Production Scheduling of Flexible Manufacturing Systems

K. lwata (2), Kobe University; A. Murotsu, University of Osaka Prefecture; F. Oba, University of Osaka Prefecture; K. Yasuda. Kobe University/Japan - Submitted by K. Okamura ( l ) , Kyoto University/Japan

S m i a r y : Th is paper deals w i t h the prod t ic t ion sc'ledul i n g o f a f l e x i b l e manufactur ing systel!: which cons is ts o c machine t o o l s , Suf fe r storages, and m a t e r i a l and c u t t i n g t o o l t r a n s p o r t d t i o s systems. .pachine t o o l s f o r e a c i processing stage o f p a r t s a r e Dermit ted. Par t i :L la r c u t t i n g t o o l s f o r conmicn use d r e a u t o m a t i c a l l y de! ivered by a c u t t i n g t o o l t r a n s p o r t a t i o n systepl. The problem i s t o determine t i le schedules o f nach in ing and t r a n s p o r t i n g p a r t s , and o f t r a n s p o r t i n g c u t t i n g t c o l s s imu l taneous ly so a s t o minimize the 11,dkespan o f p roduc t ion . A h e g r i s t i c procedure i s p reser ted t o o b t a i n b e t t e r scnedules by us ing t i le d e c i s i o n r u l e s . A new d e c i s i o n r u l e , named E S T A ( E a r l i e s t S t a r t i n q Time w i t h A l t e r n a t i v e s cons idered) , i s proposed t o achieve a h i g i b t i ' i z a t i o ? o c the machine t o o l s and the t r a n s p o r t a t i o n systems. Pn exper imental comparison i s performed t o i n v e s t i g a t e the e f fec t i veness o f the proposed dec is ion r u l e s through a case s tudy .

Tne p a r t s a re produced randomly, and a l t e r n a t i v e Each machine t o o l has a b u f f e r o f s p e c i f i e d c a p a c i t y a n d some

1. IIiTRODUCTION

The i n t r o d u c t i o n o f F l e x i b l e Xanufac tur ins Systems (24s) i n t o t h e manufactur ins i n d u s t r y has been an impor tan t new s tep i n the de- velopment o f the f u l l y automated inanufactur ing system. Through t h e implementat ion of an FMS i n t h e m i d - v a r i e t y , mid-volume manufactur ing area, s i g n i f i c a n t b e n e f i t s have been r e a l i z e d . However, the i n i t i a l i n s t a l l a t i o n c o s t o f an FMS i s s t i l l h i g h , s o t h a t i t i s necessary t o e s t a b l i s h a new methodology f o r designing, c o n t r o l l i n g , and e v a l u a t i n g much :nore e f f i c i e n t and h i g h p r o d u c t i v e FMS.

Ex tens ive researches have been made on the p r o d u c t i o n schedu l ing problem which i s one o f major groblems encountered i n t h e opt imal p roduc t ion c o n t r o l of inanufact l r r iqg systems [ I ] . However, many of these researches l a c k cons idera t ions f o r t h e c h a r a c t e r i s t i c s o f an FMS such as system s t r u c t u r e , complex i ty , and f l e x i b i l i t y , w i t h the r e s u l t t h a t i t i s imposs ib le t o app ly these r e s u l t s d i r e c t l y t o the produc t ion schedu l ing o f FMS's i n p r a c t i c e . Several researches deal w i t h the complex co inb ina tor ia l problem assoc ia ted w i t h the produc t ion schedul ing o f F M S ' s and prov ide a n a l y t i c a l o r h e u r i s t i c techniques [ 2 , 3 ] . I n d model cons t ruc- t i o n f o r t h e produc t ion schedu l ing o f FHS's, i t i s necessary t o i n c l u d e the f o l l o w i n g c a p a b i l i t i e s i n a produc t ion schedul ing model t o make i t more r e a l i s t i c :

- C a p a b i l i t y t o handle var ious i t 5 c o n f i g u r a t i o n s and/or d i f f e r - e n t m a t e r i a l hand l ing systems.

- C a p a b i l i t y t o handle many k inds of s t a t i o n such as machine t o o l , load ing /un load ing s t a t i o n , i n s p e c t i o n f a c i l i t y , and b u f f e r storages.

da te machine t o o l s which can per fo rm d predetermined o p e r a t i o n f o r each process ing stage o f p a r t s .

- C a p a b i l i t y t o schedule p a r t movements between s t d t i o n s v i a the m a t e r i a l t r a n s p o r t a t i o n system.

- C a p a b i l i t y t o cons ider c a p a c i t y c o n s t r a i n t s o r bu f fe r storages.

- C a p a b i l i t y t o schedule automated t r a n s p o r t a t i o n of some

The purpose o f t h i s paper i s t o p rov ide an e f f e c t i v e schedul ing method f o r t h e complex produc t ion schedul ing o f FNS's. t i o n schedul ing model f o r FMS's i s presented i n c o n s i d e r a t i o n o f the above-mentioned c a p a b i l i t i e s and t h e produc t ion schedu l ing problem i s s t a t e d as a h i e r a r c h i c a l decis ion-making problem which comprises t h r e e l e v e l s , i . e . , s e l e c t i o n o f machine t o o l s , se lec- t i o n o f c u t t i n g t o o l s , and s e l e c t i o n o f t r a n s p o r t devices f o r c a r r y i n g a p a r t and a c u t t i n g t o o l . Three k inds o f d e c i s i o n r u l e t o detennine t h e schedules o f machining and t r a n s p o r t i n g p a r t s . and o f t r a n s p o r t i n g c u t t i n g t o o l s a re proposed and a h e u r i s t i c procedure i s presented t o o b t a i n b e t t e r schedules by u s i n g the d e c i s i o n r u l e s . A case study f o l l o w s i n the l a s t sec t ion .

- C a p a b i l i t y t o s e l e c t an appropr ia te machine t o o l among candi-

p a r t i c u l a r c u t t i n g t o o l s t o s t a t i o r s .

A produc-

2 . PRODUCTION S C H E D U L I N G MODEL FQR FMS

An FPS i s a computer - in tegra ted system which incorpora tes a DNC machine shop w i t h an automat ic m a t e r i a l h a n d l i n g system i n manufactur ing p a r t s . I t combines b o t h c h a r a c t e r i s t i c s o f a j o b shop and a f l o w shop. Al though var ious types o f FMS have been developed i n t h e l a s t decade [ 4 ] , FMS c o n f i g u r a t i o n s can be c l a s s i f i e d i n t o t h r e e t y p i c a l ca tegor ies , i . e . , F l e x i b l e Manufac- t u r i n g L ine , Closed- loop o r Network Type F l e x i b l e Manufactur ing System, and F l e x i b l e Manufactur ing C e l l [5]. Due t o such complex na ture , i t i s d i f f i c u l t t o c o n s t r u c t a genera l i zed produc t ion schedul ing model f o r FMS's .

In t h i s paper, an FMS i s model led as a system c o n s i s t i n g o f ma- ch ine t o o l s , a load ing /un load ing s t a t i o n , b u f f e r storages, and m a t e r i a l and c u t t i n g t o o l t r a n s p o r t a t i o n systems which a r e the b a s i c components of FMS's. The f o l l o w i n g are t h e main assump- t i o n s f o r t h e p r o d u c t i o n schedu l ing model f o r the FMS considered here:

There a r e : 'mu l t i -purpose machine t o o l s , '& ( m = ? , ; , ._.. :.'), which are capable of 2erforming d i f f e r e n t k inds of machining opera t ion .

The f i r s t (.-=;) and the l a s t (r='*) machine t o o l s i n t h i s FMS correspond to the load ing and un load ing s t a t i o n s , respec t ive- l y . Each machine t o o l has a b u f f e r s to rage 2, o f s p e c i f i e d capac- i t y ,."..

There are :i t r a n s p o r t devices such as c a r t s , !i;, ( > = j , ? , . . . , k' 1, which can c a r r y p a r t s mounted on p a l l e t s between machine t o o l s ( s t a t i o n s ) and nove d l m g a t r a c k .

Some p a r t i c u l a r c u t t i n g t o o l s - - ( ' = . ,i: .... .i.) which may be ccnnnonly used t o per fo rm machining opera t ions on several machine t o o l s a re prepared i n the c e n t r a l t o o l storage and a u t o m a t i c a l l y d e l i v e r e d v i a a c u t t i n g t o o l t r a n s p o r t a t i o n sys tein.

Each p a r t !'!, ( ; = 2 , > , . . . , i,) i s processed i n a s p e c i f i c opera- t i o n a l sequence based on i t s own order o f processing stages.

There are a l t e r n a t i v e machine t o o l s which can perform the r e q u i r e d opera t ions

For each p a r t , t b e shop a r r i v a l t ime and o p e r a t i o n t ime (ma- ch in ing , load ing , and Jnloading) a re given. and t h e p a r t t r a n s f e r t ime between machine t o o l s and the c u t t i n g t o o l t r a n s f e r t ime between t o o l s to rage dnd machine t o o l s a r e g iven.

Setup t ime i s dependent on the p a r t l o a d i n g sequence and i s y i ven.

each process ing stage o f p a r t s .

A schematic diagram o f an FMS der ived from these assumptions i s shown i n F ig . 1. T k ? system inc ludes f o u r machine t o o l s ( M / C ) , Four b u f f e r storages ( B u f f e r ) , and a load ing /un load ing s t a t i o n . The m a t e r i a l hand l ing system (MHS) c o n s i s t s o f a c losed- loop n a t e r i a l t r a n s p o r t a t i o n system and a c losed- loop c u t t i n g t o o l t r a n s p o r t a t i o n system. t r a c k and d f low o f p a r t s w i t h i n t h e system i s u n i - d i r e c t i o n a l .

Two c a r t s can independent ly move a long a

Fiy. 1 Schematic diagram of closed-loop FMS

Annals of the ClRP Vol. 31/1/1982 31 9

3 . PROBLEM STATEMENT

In t h e production scheduling model for the FMS's mentioned above, the following production shcedul ing problem i s considered: "Determine the schedules o f machining and transporting par ts , and of transporting saxe particular cutting torlls simultaneously so as to minimize the makespan of production.

The hierarchical structure of the decision-making in the produc- tion scheduling problem stated above i s illustrated in Fig. 2. The structure conprises three levels, i .e., selection of machine tools, selection of cutting tools, and delection of transport devices. level : (1) First level (Selection of machine tools): The decision-making

The following decision-making steps are taken a t each

a t this level i s to select an appropriate machine tool among candidate machine tools which can perform a machining opra- tion for each processing stage o f a l l parts, and simultane- ously determine the loading sequence of parts on each select- ed machine tool. T h i s results in determining the schedules of machining parts.

lowing case where standard cutting tools used for machining parts on each machine tool are prepared in i t s own tool maga- zine, and only some particular cutting tools which are for comon use i n some machining operations on several machine tools are pooled in the central tool storage. In such a case, each of these particular cutting tools must be delivered from the central tool storage or a machine tool t o another machine tool which requires i t . The decision-making a t the second level i s to determine the schedule of tool allocation and tool delivery. This corresponds t o the determination of the schedule for transporting cutting tools.

(3) Third level (Selection of transport devices): When a cart is used as a means of transporting parts w i t h i n the machine shop as shown in Fig. 1, i t i s necessary to select an appropriate cart among candidate carts which can carry the part. Sched- u l i n g the movements of carts corresponds t o the determination of the schedule for p a r t movements, i .e., the shcedule for transporting parts.

(2 ) Second level (Selection of cutting tools): Consider the fol-

For a mathematical formulation of t h e production scheduling problem for FMS's, ten different kinds of operation for each part are defined and sumnarired in Table 1. The operations 4.8,9,10 are related w i t h the decision-making a t the f i r s t level, and the operations 1.2,3 and 5.6,7 are related with the second and t h r l d levels, respectively. Noting here that the decision-making a t each level in the production scheduling i s equivalent to deter- mining both the starting and the finishing times of each opera- tion for a l l the parts to be manufactured on the time scale. th i s paper, the equations and constraints on the time relations of ten kinds of operation for a part are formulated in the same manner as presented in [6,7].

Table 2 shws a s m r y of the time relations of t h e operations considered here. stage of the part PC ( W . 2 ,..., P : j=?,2, . . , J { ) when the machine tool .% carries out the machining operation, designated as C&(i. j). using the cutting tool LZ. The symbols T,[X] and T [XI re- present the starting time and the finishing time o f opifration X , respectively, and the symbol t [X] i s the time required t o per- form the operation X. Other s$mbols are used as follows: t ( t ,n+,m) is the cutting tool transfer time to the machine tool & from the machine tool I%+ on which the cutting tool Lt was used before, and ,rn*,m) is the part transfer time by the transport device 2':o the machine tool Mrn from the machine tool M,,,* which performed the operation for the j - 7 t h processing stage of part P ~ a n d Q,, is the number o f parts stored in the buffer storage E~ a t any time.

In

These are formulated for the j t h processing

iOol~TTS loading

~ e c I sion-mkim

A Particular cutting tool Is tronsferrecl from the central tool storoge or tool mgaotlne to a ITS and Is fixed on I t .

Selection of mchine tools

Mochine tools 1 1 mkeswn

Selection of cut t lm tools . -

I mhlne cuttino tools 1 1 Makespan

Selectim of transwrt devices

Fig. 2 Hierarchical structure of dccision- lnakino in production rchedulinq

The makespan of production i s defined as the length of time re- quired t o complete all the parts to be manufactured. the makespan, T. i s given by

Therefore,

T = max { TJP+.] : - min ( TJ[Pi] ':

where T f [ p i ] i s the finishin cessind a part ?:. and T,(?;] i s the starting time o f the f i r s t operation.

:<i<p * " :?'+ - - time of the las t operation in pro-

Table 1 Definition of operations

I -~ merot Ion 4 t a n Def in1 t l on

P mrtlculor cutting tool is delivered to LronsoortinS ;hf$estlnotlon where I t is reoulred vlo 1 loo!

Tool -7TS unload i nq

Setul:

Dort-mS ioodlncl part trcnsDortinP Dart 4 1 2 unloodi ng

Lood I no

PoCh i n I ng

':n I riol i nn

A wrt icu lar cuttlng tool Is transferred from a TTS to the central tool storage or tool mogazlne and Is stored in i t . A mochlne tool is set UD to start the rewl red mchin in9 operat 1 on. A D r t Is mounted onto an MS from a buf?er s t o r m . A Dart i s moved to the destination where lt Is rewired vlo an NTS.

A Part is transferred form an MS !nta o buffer storage. A W r t i s loaded onto a mochlne tool to be machined. A flort Is mochlned on a mchlne tool, such 0s turnlng, milling, and drilling. A Dart is unloaded fran a mochlne tool irlto o buffer stornae.

!!I t t ~ , . jden?:ficotiorr rimer to distlnpulsh mro t ions i T S : ~ o o l irorisPortflt ion fvstem YT:. : 'IOierlnl rrflnwortm Ion svstm

Table 2 Time relations of operations

3 -

320

Due t o the complexity o f the production scheduling problem, i t i s impossible t o f ind an optimal so lu t ion minimizing the sakespan o f production f o r a large-scale problem i n terms o f computational t ime. I n t h i s paper, a heu r i s t i c approach by using a decision ru le i s provided t o obtain a good feasible so lut ion f o r a large- scale problem i n a pract ica l sense.

4 . DECISION RULES

To obtain a feasible production schedule, many decision-making must be performed as mentioned i n the previous section. sion ru le i s defined as a ru le t o se lect an appropriate machine too l , pa r t i cu la r cu t t i ng tool, and transport device among the alternatives. There are over a hundred d i f f e r e n t kinds of dis- patching ru le [S], these are s t a t i c rules by nature. On the other hand, decision rules have dynamic character is t ics i n the sense o f considering the system state a t present and i n future. The decision ru les presented here are designated as SOTA, ESTA, and EFTA rules shown i n Table 3. The basic ideas o f these rules are as follows: (1) SOTA (Shortest Operation Time w i th Alternatives considered):

I n the conventional dispatching rules,SPT r u l e based on the machining t ime and SST ru le based on the setup time are fami l iar . SOTA r u l e i s s im i l a r t o such rules execpt t o consider a l ternat ives f o r the machine too ls and transport devices that can carry out the operations 9 and 6, respec- t i ve l y , f o r the processing stage o f parts. For the selection o f machine tools, the operation t i m e i s defined as the sum o f the times f o r the operations 4.8,9,10 i n Table 1, and for the selection o f transport devices, i s the sum o f the times f o r the operations 5.6.7. the machine too l and transport device w i th the shortest operation time.

(2) ESTA (Ear l iest Star t ing Time w i th Alternatives considered): ESTA r u l e i s a r u l e newly developed i n t h i s study and aims a t achieving a high u t i l i z a t i o n o f machine tools, pa r t i cu la r cu t t i ng tools, and transport devices and addi t ional ly smooth- i ng out the loading. chine tool, pa r t i cu la r cu t t i ng tool, and transport device, each w i th large i d l e t i m e so far .

EFTA ru le i s a combination of SOTA r u l e and ESTA rule. and aims a t minimizing the flow t i m e o f parts. The deta i ls of EFTA ru le and i t s effectiveness are reported i n [7].

A deci-

SDTA r u l e i s one which selects both

ESTA r u l e i s one which selects the ma-

(3) EFTA (Ear l i es t Finishing Time wi th Alternatives considered):

5. SCHEDULING PROCEDURE

The proposed scheduling procedure consists o f three main steps corresponding t o the hierarchical s t ructure o f the decision- making shown i n Fig. 2. the scheduling procedure i s stated i n essence.

I n order t o i l l u s t r a t e the procedure f o r the selection o f machine too ls and the determination o f the loading sequences of par ts a t the f i r s t decision-making level, a hypothetical example i s con- sidered, where two parts, PI and ? , are manufactured i n two processing stages w i th in such an Fk shown i n Fig. 1. The machine too ls avai lable f o r each processing stage f o r the pa r t PI are MI and ! 4 ~ , and :Y3 and M4, respectively. machine too ls f o r the pa r t P2 are 4 and :W3, and M and #!z, re- spectively. A network graph i s used t o describe t h s s i t ua t i on i n the same way as so f a r reported i n [6,7]. network graph f o r the example. When the Jth machining operation i n the operational sequence o f a pa r t Pi i s performed on a ma- chine too l I+,the corresponding machining node i s designated as shown i n Fig. 3 (b). Therefore, the selection o f machine too ls i s equal t o the selection o f machining nodes. graph, an arrow ( -+ ). which connects nodes according t o the technological order o f processing f o r each part, indicates the precedence re la t ions between the nodes.

The network graph shown i n Fig. 3 (a) suggests the fo l lowing : The pa r t PI i s machined on the machine too l s 4 and Mg for the f i r s t and the second processing stages, respectively. This i s shown by a seqwnce o f th ick arrows ( ~ ). For the pa r t P2, the machine too l #3 i s determined f o r only the f i r s t processing stage. Another arrow ( ) from node 2 t o node 8 indicates the precedence re la t i on which determines the loading sequence of the par ts on the c o n f l i c t machine too l I V ~ t ha t may be simultane- ously used t o perform s m machining operations f o r d i f ferent

I n the following, a fundamental idea o f

The corresponding

Figure 3 (a) i s the

I n the network

kinds o f pa r t o r the successive machining operation on the same part. I t i s assuned tha t the machine too l M4 has j u s t been selected f o r the second processing stage o f the pa r t PI by using one o f the three decision rules. i.e.. SOTA, ESTA, and EFTA rules. The resu l t i s the network graph shown i n Fig. 3 (a). The next step i n the scheduling procedure i s t o sz lect an appropriate cu t t i ng too l among the candldste cu t t i ng too l s which can be used t o perform the machining operation on the pa r t PI designated by the node 3. and t o schedule the too l transportat ion under the t i m e re la t ions and constraints s u m r i z e d i n Table 2. cu t t i ng too l i s not necessary f o r the machining operation. t h i s step may be skipped. A f te r an approporiate selection o f the ma- chine too l and the cu t t i ng too l , the next decision w i th respect t o the selection o f transport devices must be made. A transport device t o be selected must be capable o f transport ing the par t PI from the machine tools,# t o 4. One o f the three decision rules i s applied i n the selectfon o f an appropriate transport device among the candidates available. F ina l ly , f o r the selected ma- chine too l , a pa r t i cu la r cu t t i ng too l i f necessary, and the transport device, both the s ta r t i ng time and f i n i sh ing time o f each Operation defilred i n Table 1 are ajusted and determined so as t o sa t i s f y t h e f r t ime re la t ions and constraints surmarized i n Table 2. These steps mentioned above cMlpletes one cycle i n the scheduling process. The next cycle begins w i th the se lect ion o f a machine too l , MI o r M2, which can perform the machining opera- t i o n f o r the second processing stage o f the pa r t Ps. corresponding nodes t o be selected are shown i n the area enclosed w i th a broken l i n e i n Fig. 3 (a).

I f a pa r t i cu la r

The

Similar cycles repeatedly proceed by using the decision ru les proposed i n the previous section u n t i l a feas ib le schedule i s

i t a i ned.

6. CASE STUDY

The ef fects o f the proposed decision ru les are investigated through a case study. The FMS configuration i n the case study a s imp l i f i ed version found i n the manufacturing indust ry and schematically i l l u s t r a t e d i n Fig. 4. The FMS consists o f three machine too l s which can p e r f o n several d i f ferent kinds o f ma- chining operation, two types o f bu f fe r storaaes i ns ta l l ed i n

i

front o f each machine t&l, two car ts which can move along a track i n both direct ions, a loading s ta t i on and an unloading stat ion, and a cu t t i ng too l transportat ion system. Each bu f fe r capacity i s equal t o a unit. Ten d i f f e ren t kinds o f par t are manufactured i n t h i s FHS. Each pa r t i s processed through ten processing stages according t o a specif ied sequence, and two a l - ternat ive machine too ls are permitted f o r each processing stage o f a part. The machining time, setup t ine, loading/unloading times, t ransfer time. etc. are selected from the sequence o f random numbers uniformly dfs t r ibuted and given i n advance.

32

U t l

Loadina s tat ion

LHJ \

Unloading s ta t i on

Q Tool C P D n R ~mrt mice [ tort

Fig. 4 FMS configuration for case study

To investigate the ef fects o f the proposed decision rules, the computational experimentswere carr ied out f o r the combination o f three decision rules. were examined, i.e., 1) Makespan, 2) Mean f l o w t ime , 3) Mean u t i l i z a t i o n o f three machine tools, and 4) Mean u t i l i z a t i o n o f two carts. The resu l t o f production shceduling f o r a l l the com- binations o f the three decision rules i s shown i n Table 4. It i s found that the combination o f ESTA r u l e f o r the selection of machine too ls wi th ESTA ru le f o r the selection o f transport devices y ie lds the maximum values o f the mean u t i l i z a t i o n o f the machine too ls and also transport devices, and that the combina- t i o n o f EFTA r u l e f o r the selection o f machine too ls wi th EFTA r u l e for the selection of transport devices y ie lds the minimum values o f the makespan and also mean f low time.

Four kinds o f the scheduling performance

7. CONCLUSIONS

This paper deals wi th a production scheduling problem f o r a f l e x i b l e manufacturing system. A new scheduling method f o r obtaining a good feasible schedule f o r an FMS i s presented. The method i s a heu r i s t i c procedure using the decision ru les and may be used as a powerful t oo l t o control the operation o f an FMS i n a pract ica l sense. A decision rule, named ESTA. i s proposed and the effectiveness of ESTA ru le i s examined through ccinputational experiments. It i s found that ESTA r u l e i s e f fec t i ve f o r achiev- i ng a high u t i l i z a t i o n o f manufacturing f a c i l i t i e s , and tha t EFTA r u l e proposed i n the previous paper i s e f fec t i ve f o r reducing the makespan and mean f low t i m e o f production.

ACKNOWLEDGMENTS

The authors would l i k e t o express t h e i r thanks t o Kozo Kata o f Kobe University f o r h i s help in preparing the manuscript.

Table 4 Comparison of decision rulca

ScleCtlOtl O f nmhine tools SOTA I ESTA I EFTA

1): nOlcesoan Inln) 2): k a n flow tile tmln) 3): Mean utllltotlon of nmhtne tools ( X I 9): !4em utllltotlm of t ransDon devlces (73

REFERENCES

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