OPTIMIZATION OF PALLETIZATION IN A PRODUCTION JOB SHOP

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

Arun Jayaraman
Susan Khoubyari
Production Modeling Corporation
Three Parklane Boulevard
Suite 910 West
Dearborn, Michigan 48126 U.S.A.

This article was presented at the Simulation for Manufacturing Improvement Conference and Exposition sponsored by the Society of Manufacturing Engineers in Chicago, May 14-15, 1996, and appears in SME's copyrighted notebook of that conference.

ABSTRACT

We describe the application of simulation and statistical analysis to the problem of optimization of palletization in a production job shop. These analyses enabled management responsible for the production of this job shop to optimize the number of pallets, the size (carrying capacity) of the pallets, the associated work-in-process levels, and policy regarding level of safety-stock kept on hand at various places in the job shop. Additionally, management also confirmed throughput levels for various values chosen for these quantities.

1 INTRODUCTION

Simulation is the art and science of creating a representation of a process or system, using that representation for the purpose of experimentation and evaluation [5]. The results of those experiments and evaluations may then be used in a variety of ways to impel ongoing process improvement. In the manufacturing process described in this paper, the process improvements involved optimized palletization in conjunction with improved inventory levels, reorder policies, and shift-staffing patterns.

Palletization is the assemblage and securing of individual items or workpieces on a platform that can then be moved by a conveyance such as a truck, forklift, or crane, and conveniently stored (for example, in racks) between moves. Palletization is one approach for exploiting the "unit load" concept -- moving workpieces in groups is much more economical than moving them individually [12]. Effective palletization can improve cycle times, reduce time and labor costs of setup, and increase agility when dealing with rapid fluctuations in demand mix at low investment expense compared to upgrades of machines and fixtures [9].

First, we describe the operations within the production shop whose operational-improvement requirements defined the goals of the simulation analysis. We then describe the simulation model itself, indicating the sequence of steps undertaken to build it and the resolution of typical modeling challenges encountered during these steps. Next, we summarize the improvements achieved by statistical analyses of model output and indicate directions for future investigations.

2 DESCRIPTION OF THE PRODUCTION SYSTEM

The job shop is an assembly system for a consumer product. The shop is naturally and organizationally subdivided into four major divisions: the shearing division, the components pressing-and-stamping division, the cleaning division, and the welding-and-mastics operations division. Raw material, namely incoming coils of steel, arrives at the shearing division. There, blanks are sheared from these coils. Next, in the components pressing-and-stamping division, the structural pieces of the consumer product are formed from these blanks. At the cleaning division, these blanks are washed. The welding-and-mastics division then fabricates subassemblies from the blanks while incorporating insulation against both heat and noise. Downstream from the job shop, these subassemblies are united with other sub-assemblies; hence, in the context of this study, the final assembly operation is the customer of the job shop being modeled. Palletization, implemented by pallets and by racks for workpiece movement, is used to transport blanks and stampings both within individual divisions and among several divisions. Both "pallets" and "racks" hold multiple (several hundred) workpieces. Since these transport devices are both expensive (cost in the middle four figures apiece) and large (implying significant investment in floor space and movement cost), optimization of their number and size was of high importance to the managers and engineers seeking the help of simulation analyses for achieving efficiency of production and optimization of cost-effectiveness.

Components of the product being manufactured flow from one work area to another, and from one division to another, as shown in Figure 1. The components flow only downstream. Wooden pallets are loaded at the shearing operation for transport of sheared blanks to the pressing and stamping operations; after unloading by a "destacker," the empty pallets then return upstream to the shearing division. Racks are loaded with stamped and pressed blanks just subsequent to the pressing and stamping operations for transport to the cleaning division; the empty racks then return to the pressing and stamping division. Downstream beyond the cleaning division, all transport is via conveyors. Five safety stocks are maintained within this job shop; no division is far from a safety stock. Specifically, sheared stampings are kept at the shear line in the components pressing-and-stamping division (S1), and both sheared stampings (S2) and pressed stampings (S3) are kept at the press lines in that division. Likewise, an inventory of pressed stampings is maintained at the wash line in the cleaning division (S4), and another just downstream from the welding-and-mastic operations division (S5). Locations of these safety stocks are likewise noted in Figure 1.

3 DESCRIPTION OF THE SIMULATION MODEL

Specific immediate goals of the model were determination of the most cost-efficient number of pallets and of racks, and of pallet size, measured as the number of blanks each pallet can carry. These optima were required as a function of raw-material coil size, inasmuch as the incoming coils of steel could be ordered in various sizes. Metrics for the achievement of these goals were throughput (jobs per hour), the number of times a shortage of blanks occurred, the number of times a shortage of pallets occurred, and the average work-in-progress (WIP). In actual operation of the real system, inventory levels of WIP were traditionally kept at overcautiously high levels due to the high cost of tooling changeovers; hence, the users also requested detailed predictions of these WIP levels associated with the recommended palletization parameters. Since the input rate to the final assembly division was suspected of being a system bottleneck, the model was also required to confirm the capability of the system to deliver input to that division. Additionally, the model users desired the ability to input production-run specifications conveniently and receive, interactively, the recommended parameter values for optimizing the time and cost of that production run. Longer-term goals were optimization of reorder points in conjunction with the WIP-level predictions noted above, optimization of shift patterns in each division as a function of fluctuating market demands, and the design of and an implementation plan for a Kanban system. A Kanban inventory-control system is the type of system most often used to implement a Just-In-Time (JIT) system to meet production demands and reduce inventory costs simultaneously, by tracking production-floor inventory and making decisions based on the actual production performance at each division [4]. In the material flow shown above, expectations for "Kanban" control are that the emptying of a rack at S2 will trigger subsequent availability of stock at S1, and likewise, the emptying of a rack at S4 will trigger subsequent availability of stock at S3.

The final assembly division is the generator of demand for the job shop's shearing, pressing-and-stamping, cleaning, and welding-and-mastics divisions. Therefore, since the conceptual operation of the production system is a pull, not a push, system, the model is likewise built using fundamentally "pull" logic. Partly due to the users' desire to become self-sufficient in experimenting with the model via development of a mentoring relationship with the model developers, partly due to the originally low level of availability of detailed operational data, and partly due to the ability of simulation to provide urgently needed overall feasibility assessments early in a simulation study, the original model development was undertaken at a low level of attention to operational detail. For example, raw material was assumed always available in arbitrarily large quantity (as observed in practice), and changeover times were estimated based on current process experience. Beginning with an overview level of model construction helped the analysts reach an early understanding of the production system, and also helped the construction of a model which was relatively easy to validate and also credible (not only correct, but acknowledged to be correct by its users) [10].

3.1 Input Data

The basic input data to the system included processing times and changeover times for all stations within each of the operations shown in Figure 1. Palletization times (both the time required to load sheared blanks into pallets and the pressed blanks onto racks, and the corresponding unloading times of pressed blanks from pallets and blanks from racks) and rack-transport times were likewise required input. The coil weight was also an input, inasmuch as it specifies the number of stampings that can be sheared from each incoming steel coil.

Operational data added to the model inputs as the level of detail within the model increased included shift patterns and the machine-reliability data. Additional input data directly related to the users' experimentation with the model were the total number of pallets and the total number of racks in the system, the sizes (capacities) of these pallets and racks, the current or proposed safety stock levels and reorder points, and the final assembly level (target throughput relative to the job shop, or target input relative to the downstream, final assembly division).

3.2 Software Modeling Issues

The ProModel modeling software used in this project provided several valuable features justifying its choice. First, its ability to provide a "run-time" executable file of the simulation enabled the end users to experiment with various values of their decision variables (e.g., number and capacity of pallets) easily and quickly. The software also provided a macro capability and the ability to coalesce separately verified and validated submodels into a model at either the macro or the micro level [1]. The high quality of ProModel's bit-mapped graphics and its capability of showing important quantities (e.g., safety stock level) dynamically on the monitor screen during model execution helped the modeling team communicate effectively with users and their managers. Its ability to support concurrent construction of a model and its corresponding animation increased the productivity of the modelers.

Several modeling techniques were used to reduce the number of entities in the computer model of the system during execution. For example, parts were processed as a batched (single) entity, such as a pallet, instead of individual entities whenever possible. Global variables were then used to track work-in-process and the total number of physical parts currently represented by each of the batched entities. Additionally, the individual entities representing components currently loaded onto racks or pallets were not individually modeled. This attention to minimizing the number of entities helped the output statistics (discussed below) more obviously and intuitively match the quantities of direct interest to the model users, thereby increasing both the credibility and the ease of use of the model [6]. Additionally, the smaller number of entities lowered the computer memory and run-time requirements of the model while simultaneously permitting faster, more complete model verification [11].

The ProModel modeling software is, by default, adapted to push systems. To accommodate the "pull" logic needed in this model, ProModel's "SEND" command was used to control batch movements. This command causes an entity to remain at its current location until a specified destination (typically downstream for a pull system) issues a "SEND," conceptually matching a real-world downstream demand communicated upstream. Off-shifts were modeled as downtime, since the then current version of ProModel permitted priority distinctions between downtimes, but not between shifts. By "competing," in a prioritization sense, with division operations and random downtime events, the single shift used in the model permitted correct representation of labor reallocations among the four divisions.

Macros were defined in ProModel to give mnemonic names to various numeric quantities. Additionally, the model-building team elected to define run-time interfaces corresponding to a subset of these macros. The advantages of this choice were ease of model maintenance and enhancement, plus ease of user interaction and experimentation with various scenarios available within the model.

3.3 Analytical Modeling Issues

Both empirical evidence and sensitivity analyses strongly suggested that downtime frequencies and durations were of high significance. Since virtually no downtime data were available, the thorny issue of correct modeling of downtimes therefore assumed equivalently high significance [14], and received much attention. After considerable discussion among the user engineers and the modeling team, the family of gamma distributions was used to model downtime durations; this family of distributions is often recommended to fit empirical data when the mode is less than the median, which in turn is less than the mean. Availability of estimates of mean downtime duration and the fraction of total time absorbed by downtime (1.0 - efficiency) supported calculations of, and subsequent use of, the shape parameter and the scale parameter specifying a particular gamma distribution [7]. The software tool ExpertFit, available as an accessory to the ProModel tool, conveniently automates the choice of a specific gamma distribution given these heuristic estimates describing expected machine performances [13].

The triangular density was used to model the number of stampings that could be sheared from an incoming coil of nominal weight. Experience demonstrated that coils of identical nominal weight varied noticeably in actual physical weight, and also that the number of stampings that could be sheared from incoming coils of equal physical weight varied slightly. Three intrinsic properties of the triangular density contributed to its high practical value for this purpose:

Since the production process is operationally a steady-state, not a terminating, system, the issue of initialization bias removal to achieve steady state operation required attention. The warm-up time was shortened by initializing the system conditions (specifically, the buffer safety stock levels) to typical, non-zero values, as recommended by [2]. Validation runs subsequently confirmed that the simulation model then achieved steady state in a few minutes of real-world time, corresponding to a few seconds of computer execution time.

4 OUTPUT RESULTS AND ANALYSES

The simulation outputs of most direct interest to the users were system throughput, availability or shortages of pallets, availability or shortages of racks, and inventory levels. Optima determined for the current level and mix of downstream demand are given in the following table:

Table 1: Optima under Current Conditions
ItemOptimum
racks20 per part type
pallets13 per part type
blank safety stock3600
reorder point5 racks
optimum coil sizesupplier's maximum

These optima were determined by building confidence intervals based on multiple replications. Since item settings were decidedly interdependent, not independent, the Bonferroni inequality was used to assess the number of replications required and their length relative to the global-optimum confidence level required to support management decisions. In the context of this study, this classical approach was preferable to the "joint confidence ellipsoid" of [8] in the senses of being slightly less conservative and not requiring the assumption of multivariate normality [3].

5 CONCLUSIONS AND DIRECTIONS FOR FUTURE WORK

The existing analyses will be extended to study of the most effective operational procedures for sharing labor between divisions, and particularly within the pressing operations, to achieve required throughput, at minimum average WIP inventory levels, under various conditions of downtime occurrences within divisions and fluctuations in demand emanating from the downstream final assembly division. The model will thus be of ongoing use, and drive ongoing data-collection efforts, since both long-term trend and seasonal variations in downstream demand, driven by the marketplace, are known to exist. Furthermore, the model shows only mild superiority of the current optima listed in Table 1 relative to nearby values (i.e., use of 12 or 14 pallets per part type versus the current optimum of 13). Hence, both the modelers and users of the model confidently expect high added value obtained by ongoing use of the model to fine-tune production facilities and procedures.

Construction and analysis of a model of the final assembly division is planned, both to extend the benefits of palletization optimization there and to identify all quantitative relationships between the rate of its input arriving from the job shop and optimization within the final assembly division.

Since the latest version of ProModel permits setting shift priorities, the shifts now modeled as downtimes will be modeled as shifts. This enhancement will disassociate shifts from downtimes, thereby increasing ease of maintenance of the model.

ACKNOWLEDGMENTS

Wesley Peters, an industrial and process engineer expert in simulation, contributed greatly to the accuracy of technical detail and the clarity of its presentation throughout this paper.

Steve Weiss and Nick Matziuk, simulation and software consultants with Production Modeling Corporation, Dearborn, Michigan, likewise made valuable contributions to its clarity, organization, and layout.

APPENDIX: TRADEMARKS

ExpertFit is a trademark of Averill M. Law & Associates.
ProModel is a trademark of PROMODEL 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].

ARUN JAYARAMAN is an Applications Engineer at Production Modeling Corporation, Dearborn, Michigan. He holds a B.S. degree in mechanical engineering from Annamalai University, Madras, India and a Master of Engineering degree in Industrial and Systems Engineering from Virginia Polytechnic Institute and State University. During his two years of work at PMC, his primary consulting interests have included discrete event simulation applied to manufacturing, MTM analysis, and robotic simulations.

SUSAN KHOUBYARI is a Systems Consultant at Production Modeling Corporation, Dearborn, Michigan. She holds B.S. and M.S. degrees in Industrial Engineering from the State University of New York at Buffalo. She has been working at PMC for five years, where she is responsible for managing discrete event simulation projects and finite-capacity scheduling systems, as well as training in project management concepts and software packages. She is a senior member of the Society of Manufacturing Engineers.