad are, 6,, ad reectvely. Utlato U = R = ( R ) Idetfcato of bottleeck tato Bottleeck tato = max for the tato are 5,.58,.5 ad.5 reectvely. S Bottleeck tato tato Performace meaure of FMS 79 March 0

9 Natoal Ittute of Techology Calcut Deartmet of Mechacal Egeerg R = 0. The utlato for tato, 0.9, 0.9 ad 0.7 reectvely. MLT = = 56.5 m N = R + + = = N = =. R ( MLT ) MLT whe 8 tem the ytem = MLT = 56.5 m A FMS Szg roblem A FMS ued to roduce four art. The FMS cot of oe load/uload tato ad two automated roceg tato (rocee X ad Y). The FMS alo clude a automated coveyor ytem wth cart to traort art betwee erver. The cart move the art from oe erver to the ext, dro them off, ad roceed to the ext delvery tak. Average tme requred er trafer.5 m. All art follow the ame routg, whch. The roduct demad ad roceg tme at each tato are reeted below a table. Aume that each oerato carred out oly oce for a tem. Product Demad Stato tme Stato tme Stato tme Stato tme (M.) (M.) (M.) (M.) A B C D Determe the workload of each tato (cludg the materal hadlg ytem) ad detfy the bottleeck tato. Requred roducto 0 art er hour dtrbuted accordg to the roduct mx dcated. Ue the bottleeck model to determe: (a) the mmum umber of erver at each tato ad the mmum umber of cart the traort ytem that are requred to atfy roducto demad ad (b) the utlato of each tato for the above awer. Soluto For =,, (L/U tato, Proce tato X ad Y) = j k t jk f jk Whe = (Materal hadlg ytem) t + = t + j Performace meaure of FMS 80 March 0

10 Natoal Ittute of Techology Calcut Deartmet of Mechacal Egeerg t = j f jk j k Product A B C D Demad P j = (+)0.+5x0.+5x0.+5x0. = 5 m. = 5x0.+0x0.+0x0.+0x0. = 7.5 m. = 5x0.+0x0.+0x0.+5x0. =.5 m. For = t = [Every roduct ha ame umber of trafer] = x.5 = 0.5 m. Bottleeck tato tato (Aumg oe erver er tato) Requred Producto rate = 0 art er hour Number of erver requred at each tato S = mmum teger R ( R = 0 art er hr. = /6 art er m. For tato,,, ad ) R value are 0.8,.58,.5 ad.75 reectvely. Therefore, umber of erver at tato,,, ad are, 5,, ad reectvely. Utlzato U = R = ( R ) Idetfcato of bottleeck tato Bottleeck tato = max Performace meaure of FMS 8 March 0

11 Natoal Ittute of Techology Calcut Deartmet of Mechacal Egeerg S for the tato are 5, 5.5,.5 ad 5.5 reectvely. Bottleeck tato tato R = 0.8 The utlzato for tato 0.9,, 0.8 ad 0.95 reectvely. QUESTIONS:. A FMS ued to roduce four art. The FMS cot of oe load/uload tato ad two automated roceg tato (rocee X ad Y). The FMS alo clude a automated coveyor ytem wth cart to traort art betwee erver. The cart move the art from oe erver to the ext, dro them off, ad roceed to the ext delvery tak. The umber of erver at each tato oe. Aume oly oe cart to traort. Average tme requred er trafer.5 m. The tato equece for the art to roce gve the Table. For examle, art A ue the tato the equece. The art demad ad roceg tme at each tato are gve Table. Aume that each oerato carred out oly oce for a tem. Table Stato equece requred for varou art Part Routg equece (Stato) A B C D Table Part demad ad roceg tme Part Demad Stato tme Stato tme Stato tme Stato tme (M.) (M.) (M.) (M.) A B C D Determe the workload of each tato (cludg the materal hadlg ytem) ad detfy the bottleeck tato. Alo calculate average maufacturg lead tme whe the ytem below crtcal codto.. A FMS cot of three tato lu a load/uload tato. Stato load ad uload art from the FMS ug two erver (materal hadlg worker). Stato erform horzotal mllg oerato wth two erver (two detcal CNC horzotal mllg mache). Stato erform vertcal mllg oerato wth three erver (three detcal CNC vertcal mllg mache). Stato erform drllg oerato wth two erver (two detcal drll ree). The mache are coected by a art hadlg ytem that ha two work carrer ad a mea traort tme =.5 mute. The FMS roduce four art A, B, C, ad D, whoe art mx fracto ad roce routg are reeted the table below. Aume that each oerato carred out oly oce for a Performace meaure of FMS 8 March 0

12 Natoal Ittute of Techology Calcut Deartmet of Mechacal Egeerg tem. At ay tme, there are art the ytem. Determe the average maufacturg lead-tme ad average watg tme of art. Part Part Mx Fracto Oerato Number Decrto A 0. Load H. Mll V. Mll Drll 5 Uload B 0. Load Drll H. Mll V. Mll 5 Drll 6 Uload C 0.5 D 0.5 Load H. Mll Drll Uload Load V. Mll Drll Uload Stato Proce Tme (m.) A FMS ued to roduce four art. The FMS cot of oe load/uload tato ad two automated roceg tato (rocee X ad Y). The FMS alo clude a automated coveyor ytem wth cart to traort art betwee erver. The cart move the art from oe erver to the ext, dro them off, ad roceed to the ext delvery tak. Average tme requred er trafer.5 m. All art follow the ame routg, whch. The roduct demad ad roceg tme at each tato are reeted below the table. Aume that each oerato carred out oly oce for a tem. Stato tme Stato tme Stato tme Stato tme Product Demad (M.) (M.) (M.) (M.) A B C D Determe the workload of each tato (cludg the materal hadlg ytem) ad detfy the bottleeck tato. Aume that every tato ha oe erver.. A FMS ued to roduce four art. The FMS cot of oe load/uload tato ad two automated roceg tato (rocee X ad Y). The FMS alo clude a automated coveyor ytem wth dvdual cart to traort art betwee erver. The cart move the art from oe erver to the ext, dro them off, ad roceed to the ext Performace meaure of FMS 8 March 0

13 Natoal Ittute of Techology Calcut Deartmet of Mechacal Egeerg delvery tak. Average tme requred er trafer.5 m. The followg table ummarze the cofgurato of FMS: Stato Number of erver Stato Load ad uload Stato Proce X 6 Stato Proce Y Stato Traort ytem All art have ame umber of oerato ad the art ue tato ad oly oce. The roduct mx ad roceg tme at each tato are reeted the table below: Product Product mx Stato (m) Stato (m) Stato (m) Stato (m) A B C D Determe the crtcal level of work--roce. Alo, determe the maufacturg lead tme whe tem the ytem. 5. A FMS ued to roduce four art. The FMS cot of oe load/uload tato ad two automated roceg tato (rocee X ad Y). The umber of erver for each tato tye to be determed. The FMS alo clude a automated coveyor ytem wth dvdual cart to traort art betwee erver. The cart move the art from oe erver to the ext, dro them off, ad roceed to the ext delvery tak. Average tme requred er trafer.5 m. The followg table ummarze the FMS: Stato Load ad uload Stato Proce X Stato Proce Y Stato Traort ytem Number of huma erver (worker) to be determed Number of automated erver to be determed Number of automated erver to be determed Number of cart to be determed All art follow the ame routg, whch Aume that each oerato carred out oly oce for a tem. The roduct mx ad roceg tme at each tato are reeted the table below: Product Product mx Stato (m) Stato (m) Stato (m) Stato (m) A B C D Performace meaure of FMS 8 March 0

14 Natoal Ittute of Techology Calcut Deartmet of Mechacal Egeerg Requred roducto art/hr, whch dtrbuted accordg to the roduct mx dcated. Ue the bottleeck model to determe: () the mmum umber of erver at each tato ad the mmum umber of cart the traort ytem thoe are requred to atfy roducto demad ad () the utlzato of each tato for the awer above. Ue arorate model to determe the followg: () the crtcal value of work--roce vetory (v) the maufacturg lead tme f there are 8 tem the ytem? 6. A flexble maufacturg cell cot of two machg worktato lu a load/uload tato. The load/uload tato tato. Stato erform mllg oerato ad cot of oe erver (oe CNC mllg mache). Stato ha oe erver that erform drllg (oe CNC drll re). The three tato are coected by a art hadlg ytem that ha three work carrer. The mea traort tme.5 m. The FMC roduce three art, A, B, ad C. The art mx fracto ad roce routg for the three art are rereeted the table below. The oerato frequecy =.0 for all oerato. Determe: () maxmum roducto rate of the FMC, () correodg roducto rate of each roduct, () utlzato of each mache the ytem, ad (v) umber of buy erver at each tato. Wrte dow the aumto the above tuato. Alo comute the roducto rate, maufacturg lead-tme, ad watg tme whe the ytem cota ad 6 ut. Part Part Mx Fracto Oerato Decrto Stato Proce Tme (m.) A 0. Load Mll Drll Uload 0 B 0. Load Mll Drll Uload 5 0 C 0.5 Load Drll Mll Uload 7. A FMS ued to roduce three roduct. The FMS cot of a load/uload tato, two automated roceg tato, a ecto tato, ad a automated coveyor ytem wth a dvdual cart for each roduct. The coveyor cart rema wth the art durg ther tme the ytem, ad therefore the mea traort tme clude ot oly the move tme, but alo the average total roceg tme er art. The umber of erver at each tato gve the followg table: Performace meaure of FMS 85 March 0

15 Natoal Ittute of Techology Calcut Deartmet of Mechacal Egeerg Stato Stato Stato Proce X erver Stato Proce Y erver Number of erver Load ad uload worker Stato Iecto erver Traort ytem Coveyor 8 carrer All art follow ether of two routg, whch are or, the dfferece beg that ecto at tato are erformed o oly oe art four for each roduct ( f = 0.5). The roduct mx ad roce tme for the art are reeted the table below: jk Product j Part mx j Stato Stato Stato Stato Stato (m) (m) (m) (m) (m) A B C The move tme betwee tato m. Ug the bottleeck model, how that the coveyor ytem the bottleeck the reet FMS cofgurato, ad determe the overall roducto rate of the ytem. Determe how may cart are requred to elmate the coveyor ytem a the bottleeck. Performace meaure of FMS 86 March 0