INTEGRATED USE OF MACRO AND MICRO MODELS WITHIN A SIMULATION STUDY

Edward J. Williams
206-2 Engineering Computer Center
Mail Drop 3
Ford Motor Company
Dearborn, Michigan 48121-2053 U.S.A.

Igal Ahitov
Production Modeling Corporation
Three Parklane Boulevard
Suite 910 West
Dearborn, Michigan 48126 U.S.A.

ABSTRACT

Efficient, cost-effective manufacturing demands attention to production-system layout (in both the geometric and workflow senses), choices of material-handling equipment and methods, analytical and practical justification of the algorithms to be used for inventory control and scheduling (beginning with the choice between a "push" and a "pull" system), and choice of changeover policies. Rarely indeed can these analyses be undertaken in isolation; feedback and interrelationships among these subjects of production-system engineering almost always exist, whether for good or ill. Additionally, purely formula-driven ("closed-form") techniques of analysis are characteristically inadequate due to their inability to accommodate random, stochastic variations during the actual operation of the production system. Discrete process simulation, used in conjunction with (not as a replacement for) traditional mathematical modeling, greatly increases the engineer's ability to design, configure, and operate an efficient, cost-effective production system.

In this paper, we describe a multifaceted study of an assembly system for an automotive component. Since this study undertook concurrent and synergistic assessments of manufacturing-cell layout, material-handling requirements, scheduling policies, inventory-control policies, and changeover strategies, it required the development of both macro and micro simulation models. We present recommendations for successful simulation studies incorporating both macro and micro models in the context of presenting a description of this system, the corresponding models of it, and results obtained from the models.

1 INTRODUCTION

A manufacturer and assembler of a key automotive component wished to improve efficiency from the viewpoints of achieving and confirming specified throughput and high efficiency of individual processing stations via improvement and enhancement of cell layouts, material-handling procedures, scheduling and inventory-control policies, and choice of changeover strategies. Simulation was chosen as the fundamental analytical tool to identify and validate the appropriate modifications appropriate for application to the existing production system (Clark 1995).

Consequently, the manufacturer's engineers and managers met with the simulation modeling and analysis consultants to define all study objectives explicitly and categorize them by the areas of potential improvement listed above. Hence, this required step within proper simulation project management (Nordgren 1995) led to the realization that five models, some having a higher level of detail than others, would have to be built and analyzed. In compliance with a fundamental guideline for simulation project success, the team decided upon a steady progression of analyses, beginning with simple, overview models and evolving toward more complex, detailed models (Musselman 1994). It is easier to add detail to a simple, correct model than it is to add correctness to a complex, wrong model.

Macro models are by definition overview models with a "coarse" level of detail; by contrast, micro models are highly specific, localized models with a "fine" level of detail. Objectives (including accuracy requirements) of a study, special issues to be addressed in the study, and availability of time and data are typical determinants of the level of detail of a model. For example, macromodels can perform "rough cut" analyses to confirm throughput rates, identify bottlenecks, or evaluate inventory levels between lines or departments, whereas micromodels can perform detailed analyses to confirm throughput rates, identify labor requirements, or evaluate localized operational policies (Ülgen, Shore, and Grajo 1994).

2 DESCRIPTION OF MANUFACTURING SYSTEM AND INPUT DATA

Parts enter the system through a dial (rotary index table). Such rotary index tables have the advantages of compactness (small "footprint"), the ability to load and unload workpieces at one station without interruption of machining operations, and flexibility to undertake a sequence of operations of which some are manual and some are automated (DeGarmo, Black, and Kohser 1988). The dial contains twenty-four substations, each with processing time 7.2 seconds and indexing time 1.4 seconds. The substations within the dial break down independently of one another. When any one substation breaks down, all other substations must suspend operations while repairs are made. The dial sends good processed parts downstream to the first of five processing stations via a conveyor with a capacity of 26 parts. Since this conveyor is synchronized with the dial, a good part is loaded on the conveyor every 1.4 seconds. After processing at station 1, parts are automatically loaded to pallets in groups of six. After being loaded, the pallets carry the parts to stations 2, 3, 4, and 5 in sequence; all pallets visit all stations. The parts are tested at station 4; good ones continue to station 5 to be unloaded and defective ones are discarded. Empty pallets return to station 1. These data are summarized in Table 1, below. The mean cycles to failure (MCTF) for the dial are in units of "number of parts processed;" the other MCTF data are in units of "number of pallets processed." Current buffer size (capacity in number of pallets just upstream from each station) is shown also. Initial choices of these buffer sizes were made largely on the basis of heuristics such as placement of the larger buffers just upstream and downstream from bottlenecks, and/or toward the center of the line rather than near either of the ends (Powell and Pyke 1996).

Table 1: Individual Station Simulation Input Information
Station # Station Name Cycle Time Breakdown Breakdown Yield Buffer
(seconds) MCTF MTTR (sec) (%) Size
Dial 7.2 419 180 95
1 Load from dial 0.0 n/a n/a 100 8
2 Lubrication 4.25 35000 300 100 3
3 Subassembly 50.25 333 180 100 9
4 Functional test 62.585 6000 180 95 4
5 Unload 45.0 n/a n/a 100 9

3 MACROMODELING ISSUES

Since the results of this simulation study would be applied to improvement and enhancement of an existing system (in contrast to assessment of the design for a proposed system), a key step in validation and establishment of credibility (face validity) was the construction of models checked directly against the real system, with proposed enhancements to be modeled only after successful validation of the "base" models (Banks, Carson, and Nelson 1996). The validation checks against the real system included reconciliation of process- and data-orientation viewpoints of the model with each other and with the target system (Giannasi, Lovett, and Godwin 1996). Further, in this study, the excellent advice "model boundary should be kept at a minimum in the beginning of the study" (Ülgen et al. 1994a) pointed to initial use of macro models.

The modeling tool chosen was SIMAN/ARENA. The SIMAN (SIMulation ANalysis) modeling language provided needed constructs such as resources, queues, and conveyors, the ability to separate process-flow logic from numerical data and parameters conveniently, and the convenience of "macro"-stations applicable to situations in which different work centers share a significant portion of process logic (Profozich and Sturrock 1995). The ARENA simulator, hierarchically above and compatible with the SIMAN language, provided convenient animation-building facilities, a point-and-click interface, and application-specific templates (model-building blocks convenient to broad categories of simulation applications) such as the Advanced Manufacturing Template (Hammann and Markovitch 1995), (Fletcher, Breyer, and Tarlos 1996).

4 MICROMODELING ISSUES

To model downtimes within the various subsystems, the mean numbers of operations to breakdown and the mean durations of breakdowns (see, for example, Table 1 this page) were used as the single parameter of exponential distributions after discussions with the model users. Exponential distributions were well-suited to this purpose, inasmuch as the means and standard deviations of the limited empirical data initially available, and the modes of the MCTF and MTTR data were approximately equal to their minima (Williams 1994). Subsequent examinations of more extensive empirical data which became available during the course of the study, using the BestFit software (Jankauskas and McLafferty 1995), confirmed the suitability of the exponential for these purposes. The explicit acknowledgment of assumptions and the analyses of input data are essential steps in selling the subsequently obtained simulation results to management (Ülgen et al. 1994b); i.e., ensuring that managerial decisions dependent on the model are based on full understanding of the model results and concurrence with its recommendations (Robinson and Bhatia 1995).

5 SYSTEM ANALYSIS AND RESULTS

Since the manufacturing process is a steady-state, not a terminating simulation, valid statistical inferences depended on the determination of a sufficiently lengthy warm-up period. The need to determine this warm-up period is a characteristic of the replication/deletion approach used in this study for estimation of steady-state performance (Law and Kelton 1991). The simulations were run for a period of 101 hours; the first hour's results were discarded as the initial transient. The ability of the system to reach steady-state within one hour was proved by use of the "forward-look" graphical procedure advocated by (Welch 1983).

At the overall (macro) system performance level of the base model, results were:

Table 2: Baseline System Throughput and Rejection Rates
Rate Average Maximum Minimum
(parts/ (parts/ (parts/
hour) hour) hour)
new parts 356.24 410 274
throughput 323.73 333 260
rejects 33.02 45 16

To obtain the numbers in Table 2, the approach of "batch means" was used, with five replications of batches of size twenty runs each (Pegden, Shannon, and Sadowski 1995; Alexopoulos 1995). Statistical analysis of the output results established that each entry in the above table was accurate to within 4 parts per hour at an (significance level) of 0.05. Use of common random numbers (CRNs) helped achieve these narrow confidence intervals when comparing alternative configurations under consideration, such as different numbers of pallets, different hypothesized downtime occurrences and durations, different machine yields, and/or different buffer capacities. (Donohue 1995). Intuitively, CRNs impose "equality of random load" on alternatives undergoing "competitive" evaluation, hence comparing them under equal conditions and therefore fairly. Analytically, CRNs reduce the variance of the point estimator of system difference Y1-Y2 (where Y is a performance metric common to both alternative 1 and alternative 2) by inducing a positive correlation between Y1 and Y2.

At the detail (micro) system performance level of the base model, results were:

Table 3: Baseline System Performance by Station
station %work %blocked %idle %down
dial 85.08 9.49 0.00 5.43
1 80.97 9.00 10.03 0.00
2 6.67 80.09 13.24 0.00
3 78.90 18.82 1.22 1.06
4 98.27 0.00 1.73 0.00
5 70.66 8.00 21.34 0.00

As expected, due to its maximal cycle time, station 4 had the highest percentage of actual working time; it is the bottleneck of the system. The percentage of time blocked was highest for station 2, since it has a relatively short cycle time and is upstream from station 4. The dial was never idle; indeed, it can introduce parts into the system faster than station 4 can accommodate them. Hence, the dial paces itself according to the capacity of station 4. Station 5 had the highest percentage of idle time, a naturally expected consequence of its being immediately downstream from the bottleneck station.

6 CONCLUSIONS AND INDICATIONS FOR FURTHER WORK

In this study, simulation successfully confirmed the production capacity and operational feasibility of a manufacturing and assembly system. Predictions of the simulation matched subsequent operational experience with the revamped system. The study comprised the building, verification, validation, and analysis of three macro models examining scheduling, inventory control, and changeover policies, and of two micro models examining details of manufacturing-cell layout and material-handling requirements.

The rapid and accelerating pace of market-driven demand shifts in the automotive industry augurs stringent requirements for nimbleness (Keenan 1996), rapid information flow (Sorge 1996), performance monitoring (Minahan 1996), and knowledge and technology transfer (Mercer 1996) within the supply chain. As such change requirements reach this manufacturing and assembly system, these thoroughly documented models are ready for reuse (Law and McComas 1991) to ensure that needed systems adjustments are timely and cost-effective. Additionally, such ongoing use of a simulation model increases the financial attractiveness of simulation to management by permitting amortization of the model building costs over a longer lifetime - one approaching the lifetime of the production facility itself.

ACKNOWLEDGMENTS

Dr. Onur Ülgen, president, Production Modeling Corporation, and professor of industrial and manufacturing systems engineering, University of Michigan - Dearborn, and John M. Dennis, simulation analyst, Ford Motor Company, have provided criticisms and suggestions valuable to the clarity and organization of this paper.

APPENDIX: TRADEMARKS

Advanced Manufacturing Template, ARENA, and SIMAN/Cinema are trademarks of Systems Modeling Corporation.

BestFit is a trademark of Palisade Corporation.

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AUTHOR BIOGRAPHIES

EDWARD J. WILLIAMS holds bachelor's and master's degrees in mathematics (Michigan State University, 1967; University of Wisconsin, 1968). From 1969 to 1971, he did statistical programming and analysis of biomedical data at Walter Reed Army Hospital, Washington, D.C. He joined Ford in 1972, where he works as a computer software analyst supporting statistical and simulation software. Since 1980, he has taught evening classes at the University of Michigan, including both undergraduate and graduate simulation classes using GPSS/H, SLAM II, or SIMAN. He is a member of the Association for Computing Machinery [ACM] and its Special Interest Group in Simulation [SIGSIM], the Institute of Electrical and Electronics Engineers [IEEE], the Society for Computer Simulation [SCS], the Society of Manufacturing Engineers [SME], and the American Statistical Association [ASA]. He serves on the editorial board of the International Journal of Industrial Engineering - Applications and Practice.

IGAL AHITOV holds a bachelor's degree in mechanical engineering from Stevens Institute of Technology (1993) and a master's degree in industrial and systems engineering from Georgia Institute of Technology (1995). In 1995, he joined Production Modeling Corporation in Dearborn, Michigan, where he works as an applications engineer in the simulation field. He is a member of the Society of Manufacturing Engineers [SME].