Computers ind. Engng Vol. 14, No. 4, pp. 455-464, 1988 0360-8352/88 $3.00 + 0.00 Printed in Great Britain, All rights reserved Copyright © 1988 Pergamon Press plc

M O D E L L I N G C O M P L E X M A N U F A C T U R I N G S Y S T E M S U S I N G D I S C R E T E E V E N T S I M U L A T I O N

BERNARD J. SCHROER a n d FAN T. TSENG

College of Administrative Science, Johnson Research Center, University of Alabama in Huntsville, Huntsville, AL 35899, U.S.A.

(Received for publication 22 October 1987)

Abstract--This paper presents an approach in simulating complex manufacturing systems. The approach is founded on developing several general purpose simulation generators for an assembly station, a manufacturing cell, and an inventory transfer function. These simulation generators can then be linked together to create a model of a complex manufacturing system. A typical manufacturing system is modelled using these simulation generators and the results summarized.

1. INTRODUCTION

Applying discrete event simulation techniques for modelling manufacturing and production systems have been performed for many years [1,2]. In fact, most of the common discrete event simulation languages have been implemented on the major computer mainframes.

In recent years there has been a renewed interest in using simulation for studying manufactur- ing and production systems. There are a number of factors which have contributed to this renewed interest. One of the major factors has been the wide introduction and acceptance of microcomputers. These microcomputers have capabilities that for many years were only available on large mainframes. A second factor for this renewed interest is the conversion of the common simulation languages for the microcomputer. Furthermore, a variety of new simulation languages have also been written. A survey of these simulation languages is given in Simulation [3,4]. Coupled with these traditional simulation languages has been the recent introduction of several new simulation languages specifically designed for manufacturing simulation such as SIMAN [5].

A third factor contributing to this renewed interest has been the adding of very elaborate computer graphics to many of the simulation languages. This graphics capability is most notice- able on the microcomputer based simulation languages. For example, SIMAN [5], and GPSS/PC [6] have elaborate graphics capabilities.

In addition to these factors, the excitement generated by Artificial Intelligence, or AI, as a simulation assist has refuelled interest. For example, research is being conducted on interfacing natural languages with simulation [7], simulating a manufacturing system using an expert system assist [8] and building expert systems for system analysis [9]. Also, several AI software developers are currently writing simulation development tools such as SIMKIT [10] and Carnegie Group's Inc. SIMULATIONCRAFT [11].

With all these simulation advances, problems still exist in making the modelling process simpler and faster, especially for the less trained simulationists. Some of the AI development tools are an attempt to simplify the modelling process by creating a library of machines, robots, manufacturing cells, and transport systems. However, these tools only operate on expensive AI processors costing a minimum of U.S.$30,000. Also, these AI software tools are expensive costing well over U.S.$50,000.

One approach to simplifying the simulation of manufacturing systems is to develop a set of general purpose routines or macros that can serve as the building blocks in a simulation. In this paper these routines are called generators. This paper presents an approach to building three general purpose simulation generators for modelling an assembly station, a manufacturing cell and an inventory transfer function.

455

456 BERNARD J. SCHROER and FAN T. TSENG

2. MANUFACTURING SYSTEM

Most manufacturing systems can be represented by the following three simulation generators: an assembly station generator, a manufacturing cell generator and an inventory transfer gener- ator. Each generator is written as a subroutine using GPSS/PC. If a mainframe version of GPSS were used, these subroutines could more easily be written using the MACRO command.

In addition to the generators, stock points are required to indicate Work In Process (WIP) inventory. Whirlygigs may be required for transferring the WIP between the stock points. Each of these generators, stock points and whirlygigs can be represented by the icons as shown in Fig. 1. These icons can then be combined to describe a manufacturing process.

I i I assembly station generator

©

C-i-3

manufacturing cell generator

inventory stock point

inventory transfer generator

Fig. 1. Manufacturing system icons.

2.1. Assembly station generator

Figure 2 outlines the logic within the assembly station generator and is representative of a typical assembly station. Items arriving at the station first wait in a queue until the assembly station becomes available. Once an item seizes the assembly station, it waits in another queue until a part at the assembly cell stock point is available to be added to the item. An elapsed amount of time is then simulated while the part is added to the item. The inventory at the stock point is then reduced by one and the item releases the facilities. In GPSS terms, the part and assembly facilities are released.

Before exiting the generator a check is made to determine if a subassembly line is feeding the station. If so, the transaction exits the subroutine. If not, a second check is made to determine if the inventory is empty at the stock point. If a cart is empty a signal is sent indicating an empty cart. If not, the transaction exits the subroutine. It should be noted that the inventory at the stock point can be defined in terms of number of carts with a fixed number of parts per cart. A signal is sent when a cart is empty.

2.2. Manufacturing cell generator

Figure 3 outlines the logic within the manufacturing cell generator and is representative of a cell making one type of part from a given number of subparts. Parts are only made within the manufacturing cell when a signal is received from an assembly station that a cart is empty and the empty cart has been moved by the whirlygig to the manufacturing cell.

Orders (i.e. signals) first wait in a queue until the manufacturing cell becomes available. Once the order seizes the cell, it waits in another queue until all the sub-parts are on hand to make a part. If there are insufficient sub-parts a signal is sent to have a full cart of sub-parts transferred to the manufacturing cell.

Once sufficient sub-parts are available, the manufacturing cell is seized and the parts made. An elapsed amount of time is simulated while the parts are made. Parts are made until the order is filled. The order then releases the manufacturing cell and the inventory (i.e. number of full carts of parts) is increased by one at the manufacturing cell stock point.

Modelling complex manufacturing systems 457

I point inventory

generator "--r-- Wait on assam b ly station

Seize essembly station

Wait on part

I Seize part

Add part to assembly

Reduce part Inventory by one

Release part and assembly stations

Note I. Part may be e subassembly

from another llne. Likewise, the stock point inventory would then be subassemblies.

transaction empty cart

I I Fig. 2. Simulation logic within assembly station generator.

2.3. Inventory transfer generator Figure 4 outlines the logic within the inventory transfer generator and is typical of a person

moving carts between two stock points. Typical in a pull inventory system, an empty cart is returned to the manufacturing cell which signals the cell to begin making another cart of parts (an order). If a full cart of parts is available at the manufacturing cell stock point, the person returns the full cart back to the assembly station stock point. If no full carts are available the person waits.

3. MANUFACTURING SYSTEM SIMULATION

A typical manufacturing system was defined using the simulation generators (see Fig. 5) and system consists of a primary assembly line with four assembly stations. Feeding this assembly line is a subassembly line with three assembly stations. Each assembly station has an inventory stock point with an initial inventory. This inventory is defined as a number of carts with a fixed number of parts per cart. The inventory at assembly station 4 consists of the items from the subassembly line.

The system also contains three manufacturing cells. Figure 6 is a product structure tree outlining how each item is added to make the finish product. Manufacturing cell 1 makes three types of parts, P1, P7, and P8. Parts Pt and Ps are made using parts Plo and Ptl- Part P7 is made using parts P12 and Pt3. Manufacturing cell 2 makes three types of parts, P3, P5 and P9. Parts P5 and P9 are made using parts Pt4 and P15- Part P3 is made using parts P16 and P17. Parts Ps and P9 are used in manufacturing cell 3 to make parts P2 and P6.

458 BERNARD J. SCHROER and FAN T. TSENG

I Stock point inventory

~Enter

Generate order of parts

jwa too / manufacturind

7 Wait on necessary ~ L , . ~ to move I sub-parts I I

('~Ter rninate "~-- I cell manufacturin~ I [transaction J--

~ .4~ Make part V

I A6d part to cart V

~m Rel~ 1 enufacturing t

ell I

Add cart to I m anufactur in(. I stock point I

~Egexit nerator )

Fig. 3. Simulation logic within manufacturing cell generator.

The manufacturing cells within the system operate in the pull mode. That ~s, a cart of parts is not made until a signal is sent from the appropriate assembly station that a cart is empty. Therefore, it is possible to evaluate the effect of work-in-process inventory on production.

3.1. Simulation model

The simulation model was written using GPSS/PC [6] and runs on the IBM PC. Some model characteristics are:

• 23 GPSS blocks for assembly station generator • 30 GPSS blocks for manufacturing cell generator • 29 GPSS blocks for inventory transfer generator • 125 Matrix savevalues for sending values to the generators.

By using the simulation generators, the length of GPSS code for modelling the assembly and subassembly lines was quite short (see Fig. 7). For example, the code for the assembly line consisted of a set of ASSIGN and TRANSFER blocks for each station. The ASSIGN block defines the station number 1-4. The TRANSFER block with the subroutine operator SBR transfers the transaction to the assembly station generator named ASM. The RTRN1 argument indicates the block for the returning transaction from the subroutine. The ASSIGN block setting parameter 9 equal to one indicates the junction of an incoming subassembly.

Incoming ~'~ essembl~

Walt on slgnel I to transfer ~

Wait on whtrly~Ig

whtrl'~ig

Transfer I empty cart

Release whirlygig

I Spllt transaction

l Wait on full cart

Wait on whirIyg g

T I Seize whirlggig

I Transfer full cart

whlrlygig

~_~ Send slgnal I to make cart of parts

hl Reduce full J ~1 carts by one }

Fig. 4. Simulation logic within inventory transfer generator.

I ,,o7 I " ~ - t_~__J Finished product

incoming assembly

Fig. 5. Typical manufacturing system.

459

460 BERNARD J. SCHROER and FAN T. TSENG

[]

O0

]

~ 0 Finished product

[

Fig. 6. Product structure tree.

]

3840

~850 3860 387C) 3880 3890 3900 3910 3920 3930 3940 3950 3960 3 9 7 0 398(} 3990 4 0 0 0 4 0 1 0 4020 4(')30 4 0 4 0 4050 4()60 4070 4()80 4090 4100 41 i0

* MAIN ASSEMBLY LINE *

GENERATE 60,FNSXPDIS ASSIGN q,O ASSIGN 2,1 TRANSFER SBR,ASM,RTRNI ASSIGN 2,2 TRANSFER SBR,ASM,RTRNI ASSIGN 2,3 TRANSFER SBR,ASM,RTRNI ASSIGN 2,4 ASSIGN 9,1 TRANSFER SBR,ASM,RTRNI TERMINATE I

* SUBASSEMBLY LINE *

GENERATE 60,FNSXPDIS ASSIGN 9,0 ASSIGN 2,5 TRANSFER SBR,ASM,RTRNI ASSIGN 2,6 TRANSFER SBR,ASM,RTRNI ASSIGN 2,7 TRANSFER SBR,ASM,RTRNI ENTER RA4,1 TERMINATE

;Non-junction. ;Define station 1 ;Go to assembly Qenerator ;Define station 2 ;Go to assembl~' generator ;Define station 3 ;Go to assembly generator" ;Define station 4 ;Junction

;Non- junct ion ;Def ine s t a t i o n 5 ;Go to assembly generator- ;Def ine s t a t i o n 6 ;Go to assembly generat~ ;Define station 7 ;Go to assembly generator ~Add suba~semb!y ko 3~ocW p ~ i r , t

Fig. 7. GPSS main program listing.

The parameters describing each simulation generator are defined by a series of matrix savevalues. For example M S A V E V A L U E P A R T (L J) defines the initial WIP at station I. M S A V E V A L U E STIME (I,J) defines the process time at station I. M S A V E V A L U E ITEM (I,J) defines the sub-parts needed to make part I.

It was assumed that the manufacturing system had one person or whirlygig to move the inventory or carts between the stock points. Table 1 gives the initial condit ions at the stock points for each of the ten runs. All other parameters were held constant during the runs. Also , to simplify the system it was assumed that the inventory of sub-parts (Pt0-P17) was unlimited for the entire length of the simulation.

The service t imes used for the manufacturing system are given in Table 2. Arrival rates at the assembly and subassembly lines fo l lowed the negative exponential distribution. The processing times at each assembly station fo l lowed the normal distribution. The times to m o v e carts between the stock points fo l lowed the uniform distribution.

M o d e l l i n g c o m p l e x m a n u f a c t u r i n g sy s t ems

Table 1. Parameters varied within each run

Number of Number of full carts parts per

Run at each stockpoint cart

1 1 1 2 1 2 3 1 3 4 1 4 5 2 ! 6 2 2 7 2 3 8 2 4 9 3 1

10 3 2

461

Table 2. Arrival and service times

Description Distribution Mean (sec) SD (sec)

Part arrival at assembly station 1 Exponential 60 Part arrival at subassembly station 5 Exponential 60 Process time at assembly stations 1-4 Normal 60 Process time at subassembly stations 5-7 Normal 60 Process time at manufacturing cells l and 2 Normal 10 Process time at manufacturing cell 3 Normal 30 Movement of carts between stock points Uniform 4

3.2. Validation of the model Validation of the model consisted of determining the equilibrium of the manufacturing system,

the starting conditions and the stopping conditions.

3.2.1. Equilibrium. It is important to recognize that equilibrium is a property of the state probability distribution of the system and not of the particular values of the state of the system that might be observed in a particular run. Equilibrium is a limiting condition that is approached, but never actually attained. This means that there is no single point in the simulation beyond which the system is in equilibrium.

The difference between the present distribution of the simulation and the limiting distribution decreases with time during the simulation. Therefore, the problem is to find that point beyond which we are willing to neglect the error made by considering the system in equilibrium.

The Conway technique [12] was used to determine equilibrium. The technique is objective in nature. Before the model is run in a production environment, the model is set up to collect measurements on a periodic basis. Using GPSS, measurements were collected after every 100 transactions terminated from the system.

After each replication, any of the collected statistics can be plotted as a function of time to give an indication of the behavior of the system. The Conway technique is to ignore all measurements until a measurement is neither a maximum nor a minimum value of the ignored set. This ignored set of measurements is then omitted from the statistics collection.

Figure 8 is a plot of the average time to assemble a part for each replication of 100. The value of

"~ 9 0 -

o

E

8 0 - E

o

o 70

I J I I I I I [ l I J 1 2 :3 4 5 6 7 8 9 10 11

RepLication ( 1 0 0 transactions)

Fig. 8. A v e r a g e a s s e m b l y t ime per rep l icat ion .

462 BERNARD J, SCHROER and FAN T. TSENG

the sixth replication was the first measurement that was neither a maximum nor a minimum of the previous set. Therefore , the first 500 transactions were required for the system to reach equili- brium. These transactions were then excluded from the collected statistics.

The GPSS commands to collect the measurements in Fig. 8 are:

STAR T 100 --~ R E P O R T REP1 R E S E T

START 100 --* R E P O R T REP2 R E S E T

STAR T 100 ~ R E P O R T REP3 R E S E T

The R E P O R T command is a special GPSS/PC feature that causes an output file to be written after each S T A R T command. The R E S E T command clears all statistics.

After equilibrium has been determined, which was after 500 transactions in our problem, the following commands are used to collect the experimental results:

STAR T 500, NP R E S E T STAR T 500

The first 500 transactions are excluded from the collected statistics. The NP option suppresses the print option. The statistical tables are then R E S E T and the model run until 500 transactions or parts are completed.

3.2.2. Starting conditions. The length of time required to obtain the probability distribution which is independent of the starting conditions depends on the starting conditions of the system. One of the most common ways of starting a simulation is in the empty and idle, or state of zero, condition. This means that at the start of execution all queues are empty and all resources or facilities are idle.

It would be ideal if the initial conditions could be selected to correspond to the conditions when the system is in equilibrium. However , this prior knowledge is generally not available. Therefore , any initial condition would be bet ter than the state of zero. For this manufacturing system the initial conditions were a defined number of full carts of parts at the various stock points.

3.2.3. Stopping conditions, A similar problem to that of determining the starting conditions exists for stopping a simulation run. For example, a simulation can be terminated by stopping the creation of new events for the system and allowing the system to return to an empty and idle state. However , including the measurements collected from the time following termination of new events will likewise introduce a bias which can be serious, especially if the total run time is small.

To avoid this problem for the manufacturing simulation, the run is terminated after a given production. Therefore , at the completion of the run, transactions were still in the system and resources were being used.

3.3. Experiments

The experimental objective was to evaluate selected system parameters by varying the number of full carts of parts at the various stock points and to then determine the minimum work-in- process inventory without impacting a given production rate.

3.3.1. Production. Table 3 gives the production rate per hour of finished product. The production rate was 45/hr with one cart with a capacity of one at each stock point (Run 1). The production rate increased to 60 parts/hr with two carts with a capacity of two. Interestingly the

Modell ing complex manufacturing systems

Table 3. Production rates with varying assembly station inventory

Number Parts Production/ Run of carts per cart hr

1 1 1 45.3 2 1 2 60.4 2 1 3 54.5 4 1 4 56.3 5 2 1 51.2 6 2 2 60.2 7 2 3 59.6 8 2 4 58.6 9 3 1 49.7

10 3 2 60.6

463

production rate also remained at 60 parts/hr with two carts with a capacity of three (Run 7). Increasing the number of carts beyond two and the number of parts per cart beyond three did not increase production (Runs 8 and 10).

3.3.2. Assembly station utilization. Table 4 gives the utilization of the assembly stations for Runs 5 through 8. This utilization includes the time the station had been seized and was waiting for an available part. Overall the assembly station utilization was relatively high and exceeded 90% of all runs. This line balance is anticipated since the mean assembly time at each station was the same.

Table 4. Assembly station utilization

Assembly station

Run 1 2 3 4 5 6 7

5 1.000 1.000 0.914 0.849 1.000 1.000 0.908 6 1.000 1.000 0.995 1.000 1.000 0.999 0.992 7 1.000 0.997 0.997 1.000 0.987 0.986 0.981 8 0.953 0.953 0.950 0.974 0.995 0.994 0.996

3.3.3. Manufacturing cell utilization. Table 5 gives the utilization of the manufacturing cells for Runs 5 through 8. The cell utilization was approximately 83% for Run 5 and increased to over 95% for the remaining runs. The increase in cell utilization resulted from an increase in the production rate.

Table 5. Manufacturing cell utilization

Manufacturing cell

Run 1 2 3

5 0.833 0.833 0.836 6 0.973 0.971 0.985 7 0.961 0.963 0.976 8 0.956 0.950 0.963

3.3.4. Whirlygig utilization. Table 6 gives the utilization of the whirlygig. The whirlygig was Occupied 100% for Run 5 since for the cart capacity was only one. Therefore, he was constantly moving carts between the assembly station and the manufacturing cell stock points.

The whirlygig utilization decreased significantly as the cart capacity increased to two, three and

Table 6. Whirlygig utilization

Run Whirlygig

5 1.000 6 0.586 7 0.381 8 0.285

464 BERNARD J. SCHROER and FAN T. TSENG

four parts. For cart capaci ty of two parts, the utilization reduced to 58.6%, for three parts per cart to 38.1% and to four parts per cart to 28.5%.

Interest ingly, even though the utilization of the whirlygig decreased significantly, the produc- tion rate increased by over 15%. A t the same time the manufac tur ing cell utilization increased which is expected.

4. CONCLUSIONS

In summary , the use of s imulat ion genera tors is an effective me thod for rapidly construct ing discrete event s imulat ion models . Fu r the rmore , s imulation genera tors can great ly reduce the t ime in building, modify ing and validating simulat ion models . For example, it is es t imated that the t ime to build the mode l o f the manufac tur ing system in this paper was reduced by over 50%.

The real payof f in using s imulat ion genera tors is in modifying the GPSS simulation mode l such as running various "what if" scenarios. Howeve r , it should be no ted that a savings is only realized if the s imulat ion genera tors have been written. Once more complex manufac tur ing processes are model led , addit ional s imulat ion genera tors will need deve lopment . A logical next genera to r would be an inspect ion and repair genera tor .

The simulat ion genera tors are easily defined using GPSS. The GPSS/PC does not have a macro opt ion. The re fo re , the genera tors were writ ten in subrout ine format .

A n area for fol low-up research is to develop a more user friendly interface, or s imulat ion assistant be tween the mode l le r and the s imulat ion language. A proper ly designed interface should great ly reduce the user ' s need to know the details of the simulation language. Ideally, the simulat ion assistant would query the user for informat ion about the manufac tur ing process and then automat ica l ly genera te the appropr ia te GPSS code.

5. REFERENCES

1. G. Gordon. The Application of GPSS V to Discrete System Simulation. Prentice Hall, Englewood Cliffs, N.J. (1975). 2. T. J. Schriber. Simulation Using GPSS. John Wiley, New York (1974). 3. Catalog of simulation software. Simulation 47, 152-165 (1986). 4. Addendum to the simulation software catalog. Simulation, 69-73 (1987). 5. C. D. Pegden. Introduction to SIMAN. Systems Modeling Corporation, State College, Penn. (1985). 6. Minuteman (1986). 7. D. R. Ford and B. Schroer, An Expert Manufacturing Simulation System. University of Alabama in Huntsville

Research Report 485 (April 1986). 8. A. S. Elmaghraby, R. S. Demeo and J. Berry. Testing an expert system for manufacturing. Artificial Intelligence and

Simulation, pp. 62-64. Society for Computer Simulation, San Diego, Calif. (1985). 9. J. Haddock. An expert system framework based on a simulation generator. Simulation 48, 45-53 (1987).

I0. Simkit System Knowledge Based Simulation Tools in KEE, No. 1.0-USK-3. Intellicorp Inc. (February 1986). 11. Simulatowncraft. Carnegie Group Inc., Cambridge, Mass. (1987). 12. Conway (1962). 13. M. S. Fox. Industrial applications of artificial intelligence. Robotics 2,301-312 (1986). 14. T. J. Schriber. A GPSS/H model for a hypothetical flexible manufacturing system. Annals of Operations Research,

pp. 171-188. Scientific Publishing Co., Basel, Switzerland (1985). 15. R. Smith and L. Platt. Benefits of animation in the simulation of a machinery and assembly line. Simulation 48, 20-30

(1987). 16. B. Khoshnevis and A. Chen. An expert simulation model builder. Intelligent Simulation Environment, Vol. 17, No.

1, pp. 129-132. Society for Computer Simulation, San Diego, Calif. (1986). 17. C. Moreira de Silva and J. M. Bastos. The use of decision mechanisms in visual simulation for flexible manufacturing

system modelling. A1 Applied to Simulation, Vol. 18, No. 1, pp. 165-170. Society for Computer Simulation, San Diego, Calif. (1986).