Design of complex flow line system by simulation

Con~t. & Indus En,,,ng Vol 4. pp 75-85 P~rpmon Press Ltd. 1900. Printed in Great Bnt~in

DESIGN

OF COMPLEX

FLOW

LINE

SYSTEM

BY SIMULATION TURGUT M. OZAN St. Mary's Universityof San Antonio, Divisionof Engineering,San Antonio, TX 78284, U.S.A.

(RevisedOctober 1979; receivedfor publication 26 No~ember1979) ~,bstraet--During the last two decades or so, there have been several attempts to gain insights into the operational behaviourof mechanicaland manual flowlines. However,an area which has received very little attention is the area of manual flow lines with more than one type of product input with constant or variable processing times. Such lines are more complex because each product entering into the system has a different work content which causes an uneven work flow and consequent station idle time and/or congestion of semi-finishedproducts. In this paper, a flow line with mixed product supply which is deterministic in the number of arriving units and probabilisticin the structure of the product mix is considered. No buffer stocks between service stations are provided;queue formationof limitedlength is allowed;the stations are located in series on the line, and each station is allowedto use multipleservers workingin parallel. The service times are assumed to be normally distributed with known mean times and variances. The objective is to design a flow line system which would provide an even flow of work where over or under utilization of servers is avoided. This is achieved by increasingor decreasingthe number of service stations by several simulations until a utilization level is achieved which is feasible for the management. GERTS III Q network modelingand simulationtechniqueis used for the solution of the design problem. This technique leads effectively to the achievement of the objective set forth for the solution of the problem.

INTRODUCTION

Mass production is a term which emerged around the turn of this century and since then, found a widespread usage in the industrial world. Flow production is a type of mass production having the basic characteristic of the continuous flow of the product through or past a series of production facilities. Flow line production is a subsection of the flow production, with the characteristic of efficient material and product flow in the manufacture of large quantities of discrete items, as opposed to the fluid or semi-fluid products produced by flow process type of production. During the last two decades or so, there have been several attempts to gain insights into the operational behaviour of mechanical flow lines (transfer lines, assembly machines, canning and packaging lines) and manual flow lines (assembly lines). A review of this work can be found in Wild[l l, Buxey et al. [2], Smith and Brumbaugh[3] and Chiang and Ozan [4]. Concentration of research work has been on manual flow lines, processing a single product on service stations connected in series, balanced with respect to mean service times and provided with buffer stocks. The input to the line is assumed to be deterministic and continuous (perfect). The objective of the research on such lines has been basically to investigate the effects of line length, service time variability and buffer capacity on the line efficiency, as measured by average idle time or output. More recently mechanical flow line systems have also attracted some research interest. A review of the work done in this area can be found in Buzacott and Hanifin [5]. An area which received very little attention is, however, in the manual flow lines with more than one type of product (mixed-model) input, with constant or variable batch sizes and with constant or variable processing times. Such lines are more complex because of the fact that each product entering into the system has a different work content, causing an uneven work flow and consequent station idle time and/or congestion of semi-finished products. As stated by Wild[l], this type of lines "'presents the most complex design and operating problems. Indeed, some of these problems are so complex that adequate analytical solutions have not been developed". This paper has the objective to study the suitability of a simulation approach to the design of such complex flow lines. A flow line with considerable complexity has been selected from local (San Antonio) industries as the subject of study. GERTS III Q model is used for the 75

76

T.M. OZAN

simulation process. The computer simulation was performed by Maturino[10] under the supervision of the author.

DESCRIPTION OF THE FLOW LINE SYSTEM SUBJECT TO THIS STUDY

XYZ Equipment Overhaul Company of San Antonio, henceforth to be designated simply as XYZ, provides service for the maintenance, repair and overhaul of materials handling equipment. The company receives the bulk of its work from a local Air Force Base on contracts awarded as a result of competitive bidding. Presently XYZ plans for a future Air Force contract for overhauling the equipment as shown in Table 1, with basic activities, activity times and quantities expected. The present design of the flow line system is shown in Fig. 1. The input to the line is a mixed product supply, deterministic in the number of arriving units and probabilistic in the structure of the product mix. No buffer stocks are provided between stations and queue formation in limited lengths is allowed within the service stations. The service stations are located in series on the line, each service station is allowed to use multiple servers working in parallel within the station. The service times are assumed to be normally distributed with mean times as shown in Table 1. Based on the experience of the previous contract, the problems related to the line operations have been as follows: (1) Although mean times for each major service activity have been established as shown in Table 1, these times were subject to significant fluctuations because some of the arriving equipment was in much better condition than the others. (2) Because of the uncertainties in the types of the arriving equipment and the fluctuations in the service times, frequent firing and hiring of the work force were necessary, which caused managerial and technical difficulties. (3) The technical difficulties resulted from the uneven work flow and consequent station idle time and/or congestion of semi-finished products in the service stations.

Table I. Activity times and quantity of the equipment expected to be overhauled during the next planning period by the XYZ company ACTIVITY TIMES PER UNIT (So~urs)

ACTIVITIES B-I I. Teardown

Z.SO

SIOL,TI~S

EVAP.

S TON

8.00

18.00

1.00

20 TON 40 T0N TRAILIRS ,Ta~k8 Z.00 I0.00 16.00

1.50

2.00

S.00

1.50

1.50

2.00

6.00

12.00

30.00

20.00

3.00

4.00

40.00

70.00

4. Welding

6.00

S0.00

40.00

1.00

1.00

S. Body Work

2.00

20.00

I0.00

2. Stripping 3.

Assembly

S.00

I0.00

1.00

2.00

1.00

S.O0

2.00

2.00

4.00

3.00

1.00

1.50

3.00

3.00

2.00

3.00

1.00

7. Painting

2.00

3.00

1.SO

8.

3.00

s.oo

.SO

2.00

2.00

1.00

2.00

6.

Priming

Finishing

i0.00

20.00

$.00

S.00

8,00

15,00

IS,Q0

I0. Storage

.SO

.SO

.SO

.SO

.SO

1,00

1,00

11. Shipping

.SO

.SO

.SO

.SO

.50

1.00

1.00

26S

16

27

60

30

I0

8

64

4

7

14

7

2

2

9. PP ~ C

EXPECTED QUANTITIES FOR THE PLANNING PERIOD PERCENT OF TOTAL QUANTITY= ARRIVAL PRO~ABII.TTY ARRIVAL RATE

i Unit per Two Hours

(Constant)

~Y

WORK SECTI ON

FOR ~ - I

AND TRAIL.E~$.

Fig. 1.

STANO$

METHOD (1)F OPERATI ON.

G

N

MM

PROCESSED REOUI RES A PARTIGLJLAR

G

N

I

G

!

N

.-----m

G

N

!

S

8

T

I

N

G

N

I

A

R

G

N

L. I

T

N G

I

A ----tin

F

P

I

N

P

O

R

E

L

P

W

M

L

P

D

E

!

I

R

S

S

A

W

R

T

E A

$

T

WORK SECTI ON FO~ OTHF~ EQUIPMENT,

80DY

/-~-/

JAGK

40-TON

SPF'CIAL

JAGK

20-TON

~

~)~----~

JAGK

5 -TON

EA(.'~H OF UNITS

~)--

SKATE

//~)

~ - , - -

EVAPORATOR

~

~)-~---"-

STAND

TRA I L ER

8-1

----qm

E

A

R

0

T

S

3

o_.

4

78

T.M. OzArq

THE SCOPE AND METHODOLOGY FOR THE SOLUTION The flOW line system and its problems described in the foregoing section impose the following specific questions: (!) Which service stations of the system are most likely to cause idle times or congestions? (2) What are the necessary additions or deletions in the number of servers to achieve an even or balanced flow through the system? (3) In the balanced system, on average, how long is each kind of incoming equipment expected to take before it is completely overhauled? What are utilization levels of the servers and how long would the entire contract work (expected to be 416 units in total--see Table 1) take for completion? At present, there is no analytical approach to answer these questions for a flow line system as described in the foregoing section. Thus, the simulation approach was considered as the only means with some promise of useful results. DESIGN OF THE GERTS III Q MODEL FOR THE SIMULATION OF THE FLOW LINE SYSTEM GERTS III Q, Graphical Evaluation and Review Technique for Simulation, has been selected for the simulation of the flow line system subject to this study. GERTS III Q was introduced by Pritsker and Burgess[6] for the simulation of stochastic networks with queuing capabilities. The preliminary steps in this simulation are: collecting of descriptive information about the operational aspects of the system, determination of the operational variables along with their characteristics and modeling the system structure by a stochastic network suitable for simulation. The flow line system subject to this study has been already described in the foregoing section. Basic operational variables of this system are service (activity) times and arrival probabilities of each type of units (equipment) entering the system. It has been assumed that the service times are normally distributed with the average times as stated in Table 1. However, no records of the variability of service times could be found. Therefore, the variances of service times have been estimated by the approximation of normal to beta distribution, using optimistic (= a), pessimistic (= b) and most likely (= m) service times in the relationship ~r2 = (b - a)2/36. The arrival probabilities of each type of units are represented by the expected "Percentage of Total Quantity" during the contract period as shown in Table I. GERTS III Q requires that the system be represented by a GERT network called GERTS III Q Network. The adequacy of this network to represent the system depends on the quality of information available about the system operations and system variables, as well as the ability of the experimenter to represent the operational aspects of the system graphically by using GERTS III Q symbolism. For the present system, the GERTS II1 Q network is given in Fig. 2 under the title of original network. Some explanation of this network will help the reader gain a conceptual understanding of the GERTS Ill Q application in this study. Node 86 of the network is the SOURCE node, which initializes the network once it has been realized by an arriving unit. Node 87 is used to generate arrivals, one unit per 2hr, to the network which is accomplished through the self-loop at this node. Node 87 is also a MARK node, which records the time an item enters the network. Accordingly, Node 87 represents a reference point in time for STATISTIC nodes. 76, 77, 78, 79, 80, 81 and 82 which collect statistics on the average time a certain unit spends in the system and the number of units served during the simulation. Node 85 is a PROBABILISTIC node which distributes the arriving units through the network, according to their arrival probabilities. Thus, arcs (85-2), (85-3), (85-4), (85-5), (85-6), (85-7) and (85-8) represent the distribution channels for respective units, each with probabilities of the realization equal to the arrival probability of that specific unit as shown in Table 1. Service Stations of the flow-line which caused congestion problems in the past have been designated by QUEUE nodes in the network. A QUEUE node has a certain storage capacity, specified on the lower left corner of the node symbol, for the arriving unit to wait, if necessary. A unit is automatically held in the QUEUE node until it is served on the basis of first-in-firstout (FIFO) service policy. Statistics concerning AVERAGE NUMBER IN THE QUEUE, AVERAGE BUSY TIME OF PROCESSOR, AND AVERAGE BALKERS PER UNIT TIME

um no mm

® Z

O PAINT AND VE TARNISH

~)

"~ ), .-t

181rMBLIr

[LD

~0 .-I O Z

~OY WORK

O

®

NQ

NTIN@

FINISNINQ

i"~ - - - - ~ ~ bL

uu!s~lnW!S ^q W~lS^~ aU!l Muy x~luwo~ JO u~!saQ

80

T.M. OZAN

are automatically maintained on the QUEUE nodes, indicating also the number of observations and MINIMUM, MAXIMUM and STANDARD DEVIATION of each of the above stated statistics. A branch emanating from a QUEUE node represents the service activity provided for the units waiting in the queue. Service branches of the QUEUE nodes are characterized by the probability of realization of the service activity by a unit, the type of service time distribution (assumed here as normal distribution), and the average and standard deviation of the service time. The following are the service stations of the flow-line with congestion problems in the past: Nodes, 9, 10, I!, 13, 14, 15 and 16 represent single server service stations for the tear-down activity, each rendering service to one of the specific types of units. Node 25 represents a single server welding station for B-I stands and trailers. As the portion of B-I's and trailer units entering the flow line are 265 and 8 respectively (see Table 1), the branches emanating from Node 25 have a probability of realization of 97% and 3% for B-l's and trailers respectively. Node 26 is a single server welding station for Evaporators alone, while Node 27 represents a single server welding station for Skates, 6-Ton, 20-Ton and 40-Ton Jacks. Node 34 represents a single server service station for body work provided for B-I Stands and Trailers while Node 36 represents a single server service station for body work serving Skates, 5-Ton, 20-Ton and 40-Ton capacities. Nodes 43, 51, 59, 67 and 73 represent single server service stations for priming, painting, finishing, crating and storage for all units. The branches emanating from each of the above stated QUEUE nodes have their appropriate service parameters used as input data for the simulation process. Node 83 is a STATISTIC NODE which collects time statistics to produce the average time spent by a unit in the system. Node 95 is the SINK Node and requires 416 releases from the node to complete one simulation. Node 90 is the BULK NODE, which affects the routing of a unit upon its arrival at a QUEUE node because the QUEUE node is at its capacity. If the bulk statistic is required for any QUEUE node of the network, this should be indicated by a dashed line, connecting respective QUEUE and BULK nodes. For our case, in order not to obscure the essential information on the original network, these connecting lines have not been shown. Nodes 18, 19, 20, 21, 22, 23 and 24 are regular nodes for the assembly of B-Stands, Trailers, Evaporators, Skates, 5, 20 and 40-ton Jacks respectively. They are regular service centers without queuing problems. The same applies to Node 17 which represents the service station for Stripping. In this station, nine different equipments are processed and hence, the station should be represented by a probabilistic node in order that the equipment can be released to the next station in accordance with their arrival probabilities to the stripping process (i. e. Node 17). Nodes 28, 29, 36, 30, 31, 32 and 33 are, in effect, dummy nodes which route an equipment from one service center to the other. A dummy node must always be used between any two service centers represented by QUEUE nodes. The data and information about the flow-line system and GERTS Ili Q network model of the system described in the foregoing section and presented in Fig. 2, in fact, establish the basic input for the first computer simulation of the present flow-line. Specific information for the preparation of input data for the simulation process is provided in Pritsker and Burgess[6], Pritsker and Phillips [I 1], Whitehouse [7] and Moore and Clayton [8]. The plan for this simulation process was set as in the following: (1) Simulate the flow-line system represented by the GERTS III Q network model of Fig. 2, designated as the original system and locate the service stations with problems of congestion or idleness. (2) Accordingly, decrease or increase the number of servers whichever necessary, to remedy the problems. (3) Modify the GERTS III Q network model and its parameters based on the results of Step 2. (4) Simulate the modified network and repeat the Steps 2 and 3 for the modified network. (5) Repeat Steps 2--4 until a reasonably even work flow can be achieved through the system. (6) Redesign the flow-line system based on the information obtained from the above simulations and design the final flow-line system.

Design of complex

Each network (expected

(the original

and the modified)

number of units through the contract

for each simulation. The initial in the service stations.

results of the first simulation

OF THE

81

by simulation

will

be simulated

period-see

state of the network

RESULTS The

flow line system

twice,

with

Table 1) generated

416 units

into the system

will be assumed to be empty,

i.e. zero units

SIMULATiON

on the original

system, using the data and information

stated in the foregoing sections of this paper and the original GERTS III Q network model have been summarized in Table 2. For this simulation, it took 1017 man-hours for 416 units to reach the SINK

Node 95. During this time, 261 units have been completely

served and the remaining

154 units had to bulk to Node 90 because of the lack of space to accomodate in the queues.

A review of the simulation output as summarized

the units waiting

in Table 2 indicated

that, in the

original system, some of the service stations were under-utilized while some others were over-utilized. From this information, it was obvious that the number of single service stations

for Tear-down, Welding, Body Work, Crating and Storage should be reduced, while the single

Table

2. Summary

ORIGINAL

of the GERTS

III Q simulation

SYSTEU

1Sf.

with the original,

FIODIFIED

1st and 2nd modified

SYSTEM

2ND..HODIFIED

SYSTEM

&gfg 9

i

88

47t

10

lut

11

St

15

101

1s 14

2: St

16

St

2s

67;

a : : L

26 27

JOI 49t

2 :

36 34

29t 65t

43

89;

x P z L g 2

78t

4

22t

2s

65t

I 26

86\

36

891

43

77t

J 2s

62;

1 26

731

36

821

17

5

5

1

1

51

97t

59

97t

169

43

71

51

97t

59

9st

11

7

94:

18

39

8

g 5 '

89 96t

/

87

5 c( 5 a

80;

~zl

-I

189 5

88

not

\

systems

6

78;

51

39t

59

88t

7

82t

5

80t

84

511

84

86t

8

57t

67

8:

67

13t

67

2ot

s 2 i! 75

8:

7s

13t

75

70:

I -

I

82

T. M OZ^N Table 3 Summary of the quantitative information about the problem areas of the 2nd modified system WORK CENTER UNIT SERVED

TE%R DOWN

B-I Stand

SERVER ~VERACE BUSY AVERACE NODE TIME (SERVER NUMBER IN RECOMMENDATION EFFICIENCY) TIlE QUEUE 88

80%

0.38

89

78%

2.32

&

22%

0.06

Trailer Evaporator

Skate S-ton

WELDING

Server 4 helps

jack

2O-ton

Jack

40-ton

jack

Evaporator i Skate S-ton

jack

20-ton

jack

40-ton

jack

26

86~

6.~,

36

89%

1.86

BODY WORK

All

P\INTING

%11 Remaining Units

6

78%

0.$8

S1

39%

0.09

B-1 S t a n d

5

80%

7.00

Stand

59

87%

1.72

Stand

7

82%

1.75

FINISHING

units

Trailer Evaporator

8

57%

0.38

84

51%

0.15

Skate S-ton jack 20-ton

jack!

40-ton

jack

Server 89.

% p a r t time s e r v e r is lassigned. Also server 25, who i s b u s y 65% c a n help.

A p a r t time server (possibly one full time s e r v e r who helps p a r t l y to 26 a n d partly t o 36) is a s s i g n e d .

Server server

51 h e l p s 6.

Servers 8 and 04 h e l p s e r v e r s S, $9 a n d 7. T h e y may a l s o r e c i e v e some hel~ from the servers b7 and 75 who will be combined to one server.

CR%TING

%11 u n i t s

67

20%

0.02

Combined to one server with server 75.

STO1L-~GE

All u n i t s

75

20%,

0.007

Combined with server 67.

server stations for Priming, Painting and Finishing should be increased, such that an even work flow in the system can be achieved. In order to decide on the appropriate changes in the number of service stations for each type of service, the effects of such modifications on the efficiency and queue length need to be studied as suggested under Steps 2-4 of the simulation plan presented in the previous section of this paper. Accordingly, the Original System has been modified twice. Because of the restricted space, the GERTS III Q network models of the second and third modified systems will not be shown here However, the addition and the deletions made in the number of service stations

29 15 65 32 9

27 16 60 30 10

EVAPORATOR

SKATE

5~TON J A C K

2Q~TOH J A C K

40-TON J A C K

THE COMPLETION

TOTALS T I M E FOR 411 UNITS = 1 0 5 4 HOURS

411

7

416

254

STAND

TRAILER

B-1

8

(SIMULATION

265

UNITS

{24.4

- STATISTICS

92.00

66.62

78.52

82.31

68.51

94.74

73.44

NODE 83

~sIM.LATION ~SULTS)

(st.)

A V E R A G E T I M E EACH U N I T S P E N T IN T H E 2ND M O D I F I E D SYSTEM

WEEKS)

RESULTS)

A V E R A G E N U M B E R OF UNITS S E R V E D D U R I N G THE PLANNING PERIOD

Table 4, Summary of the statistical information about the 2nd modified system THE ~ u R u E E O F UNITS WHICH M E R E E X P E C T E D TO B E S E R V E D DURING T H E N E X T PLANNING P E R I O D BY T H E 2ND M O D I F I E D SYSTEM

82

81

80

79

70

77

76

STATISTICS HODE H U M B E R

3

T. M. OzAs

have been shown for each system in the SERVER column of Table 2. As it can be seen from Table 2, this second modified model requires three parallel single server stations (Nodes. 88, 89 and 4) for Teardown activity, instead of seven used in the original model. Welding Work center requires two parallel single server service stations (Nodes 25 and 26) instead of one used in the original model and the Finishing Work center requires five parallel single servers (Nodes 59, 7, 5, 84 and 8) instead of one. As it is seen from Table 2, although the second modified system provides satisfactory improvements in the server efficiency, queue length and the number of bulkers, there are still some minor problems to be remedied. In Table 3, these problems are summarized along with some practical recommendations for their solution. For all practical purposes, it is expected that these recommendations will help to achieve a reasonably even work flow through the system. Thus, further simulations have not been undertaken and the system described in Table 3 is recommended for the design of the flow line. Needless to say that simulation can continue until the management is satisfied with the result, or until a state of the system is reached which is more amenable to managerial judgement to make effective recommendations for further improvements. Table 4 exhibits a summary of the statistical information about the 2nd modified system. As it is seen, this system is capable of servicing the expected number of units in each equipment category within 24.4 weeks.

CONCLUSIONS AND COMMENTS The basic conclusion of this work is that the simulation technique can be effectively used for the design or redesign of flow-lines with more than one type of product input, with constant batch size and with variable processing times, where queues are allowed in the service stations to the extent provided by the available space. It seems that GERTS III Q network modeling and simulation provides a practical technique to be used for the design of this type of flow-lines. The basic characteristic of this technique specifically useful to the study of the flow-line problem is, perhaps, the simplicity of the design of the GERTS III Q network model for a given system. The symbolism and the concepts required for modeling are straight forward and the input data required can be obtained from direct observation or from the historical records. For the design of new flow-lines, the input data must be either experimentally synthesized or assumed on the basis of the past experience. The preparation of a schematic model of the system (see Fig. 1) before the GERTS III Q network is designed, appears to be very useful. It helps for the understanding of the operational and technical aspects of the system, thus providing a structural basis for designing the GERTS III Q network. Additionally, the combination of the schematic and the network models enables the engineer to communicate the simulation process and its results to all levels of the management. GERTS II1 Q technique is in fact only one stage in the development of a sequence of many stages each with specific capabilities and characteristics in the network modeling and analysis of systems. A recent development in this sequence is the Q-GERT Analysis Program published by Pritsker 19]. This program has additional capabilities of assigning attributes, such as priorities to transactions, capability for queue or server selection for transactions; rejoining the queue after a given time of waiting in the Bulk Node or balking to any other node of the network and the capability of the inclusion of FORTRAN based models that can be inserted by the analyst directly within the network structure. These capabilities may further enhance the effectiveness of the GERTS Simulation approach to the simulation of flow-lines with further complexities. REFERENCES I. R. Wild, Mass-Production Management. Wiley,New York (1972). 2. A. M. Buxey,N. D C. Slorck& R. Wild, Productionflowline systemdesign: a review. AIIE Trans 5, 37 (1979). 3. D. L. Smith & P. Brumbaugh,Int. J. Prod. Res. 2, 163 (1977). 4. K. Chiang & T. Ozan, Reoiew of Assembly Line Balancing--The Design o[ Complex Lines, p. 71 St. Mary's University of San Antonio, Divisionof Engineering(1978). 5. T. A. Buzacott & L. E. Hanifin, Modelsof automatic transfer lines with inventorybanks--a review and comparison AIEE Trans. 2. 197 (1978).

Design of complex flow line system by simulation

85

6. A. A. B. Pritsker & R. R. Burgess, The GERT Simulation Programs: GERTS Ill, GERTS Ill Q, GERTS Ill C and GERTS Ill R. NASA/ERC Contract NAS-12-2113, Virginia Polytechnic Institute (May 1970). 7. G. E. Whitehouse, Systems Analysis and Design UsingNetwork Techniques. Prentice-Hall, Englewood Cliffs, New Jersey (1973). 8. L. I. Moore & E. R. Clayton, Introduction to Systems Analysis with GERTModeling and Simulation. Petrocelli (1976). 9. A. A. B. Pritsker, Modeling and Analysis using Q-GERT Networks. Wiley, New York (1979). 10. S. M. Maturino, Applications of GERT HI Q and PERT Techniques. Department of Industrial Engineering, St. Mary's University of San Antonio (1974). 11. A. A. B. Pritsker & D. T. Phillips, GERT Network Analysis of Complex Queuing Systems. Research Mere. No. 72-1 (working paper) (Jan. 1972), Purdue University, School of Industrial Engineering. (This paper includes three simple application examples of GERTS Ill Q Simulation.)