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Buffer levels and choice of material handling device in flexible manufacturing systems
166
European Journal of Operational Research69 (1993) 166-176 North-Holland
Theory and Methodology
Buffer levels and choice of material handling device in Flexible Manufacturing Systems B. M a h a d e v a n a n d T . T . N a r e n d r a n
Industrial Engineering & Management Division, Dept. of Humanities & Social Sciences, Indian Institute of Technology, Madras 600 036, India Received December 1990; revised October 1991 Abstract: The determination of buffer sizes is a key issue in the design of a Flexible Manufacturing System (FMS). A study of FMS installations and the systems indicates the relationship between the buffer capacity and the type of primary and secondary Material Handling Systems (MHSs) employed. A priori knowledge about the buffer requirements enables the FMS designer to select appropriate MHS devices. This paper addresses the issue of determining buffer capacities through simulation. Using response surface methodology for efficient experimentation, the best combination of central and local buffer is obtained. Keywords: Flexible Manufacturing Systems; Material Handling System; Buffer; Simulation; Response surface methodology
1. Introduction A flexible manufacturing system (FMS) consists of three sub-systems, viz. the machining system, the material handling system (MHS) and the control system. A network of computers, which form the control system, controls and interfaces with the other two sub-systems. In contrast to a transfer line, where all the parts follow the same sequence of operations, an FMS is equipped with a material handling system (MHS) which permits the parts to traverse a variety of routes. FMSs
Correspondence to: T.T. Narendran, Industrial Engineering & Management Division, Dept. of Humanities& Social Sciences, Indian Institute of Technology, Madras 600 036, India.
often require intermediate storages to counter breakdowns, variations in process times and blocking of machines due to diversity of part routing. There are two stages at which storage can be provided in an FMS. A local storage for each machine and a common storage that is accessible to all the machines of the system are known to exist in FMS installations. Each has a role to perform and these roles overlap partially. While the primary purpose of either storage in an FMS is to ensure smooth flow of production, differences occur in their manner of operation. Local storage reduces delays in the loading of parts to machines but needs close control over the release of jobs into the system to avoid blocking of machines (Buzacott and Shantikumar, 1980; Sabuncuoglu and Hommertzheim, 1989). Com-
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B. Mahadevan, T.T. Narendran / Buffer levels and choice of rnaterial handling device in FMS
(a) Transfer of work pieces between local buffers of two machines. (b) Transfer of work pieces between a local buffer and a central buffer. (c) Transfer of work pieces between a machine and its local buffer. The first two involve inter-location transfer of work pieces and are performed by the primary MHS, while the third is a transfer at a machine location which is performed by the secondary MHS. Owing to the inherent capability of the MHS devices, the choice of secondary MHS devices is preemptive in nature in many cases. For example, when computer-controlled conveyors are used as the primary MHS, robots are necessary for localized work piece handling at specific locations. Likewise, when AGVs are used as the primary MHS, a rotary pallet shuttle mechanism or robots must be used in conjunction with them as secondary MHSs. The machine layout and MHS devices are related factors in FMSs. Owing to high system costs, the efficiency of the MHS is crucial to equipment selection. AGVs, tow-line carts and rail-guided mechanisms can operate efficiently in linear layouts only. It is preferable to use robots in systems having radial or circular layouts and conveyors and automatic monorail systems in layouts which are curvi-linear in nature. Heragu and Kusiak (1988) identified four classes of machine layouts which bear relationships to the type of MHS: circular layout, linear single row layout, linear double row layout and clustered layout. A study of FMS installations and the systems considered for study by the researchers indicates the relationship that exists between the buffer
mon storages are not constrained by such factors but are less effective in reducing material handling delays. It is often desirable to use both forms of storage. Research studies on existing FMS installations and on models of FMS show that the choice of material handling device influences the buffer capacities to be provided. Viewing this feature the other way around, this study seeks to determine the buffer requirements first so that an appropriate MHS can be chosen. A simulation approach for determining the buffer sizes is presented. The organization of the paper is as follows. The relationship between MHS devices and system configuration is discussed in Section 2. Studies on estimation of buffer requirements is included in Section 3. Section 4 contains a review of Response Surface Methodology (RSM). The shop congestion factors and job release rules are introduced in Section 5 and the simulation model is described in Section 6. This is followed by the development of the RSM procedure in Section 7. The results are presented in Section 8 and conclusions are drawn in Section 9.
2. M H S devices and system configuration in an FMS
It is convenient to classify the material handling system in an FMS into primary MHS and secondary MHS. The work piece transport in an FMS can be categorized under any one of the following:
F-r-
r-rTrl
4
r-rl-rl
r-5-
Loca[ Buffers Material
4
4
167
H a n d l i n g System
Local B u f f e r s
I Lu°=: Figure 1. Layout of the FMS at G E
=
168
B. Mahadevan, T.T. Narendran / Buffer levels and choice of material handling device in FMS
l, Gauge I ~
~
///
I
Machining] centre ]
Lathe ~~ ' /~I / /_ ] t. axis
I Pulletout
Pallet in
Control Room
Figure2. Layoutof the FMSat Lister capacity that can be provided in the system and the type of primary and secondary MHSs employed. In two different installations the variation in the computer-controlled conveyors design, viz., a two-tracked conveyor and a single-tracked conveyor, resulted in different buffer configurations of the system (Ranky, 1983; Newell and Radley, 1989). A two-tracked computer-controlled conveyor system provides both local and central buffer whereas a single-tracked loop conveyor provides only central buffer. The inner track of the two-tracked conveyor acts as a central buffer and the outer track serves as local buffer. Pick and place robots usually serve a group of machines situated radially, performing all the material handling functions including loading and unloading of jobs and tool drums. Such configurations require only a central buffer to the set of
I
I
I
I
I
*
I
I
I
I
I
I J
I
I
machine tools served by the robot; no local buffer is required. The FMS at Lister (Lister installs £750000 FMS, 1985) has a semi-circular layout of machines served by two robots. In recent system designs, a rotary pallet shuttle mechanism is provided as an interface between the machining centre and the primary MHS. In such cases, the number of indexing stations in the mechanism constitutes the local buffer for each machine tool. The use of shuttles as local buffer was discussed by Chang et al. (1986). They simulated a system with a central buffer common to all the machines and a local buffer in front of each machine tool. The 'machining cells and systems' offered by FMT Ltd., of KTM, includes Fleximatic FM100/FM200/FM300 and the FM V series. The machine tools have local buffer in the form of multiple indexing stations in a rotary pallet shuttle mechanism. Central buffer is pro-
I
I
I
I
I
I
Load & unload
I
i
I
I
Local Buffers
I lk
Material Handling System < Central Buffer
Figure3. Layoutof the systemstudiedbyFan andSackett
w,
B. Mahadevan, T.T. Narendran / Buffer levels and choice of material handling device in FMS
f
169
1 Material
Handling System
~
......
rz: q
Load & Unload C e n t r a l Buffer
Figure 4. Layout of the system considered by Stecke and Solberg
vided opposite to the row of machine tools in a linear fashion. The MHS separates the machine tools and the central buffer and moves between them.
There are several examples of AGV-based systems with different buffer configurations: only a central buffer (Stecke and Solberg 1981); -
Table 1 Relationship between MHS and buffer capacity of FMS Other MHS devices used
Availability of buffer
Installed
Central
Local
at a
32 bin A S / R S with a rail-guided stacker type transport.
Two-station work changer.
yes
yes
Caterpillar (1990)
Gantry Robot.
Two-pallet work changer buffer of 140 pallet stacker.
yes
yes
Mazak Corp (1990)
AGV.
An A S / R S for pallet storage, pallet shuttle pallet turn table.
yes
yes
Mori Seiki plant at Iga (1985)
Rail-mounted robot.
A 44-station pallet stacker area.
yes
no
Yamazaki's Oguchi works (1985)
Rail-mounted cart with shuttle mechanism.
A 15-station pallet stacker area.
yes
no
Detroit Diesel Allision Division. (Witt, 1989)
Robocarrier AGV.
Two 10-station carousels and pallet transfer mechanism.
yes
yes
Vought Aero products division (Andel, 1984)
A two-tracked loop conveyor.
Robot, gating and siding mechanisms.
yes
yes
600 Group SCAMP (Ranky, 1983)
Robot.
A common area for pallet storage.
yes
no
Lister (1985)
Rail-guided transfer mechanism.
21-station pallet stands in front of machines and load/unload station.
no
yes
GE's plant at Erie (1983)
Low profile tow line cart.
Custom-designed pallet shuttle at each machine.
yes
no
Hughes Aircraft (Burgam, 1983)
Primary MHS
a Source in parentheses
170
B. Mahadevan, T.T. Narendran / Buffer levels and choice of material handling device in FMS
- only local buffers at machine locations (FMS at GE, 1983; Carrie et al., 1984); - both central buffer and local buffer (Fan and Sackett, 1988). Figures 1 and 2 show the layouts of the FMSs at GE and Lister and Figures 3 and 4 show the layout of the system considered for study by Fan and Sackett (1988) and Stecke and Solberg (1981). Table 1 shows some examples of central and local buffer provided by the primary and secondary MHS devices in current installations. The presence of both the types of buffer and the relationship between the buffer capacity of the system and the type of MHS employed is clearly indicated by the study of FMS installations and recent research attempts. It follows that the estimation of buffer requirements is useful to the FMS designer for selecting the appropriate MHS devices.
3. Estimation of buffer requirements The determination of optimal buffer has been pursued through analytical as well as simulation models. Mohanty and Kulkarni (1989) modelled a two-station automated serial flow production line to optimize in-process inventory requirements by assuming exponential operation time. Koulamas (1989) presented a model for obtaining the optimal buffer size in two-stage machining systems. Simulation was preferred for non-Markovian failure case. Hopp et al. (1989) considered a continuous flow production process subject to failure with an intermediate buffer and suggested a procedure for determining the optimal buffer. Jafari and Shantikumar (1989) formulated a dynamic programming problem with the objective of optimally distributing the total storage space among the intermediate buffers in multi-stage automatic transfer lines. Liu and Sanders (1988) demonstrated the application of a Stochastic QuasiGradient method (SQG) to optimize the performance of asynchronous flexible assembly systems. They have developed a hybrid algorithm which uses a queueing network model to set the number of pallets in the system and an SQG algorithm to set the buffer spacings to obtain optimal system throughput. The inherent limitation of the approach has prevented the development of analytical models
for a complex system such as FMS without some
gross assumptions. In many cases, this has resulted in analyzing models that do not reflect the actual system under consideration. Early attempts to estimate buffer requirements were, by and large, confined to serial a n d / o r multi-stage production systems. Deterministic and non-Markovian processing times, limited local and central buffer, failure of machine tools and material handling system, planned interruption of the system, alternative processing sequences and other such factors, if considered simultaneously, will lead to intractable analytical models which are of little use. On the other hand, simulation models, which can easily incorporate such situations, are often found to be time-consuming. Although the speed of processing of the computers has increased considerably, paving the way for the use of simulation as a methodology for solving complex problems more realistically, use of efficient experimentation techniques in conjunction with simulation would make the approach even more attractive. The use of RSM for efficient experimentation with simulation models is well known and the current study demonstrates the use of RSM for estimating the buffer requirements.
4. Response surface methodology Response surface methodology is generally used to optimize "the performance of an unknown system (or a model of the system) that is subjected to controllable, uncontrollable and unknown variables" (Brightman, 1978). RSM can be applied to any system that has the following key elements: (1) a criterion of effectiveness known as the response of the system which is measurable on a continuous scale, and (2) quantifiable independent variables that affect the systems's performance. RSM seeks to approximate the response function by a lower-order polynomial. Denoting the criterion of effectiveness by ~7 and the decision variables as X 1, X 2. . . . , Xk, the system can be modelled by
n =f(x,,
s)
t3. Mahadevan, T.T. Narendran / Buffer levels and choice of material handling device in FMS
where s is a random variable of mean zero and of variance or2, regardless of the decision variables. Application of RSM for a first-order experiment involves a two-step procedure: 1. From an initial condition, known as the base point, a first order experiment is conducted to develop an estimate of the gradient direction. Using a 2 k factorial design or a k-dimensional simplex design, it is possible to estimate the linear equation k
= a 0 + ~_, a i S i i-1
where = An estimate of the system response under study. a 0 = T h e response of the system at the base point. X~ = Value of the i-th controllable variable. a i = Regression coefficient of the i-th controllable variable. 2. The second step involves moving from the current base point to a new point and performing the experiment again. Termination usually takes place according to a criterion suitably defined for the system. RSM offers the twin advantages of optimization of unknown systems and efficient experimentation. RSM was originally developed for statistical design of experiments as is evident from Box and Wilson (1951), Cochran and Cox (1957) and Myers (1973). One of the early applications of RSM to simulation experiments was reported by Hunter and Naylor (1970), who suggested the extension of ideas on experimental design to simulation experiments. Bengru and Haddock (1986) described a system which combines a simulation generator developed in SIMAN and an optimization subroutine. Kleijnen and Standridge (1988) developed an experimental design to determine the machine mix of an FMS using throughput as a performance measure. In order to reduce the number of simulation runs, a regression metamodel was developed. White (1987) described a method for managing the volume of experimental a n d / o r simulation data required for large-scale design studies using RSM.
171
5. Shop congestion factors and job release rule 5.1. S h o p congestion factors
The type and capacity of buffer depends on the level of shop congestion. In the case of low shop load, the required number of buffer spaces is usually less. At high levels of shop congestion it is necessary to estimate the requirement of local and central buffer carefully, to achieve high utilization of the machine tools. Two shop load congestion factors are considered in this study. If p, is the probability that an arriving part is of type i, ti, the processing time of the part in the system, and n, the number of part types, then an estimate of the mean processing time (t m) r e q u i r e d in the system is given by t m = ~ Piti • i-1
The reciprocal of the mean processing time is the mean processing rate of the system. Shop load congestion is defined as the ratio of the mean arrival rate to the mean processing rate. In the current study, the arrival rate of jobs to the system, corresponding to two shop congestion factors are determined. For medium shop congestion, "~m = gerald, M ,
and for high shop congestion, Ah = SChtxM
where M /x Am, Ah
S C m, S C h :
The number of machine tools available. The mean processing rate. The mean arrival rate for medium and high shop congestion, respectively. The medium and high shop congestion factors.
5.2. Job release rule
Earlier studies have established the need for a controlled release of the jobs into the system considering the limited storage capacity in an FMS (Buzacott and Shantikumar, 1980). Based on a simulation study, Sabuncuoglu and Hom-
172
B. Mahadevan, T.T. Narendran / Buffer levels and choice of material handling device in FMS
mertzheim (1989) showed that it is necessary to limit the number of jobs in the system to prevent blocking of machines. Improper or arbitrary release of jobs results in severe blocking of the machines. The following rule is applied for job release in the system under study: All jobs are released into the system on a First-Come-First-Served (FCFS) basis subject to an upper limit on the number of jobs in the system. If the capacity of the central buffer is C and the capacity of the local buffer is L, then the maximum number of jobs allowed into the system is L + C .
6. The simulation model
6.1. System description A system comprising a set of four machine tools, linearly placed, is considered for the study. It is similar to the system described by Fan and Sackett (1988) and Mamalis et al. (1987). Machine tools are served by a rail-guided vehicle which moves in front of them. It is assumed that sufficient space is available for providing local buffer in front of each machine tool. The local buffer is in the form a rotary pallet shuttle mechanise: Exclusive space is available for the central buffer. The number of pallet-stands to be provided in this area has to be determined. The rail-guided vehicle travels back and forth between the local buffer and the central buffer, transporting the work pieces between locations. A l o a d /
unload station is provided at one end, through which the jobs enter for processing and leave after completion. The layout of the system is shown in Figure 5. The system can simultaneously process five different types of jobs. The jobs can be processed in more than one sequence due to the versatility of the machine tools. Thus each job has a limited number of alternative sequencing possibilities. An arriving job i follows a sequence j with a probability Sij. Table 2 gives the probabilities for all possible combinations of jobs and sequences. Further information about the job characteristics is given in Table 2. A sufficient number of pallets is assumed to be available so that an arriving job is fixtured on to the appropriate pallet and can wait at the load/ unload station for the MHS. The rail-guided vehicle picks up the job and reaches the machine where the job has to undergo the first operation. If the machine is not free and if the local buffer is full, the job is placed at the central buffer, to be picked up when space becomes available at the local buffer. The procedure is repeated until the processing is completed and the job finally leaves the system. The following are the operational characteristics of the system: The arrival of jobs follows a Poisson distribution and the arrival rates influence the level of shop congestion. Failure of machine tools and MHS occurs in a Poisson fashion and their repair times are negative exponentially distributed. The system is interrupted every week for a period of 30 minutes to provide for changes in production settings. The capacity
1
/.
3
I
II
I Load &
Local
I Buffers I
II
lira
Material Handling System
Unload
I1
1 ............
Figure 5. Layout of the system considered for the current study
I
-I
Central Buffer
II
I
Machine
Machine
11
I
'1
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B. Mahadevan, T.T. Narendran / Buffer levels and choice of material handling device in FMS
Table 2 Details of jobs undergoing processing Job No,
Volume mix (%)
1 2 3 4 5
18 12 25 23 22
Machines visited Sequence
Sequence probability Sequence
No of m/c's visited Sequence
1
2
3
1
2
3
1
2
3
234 13 124 1234 14
132 24 243 1324 23
134 143 -
0.30 0.60 0.30 0.50 0.40
0.45 0.40 0.40 0.50 0.60
0.25 0.30 -
3 2 3 4 2
3 2 3 4 2
3 3 -
of the local buffer provided in front o f each machine tool is the same. T h e transit time between any pair of adjacent machines is two units of time. T h e r e is only one rail-guided vehicle to p e r f o r m the material handling function. T h e proCessing time of the jobs is deterministic. 6.2. Simulation parameters and p e r f o r m a n c e criteria
T h e simulation experiments are c o n d u c t e d separately for the two shop congestion factors. T h e capacities of central and local buffer s p a c e s are the controllable variables in these experi-
Processing time (min)
144 180 168 240 180
ments. T h e t h r o u g h p u t time o f the job ( T P U T ) is chosen as the p e r f o r m a n c e criterion. This is equal to the time elapsed b e t w e e n the arriv~tl of a job at the system and the completion of the job. In the current study, G P S S / P C is used to construct the simulation models. T h e m e t h o d of batch m e a n s has b e e n a d o p t e d for estimation of the m e a n s of variables of interest. T h e system is started f r o m an e m p t y and idle condition and the p e r f o r m a n c e of the system is observed over a length of time. By plotting the m e a n values of the variables of interest, the w a r m - u p period is determined. Figure 6 shows the plot for the system described in Section 6.1, w h e r e it is seen that
1.0 0.9 0.8-
~.
0.7 ~
0.6
~ ==
o.s 0.4
~
0.3 0.2 0.1 o _~
I 100
I 200
I 300
N u m b e r of jobs processed
I /.00 from s t a r t
I 500 up
0 m/c 1 + mlc 2 <> m/c 3 A talc /, Figure 6. ,~n illustration of the detection and elimination of initial bias in the system
600
B. Mahadevan, T.T. Narendran / Buffer levels and choice of material handling device in FMS
174
after 500 job completions, the effect of initial bias is not much. Simultaneous use of antithetic and common random numbers reduced the variance considerably. Antithetic random numbers are used between adjacent pairs of batches and common random numbers are used for comparison of alternative policies. G P S S / P C allows for easy implementation of these procedures through the use of R M U L T , PLOT, RESET, and S T A R T cards. The verification and validation of the implementation is done as follows: Movement of jobs in the system is monitored to find whether it is realistic. This is done by inspecting the 'transaction movements' through the GPSS blocks, given by the 'total count' for each block. The use of T R A C E and STEP blocks of the software greatly facilitates this process. The behaviour of the system for changes in the values of key parameters such as arrival rate, processing times and failures of facilities is observed. Any abnormal behaviour is an indication of flaws in the logic of the implementation. In addition, several 'pilot runs' were made with various values for the shop congestion factors. Based on the loading pattern in the system the values of medium shop congestion and high shop congestion factors were fixed at 0.60 and 0.80.
(2) The range of search is generally small due to the nature of the problem and due to practical considerations such as space constraints. Since the independent variables are integers in our experimentation, the response surface resembles a wire mesh with the lattice points representing the integral values. When moving from one base point to another, only the lattice points are considered. The procedure is as follows: Step 1. Identify an appropriate initial base point. Step 2. Construct a first-order search experiment. Fit a first-order regression equation from the response observed. Step 3. If a 1 + a e < ~a0, go to Step 5. Step 4. Set Xlb (new) = Xlb (old) + 2. Set X2b (new) = X2b (old) + 1. Here, Xlb = Base point for central buffer. X2b = Base point for local buffer. Go to Step 2. Step 5. Identify the combination of independent variables that gives the minimum value of TPUT, in the most recent experiment, as the best solution. For a two-variable first order regression, the coefficients a I and a 2 reflect the change in the response function due to a unit change in the variables X 1 and X 2. Since X1 and X 2 can assume only integer values, a I + a 2 is the change in the response function due to a simultaneous change in both the variables by one unit. When a near-optimal point is reached the plane is devoid of any significant tilt. This is reflected by the diminishing value of the regression coefficients. The integral constraint on the variables X 1 and
7. The RSM procedure Some of the characteristics of the system under study have to be taken into account before the application of RSM. In particular, (1) The capacities of central and local buffer have to be integers.
Table 3 Regression coefficients for high shop congestion Trial
Base Pt. a
TPUT at
Regression coefficients
No.
X1
X2
base pt.
a0
al
a2
X 1
X2
TPUT
1 2 3 4
11 13 15 17
1 2 3 4
3018.t0 1172.20 999.68 974.40
2831.25 1551.13 997.35 970.18
473.50 117.83 8.07 6.54
1253.10 394.35 16.49 6.54
12 14 16 18
2 3 4 5
1461.2 1000.0 977.8 952.6
a X1 and X 2 represent central and local buffer, respectively.
Best solution
175
B. Mahadevan, T.T. Narendran / Buffer levels and choice of material handling device in FMS Table 4 Regression coefficients for medium shop congestion Trial
Base Pt. a
TPUT at
Regression Coefficients
No.
X1
X2
base pt.
ao
al
a2
X1
Best Solution X2
TPUT
1 2
7 9
1 2
483.40 456.10
526.35 459.90
45.18 3.20
63.28 3.20
9 10
2 3
456.10 450.40
a X! and X 2 represent central and local buffer, respectively.
X 2 suggests that the response function does not improve significantly if a I + a 2 _<6 a o for very small values of 6. In the current study, the value of 6 is chosen to be 0.02.
gence is found to be faster for shops with a medium level of congestion than for shops with a high level of congestion.
9. Conclusions 8. Analysis of simulation results The simulation of the system was performed for 10000 job completions, split into ten batches of 1000 jobs each. A warm-up run of 500 job completions was used initially to minimize the effect of the 'idle and empty' condition. Antithetic variates accounted for considerable variance reduction. The validity of the GPSS model was upheld by the realistic movement of jobs in the system and by the behaviour of the system according to logical expectations for variations in the values of key input parameters. The choice of the base point for 2 x 2 factorial experiments and the progress towards the best combination of central and local buffer is shown in Tables 3 and 4. The region of experimentation was chosen, taking the shop congestion level into consideration. The design points ranged from (11,1) to (18,5) for the high congestion factor and (7,1) to (10,3) for the medium congestion factor. From the results of the study (Tables 3 and 4), a central buffer of 18 with a local buffer of 5 is seen to be the best combination for a highly congested shop while the corresponding values for a shop of medium congestion are 10 and 3. The disadvantage of large computing times for carrying out simulation studies is offset substantially by the application of RSM for efficient experimentation. In the case of high shop congestion, it requires 40 design points to move from (11,1) to (18,5). However with the use of RSM, the effort required to obtain the best values is halved. The procedure converges rapidly towards the combination of local and central buffer that yields the least throughput time. The conver-
The issues involved in the choice of material handling systems and the buffer capacity of an FMS are addressed in this study. The most desirable combination of central and local buffer, in an FMS, is a decision required at the design stage itself and has a bearing on the choice of MHS. In order to address the problem without making limiting assumptions, this study uses simulation. FMSs with medium as well as high congestion levels have been considered. The performance of the system in terms of the throughput time for various combinations of local and central buffer has been evaluated. The use of efficient simulation through RSM for determining the capacities of local and central buffer is demonstrated in this study. While specific numerical data have been used for the purpose of illustration, the model and the procedure are sufficiently general in nature and can be used for similar configurations of FMSs.
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B. Mahadevan, T.T. Narendran / Buffer levels and choice of material handling device in FMS
Buzacott, J.A., and Shantikumar, J.G. (1980), "Models for understanding flexible manufacturing systems", AIIE Transactions 12/4, 339-350. Carrie, A.S., Adhami, E., Stephens, A., and Murdoch, J.C. (1984), "Introducing a flexible manufacturing system", International Journal of Production Research 22/6, 907-916. Chang, Y.-L., Sullivan, R.S., and Wilson, J.R. (1986), "Using SLAM to design the material handling system of a flexible manufacturing system", International Journal of Production Research 24/1, 15-26. Cochran, W.G., and Cox, G.M. (1957), Experimental Designs, 2nd edition, Wiley, New York. Fan, I.S., and Sackett, P.J. (1988), "A PROLOG simulator for interactive flexible manufacturing system control", Simulation 50/6, 239-247. "FMS at GE", (1983), Manufacturing Engineering 91/3, 6667. Heragu, S.S., and Kusiak, A. (1988), "Machine layout problem in flexible manufacturing systems", Operations Research 36/2, 258-268. Hopp, W.J., Pati, N., and Jones, P.C. (1989), "Optimal inventory control in a production flow system with failures", International Journal of Production Research 27/8, 13671386. Hunter, J.S., and Naylor, T.H. (1970), "On experimental designs for computer simulation experiments", Management Science 16/7, 422-434. Jafari, M.A., and Shantikumar, J.G. (1989), "Determination of optimal buffer storage capacities and optimal allocation in multi-stage automatic transfer lines", liE Transactions 21/2, 130-135. "Japan's builders embrace FMSs", (1985), American Machinist, 129/2, 83-88. Kleijnen, J.P.C., and Standridge, C.R. (1988), "Experimental design and regression analysis in simulation: An FMS case study", European Journal of Operational Research 33/3, 257-261. Koulamas, C.P. (1989), "Optimal buffer space size in two-stage machining systems with markovian or non-Markovian tool
life processes", International Journal of Production Research 27/7, 1167-1178. "Lister installs £750000 FMS", (1985), Production Engineer 64/7, 15-16. Liu, C.°M., and Sanders, J.L. (1988), "Stochastic design optimization of asynchronous flexible assembly systems", Annals of Operations Research 15, 131-154. Mamalis, A.G., Bilalis, N.G., and Konstantinidis, M.J. (1987), "On simulation modelling for FMS", Simulation 48/1, 19-23. "Mazak unveils new CIM-based plant", (1990), American Machinist 134/2, 25-27. Mohanty, R.P., and Kulkarni, R.V. (1989), "A computer algorithm for determining buffer size in a serial flow production system", Computers & Industrial Engineering 16/1, 75-86. Myers, R.H. (1973), Response Surface Methodology, Allyn & Bacon, Boston, MA. Newell, P., and Radley, I. (1989), "The Japanese way: Hitachi Seiki Company", Production Engineer 68/2, 52-53. "Plant produces parts JIT with help from FMS", (1990), American Machinist 134/1, 91. Ranky, P.G. (1983), The Design and Operation of FMS, North-Holland, Amsterdam, 8-24. Sabuncuoglu, I., and Hommertzheim, D.L. (1989), "An investigation of machine and AGV scheduling rules in an FMS", in: K.E. Stecke and R. Suri (eds.), Proceedings of the third ORSA / TIMS conference on Flexible Manufacturing Systems." Operations Research Models and Applications, Elsevier Science Publishers BV, Amsterdam, 261-266. Stecke, K.E., and Solberg, J.J. (1981), "Loading and control policies for a flexible manufacturing system", International Journal of Production Research 19/5, 481-490. White, Jr., K.P. (1987), "Response surface methodology as a means for efficient data storage and retrieval", Annals of Operations Research 8, 351-362. Witt, C.E. (1989), "Caterpillar adds FMS to engine manufacturing", Material Handling Engineering 44/6, 78-82.
European Journal of Operational Research69 (1993) 166-176 North-Holland
Theory and Methodology
Buffer levels and choice of material handling device in Flexible Manufacturing Systems B. M a h a d e v a n a n d T . T . N a r e n d r a n
Industrial Engineering & Management Division, Dept. of Humanities & Social Sciences, Indian Institute of Technology, Madras 600 036, India Received December 1990; revised October 1991 Abstract: The determination of buffer sizes is a key issue in the design of a Flexible Manufacturing System (FMS). A study of FMS installations and the systems indicates the relationship between the buffer capacity and the type of primary and secondary Material Handling Systems (MHSs) employed. A priori knowledge about the buffer requirements enables the FMS designer to select appropriate MHS devices. This paper addresses the issue of determining buffer capacities through simulation. Using response surface methodology for efficient experimentation, the best combination of central and local buffer is obtained. Keywords: Flexible Manufacturing Systems; Material Handling System; Buffer; Simulation; Response surface methodology
1. Introduction A flexible manufacturing system (FMS) consists of three sub-systems, viz. the machining system, the material handling system (MHS) and the control system. A network of computers, which form the control system, controls and interfaces with the other two sub-systems. In contrast to a transfer line, where all the parts follow the same sequence of operations, an FMS is equipped with a material handling system (MHS) which permits the parts to traverse a variety of routes. FMSs
Correspondence to: T.T. Narendran, Industrial Engineering & Management Division, Dept. of Humanities& Social Sciences, Indian Institute of Technology, Madras 600 036, India.
often require intermediate storages to counter breakdowns, variations in process times and blocking of machines due to diversity of part routing. There are two stages at which storage can be provided in an FMS. A local storage for each machine and a common storage that is accessible to all the machines of the system are known to exist in FMS installations. Each has a role to perform and these roles overlap partially. While the primary purpose of either storage in an FMS is to ensure smooth flow of production, differences occur in their manner of operation. Local storage reduces delays in the loading of parts to machines but needs close control over the release of jobs into the system to avoid blocking of machines (Buzacott and Shantikumar, 1980; Sabuncuoglu and Hommertzheim, 1989). Com-
0377-2217/93/$06.00 © 1993 - ElsevierSciencePublishers B.V. All rights reserved
B. Mahadevan, T.T. Narendran / Buffer levels and choice of rnaterial handling device in FMS
(a) Transfer of work pieces between local buffers of two machines. (b) Transfer of work pieces between a local buffer and a central buffer. (c) Transfer of work pieces between a machine and its local buffer. The first two involve inter-location transfer of work pieces and are performed by the primary MHS, while the third is a transfer at a machine location which is performed by the secondary MHS. Owing to the inherent capability of the MHS devices, the choice of secondary MHS devices is preemptive in nature in many cases. For example, when computer-controlled conveyors are used as the primary MHS, robots are necessary for localized work piece handling at specific locations. Likewise, when AGVs are used as the primary MHS, a rotary pallet shuttle mechanism or robots must be used in conjunction with them as secondary MHSs. The machine layout and MHS devices are related factors in FMSs. Owing to high system costs, the efficiency of the MHS is crucial to equipment selection. AGVs, tow-line carts and rail-guided mechanisms can operate efficiently in linear layouts only. It is preferable to use robots in systems having radial or circular layouts and conveyors and automatic monorail systems in layouts which are curvi-linear in nature. Heragu and Kusiak (1988) identified four classes of machine layouts which bear relationships to the type of MHS: circular layout, linear single row layout, linear double row layout and clustered layout. A study of FMS installations and the systems considered for study by the researchers indicates the relationship that exists between the buffer
mon storages are not constrained by such factors but are less effective in reducing material handling delays. It is often desirable to use both forms of storage. Research studies on existing FMS installations and on models of FMS show that the choice of material handling device influences the buffer capacities to be provided. Viewing this feature the other way around, this study seeks to determine the buffer requirements first so that an appropriate MHS can be chosen. A simulation approach for determining the buffer sizes is presented. The organization of the paper is as follows. The relationship between MHS devices and system configuration is discussed in Section 2. Studies on estimation of buffer requirements is included in Section 3. Section 4 contains a review of Response Surface Methodology (RSM). The shop congestion factors and job release rules are introduced in Section 5 and the simulation model is described in Section 6. This is followed by the development of the RSM procedure in Section 7. The results are presented in Section 8 and conclusions are drawn in Section 9.
2. M H S devices and system configuration in an FMS
It is convenient to classify the material handling system in an FMS into primary MHS and secondary MHS. The work piece transport in an FMS can be categorized under any one of the following:
F-r-
r-rTrl
4
r-rl-rl
r-5-
Loca[ Buffers Material
4
4
167
H a n d l i n g System
Local B u f f e r s
I Lu°=: Figure 1. Layout of the FMS at G E
=
168
B. Mahadevan, T.T. Narendran / Buffer levels and choice of material handling device in FMS
l, Gauge I ~
~
///
I
Machining] centre ]
Lathe ~~ ' /~I / /_ ] t. axis
I Pulletout
Pallet in
Control Room
Figure2. Layoutof the FMSat Lister capacity that can be provided in the system and the type of primary and secondary MHSs employed. In two different installations the variation in the computer-controlled conveyors design, viz., a two-tracked conveyor and a single-tracked conveyor, resulted in different buffer configurations of the system (Ranky, 1983; Newell and Radley, 1989). A two-tracked computer-controlled conveyor system provides both local and central buffer whereas a single-tracked loop conveyor provides only central buffer. The inner track of the two-tracked conveyor acts as a central buffer and the outer track serves as local buffer. Pick and place robots usually serve a group of machines situated radially, performing all the material handling functions including loading and unloading of jobs and tool drums. Such configurations require only a central buffer to the set of
I
I
I
I
I
*
I
I
I
I
I
I J
I
I
machine tools served by the robot; no local buffer is required. The FMS at Lister (Lister installs £750000 FMS, 1985) has a semi-circular layout of machines served by two robots. In recent system designs, a rotary pallet shuttle mechanism is provided as an interface between the machining centre and the primary MHS. In such cases, the number of indexing stations in the mechanism constitutes the local buffer for each machine tool. The use of shuttles as local buffer was discussed by Chang et al. (1986). They simulated a system with a central buffer common to all the machines and a local buffer in front of each machine tool. The 'machining cells and systems' offered by FMT Ltd., of KTM, includes Fleximatic FM100/FM200/FM300 and the FM V series. The machine tools have local buffer in the form of multiple indexing stations in a rotary pallet shuttle mechanism. Central buffer is pro-
I
I
I
I
I
I
Load & unload
I
i
I
I
Local Buffers
I lk
Material Handling System < Central Buffer
Figure3. Layoutof the systemstudiedbyFan andSackett
w,
B. Mahadevan, T.T. Narendran / Buffer levels and choice of material handling device in FMS
f
169
1 Material
Handling System
~
......
rz: q
Load & Unload C e n t r a l Buffer
Figure 4. Layout of the system considered by Stecke and Solberg
vided opposite to the row of machine tools in a linear fashion. The MHS separates the machine tools and the central buffer and moves between them.
There are several examples of AGV-based systems with different buffer configurations: only a central buffer (Stecke and Solberg 1981); -
Table 1 Relationship between MHS and buffer capacity of FMS Other MHS devices used
Availability of buffer
Installed
Central
Local
at a
32 bin A S / R S with a rail-guided stacker type transport.
Two-station work changer.
yes
yes
Caterpillar (1990)
Gantry Robot.
Two-pallet work changer buffer of 140 pallet stacker.
yes
yes
Mazak Corp (1990)
AGV.
An A S / R S for pallet storage, pallet shuttle pallet turn table.
yes
yes
Mori Seiki plant at Iga (1985)
Rail-mounted robot.
A 44-station pallet stacker area.
yes
no
Yamazaki's Oguchi works (1985)
Rail-mounted cart with shuttle mechanism.
A 15-station pallet stacker area.
yes
no
Detroit Diesel Allision Division. (Witt, 1989)
Robocarrier AGV.
Two 10-station carousels and pallet transfer mechanism.
yes
yes
Vought Aero products division (Andel, 1984)
A two-tracked loop conveyor.
Robot, gating and siding mechanisms.
yes
yes
600 Group SCAMP (Ranky, 1983)
Robot.
A common area for pallet storage.
yes
no
Lister (1985)
Rail-guided transfer mechanism.
21-station pallet stands in front of machines and load/unload station.
no
yes
GE's plant at Erie (1983)
Low profile tow line cart.
Custom-designed pallet shuttle at each machine.
yes
no
Hughes Aircraft (Burgam, 1983)
Primary MHS
a Source in parentheses
170
B. Mahadevan, T.T. Narendran / Buffer levels and choice of material handling device in FMS
- only local buffers at machine locations (FMS at GE, 1983; Carrie et al., 1984); - both central buffer and local buffer (Fan and Sackett, 1988). Figures 1 and 2 show the layouts of the FMSs at GE and Lister and Figures 3 and 4 show the layout of the system considered for study by Fan and Sackett (1988) and Stecke and Solberg (1981). Table 1 shows some examples of central and local buffer provided by the primary and secondary MHS devices in current installations. The presence of both the types of buffer and the relationship between the buffer capacity of the system and the type of MHS employed is clearly indicated by the study of FMS installations and recent research attempts. It follows that the estimation of buffer requirements is useful to the FMS designer for selecting the appropriate MHS devices.
3. Estimation of buffer requirements The determination of optimal buffer has been pursued through analytical as well as simulation models. Mohanty and Kulkarni (1989) modelled a two-station automated serial flow production line to optimize in-process inventory requirements by assuming exponential operation time. Koulamas (1989) presented a model for obtaining the optimal buffer size in two-stage machining systems. Simulation was preferred for non-Markovian failure case. Hopp et al. (1989) considered a continuous flow production process subject to failure with an intermediate buffer and suggested a procedure for determining the optimal buffer. Jafari and Shantikumar (1989) formulated a dynamic programming problem with the objective of optimally distributing the total storage space among the intermediate buffers in multi-stage automatic transfer lines. Liu and Sanders (1988) demonstrated the application of a Stochastic QuasiGradient method (SQG) to optimize the performance of asynchronous flexible assembly systems. They have developed a hybrid algorithm which uses a queueing network model to set the number of pallets in the system and an SQG algorithm to set the buffer spacings to obtain optimal system throughput. The inherent limitation of the approach has prevented the development of analytical models
for a complex system such as FMS without some
gross assumptions. In many cases, this has resulted in analyzing models that do not reflect the actual system under consideration. Early attempts to estimate buffer requirements were, by and large, confined to serial a n d / o r multi-stage production systems. Deterministic and non-Markovian processing times, limited local and central buffer, failure of machine tools and material handling system, planned interruption of the system, alternative processing sequences and other such factors, if considered simultaneously, will lead to intractable analytical models which are of little use. On the other hand, simulation models, which can easily incorporate such situations, are often found to be time-consuming. Although the speed of processing of the computers has increased considerably, paving the way for the use of simulation as a methodology for solving complex problems more realistically, use of efficient experimentation techniques in conjunction with simulation would make the approach even more attractive. The use of RSM for efficient experimentation with simulation models is well known and the current study demonstrates the use of RSM for estimating the buffer requirements.
4. Response surface methodology Response surface methodology is generally used to optimize "the performance of an unknown system (or a model of the system) that is subjected to controllable, uncontrollable and unknown variables" (Brightman, 1978). RSM can be applied to any system that has the following key elements: (1) a criterion of effectiveness known as the response of the system which is measurable on a continuous scale, and (2) quantifiable independent variables that affect the systems's performance. RSM seeks to approximate the response function by a lower-order polynomial. Denoting the criterion of effectiveness by ~7 and the decision variables as X 1, X 2. . . . , Xk, the system can be modelled by
n =f(x,,
s)
t3. Mahadevan, T.T. Narendran / Buffer levels and choice of material handling device in FMS
where s is a random variable of mean zero and of variance or2, regardless of the decision variables. Application of RSM for a first-order experiment involves a two-step procedure: 1. From an initial condition, known as the base point, a first order experiment is conducted to develop an estimate of the gradient direction. Using a 2 k factorial design or a k-dimensional simplex design, it is possible to estimate the linear equation k
= a 0 + ~_, a i S i i-1
where = An estimate of the system response under study. a 0 = T h e response of the system at the base point. X~ = Value of the i-th controllable variable. a i = Regression coefficient of the i-th controllable variable. 2. The second step involves moving from the current base point to a new point and performing the experiment again. Termination usually takes place according to a criterion suitably defined for the system. RSM offers the twin advantages of optimization of unknown systems and efficient experimentation. RSM was originally developed for statistical design of experiments as is evident from Box and Wilson (1951), Cochran and Cox (1957) and Myers (1973). One of the early applications of RSM to simulation experiments was reported by Hunter and Naylor (1970), who suggested the extension of ideas on experimental design to simulation experiments. Bengru and Haddock (1986) described a system which combines a simulation generator developed in SIMAN and an optimization subroutine. Kleijnen and Standridge (1988) developed an experimental design to determine the machine mix of an FMS using throughput as a performance measure. In order to reduce the number of simulation runs, a regression metamodel was developed. White (1987) described a method for managing the volume of experimental a n d / o r simulation data required for large-scale design studies using RSM.
171
5. Shop congestion factors and job release rule 5.1. S h o p congestion factors
The type and capacity of buffer depends on the level of shop congestion. In the case of low shop load, the required number of buffer spaces is usually less. At high levels of shop congestion it is necessary to estimate the requirement of local and central buffer carefully, to achieve high utilization of the machine tools. Two shop load congestion factors are considered in this study. If p, is the probability that an arriving part is of type i, ti, the processing time of the part in the system, and n, the number of part types, then an estimate of the mean processing time (t m) r e q u i r e d in the system is given by t m = ~ Piti • i-1
The reciprocal of the mean processing time is the mean processing rate of the system. Shop load congestion is defined as the ratio of the mean arrival rate to the mean processing rate. In the current study, the arrival rate of jobs to the system, corresponding to two shop congestion factors are determined. For medium shop congestion, "~m = gerald, M ,
and for high shop congestion, Ah = SChtxM
where M /x Am, Ah
S C m, S C h :
The number of machine tools available. The mean processing rate. The mean arrival rate for medium and high shop congestion, respectively. The medium and high shop congestion factors.
5.2. Job release rule
Earlier studies have established the need for a controlled release of the jobs into the system considering the limited storage capacity in an FMS (Buzacott and Shantikumar, 1980). Based on a simulation study, Sabuncuoglu and Hom-
172
B. Mahadevan, T.T. Narendran / Buffer levels and choice of material handling device in FMS
mertzheim (1989) showed that it is necessary to limit the number of jobs in the system to prevent blocking of machines. Improper or arbitrary release of jobs results in severe blocking of the machines. The following rule is applied for job release in the system under study: All jobs are released into the system on a First-Come-First-Served (FCFS) basis subject to an upper limit on the number of jobs in the system. If the capacity of the central buffer is C and the capacity of the local buffer is L, then the maximum number of jobs allowed into the system is L + C .
6. The simulation model
6.1. System description A system comprising a set of four machine tools, linearly placed, is considered for the study. It is similar to the system described by Fan and Sackett (1988) and Mamalis et al. (1987). Machine tools are served by a rail-guided vehicle which moves in front of them. It is assumed that sufficient space is available for providing local buffer in front of each machine tool. The local buffer is in the form a rotary pallet shuttle mechanise: Exclusive space is available for the central buffer. The number of pallet-stands to be provided in this area has to be determined. The rail-guided vehicle travels back and forth between the local buffer and the central buffer, transporting the work pieces between locations. A l o a d /
unload station is provided at one end, through which the jobs enter for processing and leave after completion. The layout of the system is shown in Figure 5. The system can simultaneously process five different types of jobs. The jobs can be processed in more than one sequence due to the versatility of the machine tools. Thus each job has a limited number of alternative sequencing possibilities. An arriving job i follows a sequence j with a probability Sij. Table 2 gives the probabilities for all possible combinations of jobs and sequences. Further information about the job characteristics is given in Table 2. A sufficient number of pallets is assumed to be available so that an arriving job is fixtured on to the appropriate pallet and can wait at the load/ unload station for the MHS. The rail-guided vehicle picks up the job and reaches the machine where the job has to undergo the first operation. If the machine is not free and if the local buffer is full, the job is placed at the central buffer, to be picked up when space becomes available at the local buffer. The procedure is repeated until the processing is completed and the job finally leaves the system. The following are the operational characteristics of the system: The arrival of jobs follows a Poisson distribution and the arrival rates influence the level of shop congestion. Failure of machine tools and MHS occurs in a Poisson fashion and their repair times are negative exponentially distributed. The system is interrupted every week for a period of 30 minutes to provide for changes in production settings. The capacity
1
/.
3
I
II
I Load &
Local
I Buffers I
II
lira
Material Handling System
Unload
I1
1 ............
Figure 5. Layout of the system considered for the current study
I
-I
Central Buffer
II
I
Machine
Machine
11
I
'1
173
B. Mahadevan, T.T. Narendran / Buffer levels and choice of material handling device in FMS
Table 2 Details of jobs undergoing processing Job No,
Volume mix (%)
1 2 3 4 5
18 12 25 23 22
Machines visited Sequence
Sequence probability Sequence
No of m/c's visited Sequence
1
2
3
1
2
3
1
2
3
234 13 124 1234 14
132 24 243 1324 23
134 143 -
0.30 0.60 0.30 0.50 0.40
0.45 0.40 0.40 0.50 0.60
0.25 0.30 -
3 2 3 4 2
3 2 3 4 2
3 3 -
of the local buffer provided in front o f each machine tool is the same. T h e transit time between any pair of adjacent machines is two units of time. T h e r e is only one rail-guided vehicle to p e r f o r m the material handling function. T h e proCessing time of the jobs is deterministic. 6.2. Simulation parameters and p e r f o r m a n c e criteria
T h e simulation experiments are c o n d u c t e d separately for the two shop congestion factors. T h e capacities of central and local buffer s p a c e s are the controllable variables in these experi-
Processing time (min)
144 180 168 240 180
ments. T h e t h r o u g h p u t time o f the job ( T P U T ) is chosen as the p e r f o r m a n c e criterion. This is equal to the time elapsed b e t w e e n the arriv~tl of a job at the system and the completion of the job. In the current study, G P S S / P C is used to construct the simulation models. T h e m e t h o d of batch m e a n s has b e e n a d o p t e d for estimation of the m e a n s of variables of interest. T h e system is started f r o m an e m p t y and idle condition and the p e r f o r m a n c e of the system is observed over a length of time. By plotting the m e a n values of the variables of interest, the w a r m - u p period is determined. Figure 6 shows the plot for the system described in Section 6.1, w h e r e it is seen that
1.0 0.9 0.8-
~.
0.7 ~
0.6
~ ==
o.s 0.4
~
0.3 0.2 0.1 o _~
I 100
I 200
I 300
N u m b e r of jobs processed
I /.00 from s t a r t
I 500 up
0 m/c 1 + mlc 2 <> m/c 3 A talc /, Figure 6. ,~n illustration of the detection and elimination of initial bias in the system
600
B. Mahadevan, T.T. Narendran / Buffer levels and choice of material handling device in FMS
174
after 500 job completions, the effect of initial bias is not much. Simultaneous use of antithetic and common random numbers reduced the variance considerably. Antithetic random numbers are used between adjacent pairs of batches and common random numbers are used for comparison of alternative policies. G P S S / P C allows for easy implementation of these procedures through the use of R M U L T , PLOT, RESET, and S T A R T cards. The verification and validation of the implementation is done as follows: Movement of jobs in the system is monitored to find whether it is realistic. This is done by inspecting the 'transaction movements' through the GPSS blocks, given by the 'total count' for each block. The use of T R A C E and STEP blocks of the software greatly facilitates this process. The behaviour of the system for changes in the values of key parameters such as arrival rate, processing times and failures of facilities is observed. Any abnormal behaviour is an indication of flaws in the logic of the implementation. In addition, several 'pilot runs' were made with various values for the shop congestion factors. Based on the loading pattern in the system the values of medium shop congestion and high shop congestion factors were fixed at 0.60 and 0.80.
(2) The range of search is generally small due to the nature of the problem and due to practical considerations such as space constraints. Since the independent variables are integers in our experimentation, the response surface resembles a wire mesh with the lattice points representing the integral values. When moving from one base point to another, only the lattice points are considered. The procedure is as follows: Step 1. Identify an appropriate initial base point. Step 2. Construct a first-order search experiment. Fit a first-order regression equation from the response observed. Step 3. If a 1 + a e < ~a0, go to Step 5. Step 4. Set Xlb (new) = Xlb (old) + 2. Set X2b (new) = X2b (old) + 1. Here, Xlb = Base point for central buffer. X2b = Base point for local buffer. Go to Step 2. Step 5. Identify the combination of independent variables that gives the minimum value of TPUT, in the most recent experiment, as the best solution. For a two-variable first order regression, the coefficients a I and a 2 reflect the change in the response function due to a unit change in the variables X 1 and X 2. Since X1 and X 2 can assume only integer values, a I + a 2 is the change in the response function due to a simultaneous change in both the variables by one unit. When a near-optimal point is reached the plane is devoid of any significant tilt. This is reflected by the diminishing value of the regression coefficients. The integral constraint on the variables X 1 and
7. The RSM procedure Some of the characteristics of the system under study have to be taken into account before the application of RSM. In particular, (1) The capacities of central and local buffer have to be integers.
Table 3 Regression coefficients for high shop congestion Trial
Base Pt. a
TPUT at
Regression coefficients
No.
X1
X2
base pt.
a0
al
a2
X 1
X2
TPUT
1 2 3 4
11 13 15 17
1 2 3 4
3018.t0 1172.20 999.68 974.40
2831.25 1551.13 997.35 970.18
473.50 117.83 8.07 6.54
1253.10 394.35 16.49 6.54
12 14 16 18
2 3 4 5
1461.2 1000.0 977.8 952.6
a X1 and X 2 represent central and local buffer, respectively.
Best solution
175
B. Mahadevan, T.T. Narendran / Buffer levels and choice of material handling device in FMS Table 4 Regression coefficients for medium shop congestion Trial
Base Pt. a
TPUT at
Regression Coefficients
No.
X1
X2
base pt.
ao
al
a2
X1
Best Solution X2
TPUT
1 2
7 9
1 2
483.40 456.10
526.35 459.90
45.18 3.20
63.28 3.20
9 10
2 3
456.10 450.40
a X! and X 2 represent central and local buffer, respectively.
X 2 suggests that the response function does not improve significantly if a I + a 2 _<6 a o for very small values of 6. In the current study, the value of 6 is chosen to be 0.02.
gence is found to be faster for shops with a medium level of congestion than for shops with a high level of congestion.
9. Conclusions 8. Analysis of simulation results The simulation of the system was performed for 10000 job completions, split into ten batches of 1000 jobs each. A warm-up run of 500 job completions was used initially to minimize the effect of the 'idle and empty' condition. Antithetic variates accounted for considerable variance reduction. The validity of the GPSS model was upheld by the realistic movement of jobs in the system and by the behaviour of the system according to logical expectations for variations in the values of key input parameters. The choice of the base point for 2 x 2 factorial experiments and the progress towards the best combination of central and local buffer is shown in Tables 3 and 4. The region of experimentation was chosen, taking the shop congestion level into consideration. The design points ranged from (11,1) to (18,5) for the high congestion factor and (7,1) to (10,3) for the medium congestion factor. From the results of the study (Tables 3 and 4), a central buffer of 18 with a local buffer of 5 is seen to be the best combination for a highly congested shop while the corresponding values for a shop of medium congestion are 10 and 3. The disadvantage of large computing times for carrying out simulation studies is offset substantially by the application of RSM for efficient experimentation. In the case of high shop congestion, it requires 40 design points to move from (11,1) to (18,5). However with the use of RSM, the effort required to obtain the best values is halved. The procedure converges rapidly towards the combination of local and central buffer that yields the least throughput time. The conver-
The issues involved in the choice of material handling systems and the buffer capacity of an FMS are addressed in this study. The most desirable combination of central and local buffer, in an FMS, is a decision required at the design stage itself and has a bearing on the choice of MHS. In order to address the problem without making limiting assumptions, this study uses simulation. FMSs with medium as well as high congestion levels have been considered. The performance of the system in terms of the throughput time for various combinations of local and central buffer has been evaluated. The use of efficient simulation through RSM for determining the capacities of local and central buffer is demonstrated in this study. While specific numerical data have been used for the purpose of illustration, the model and the procedure are sufficiently general in nature and can be used for similar configurations of FMSs.
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