PMC White Papers | MODELING OF CHAIN CONVEYORS AND THEIR EQUIPMENT INTERFACES

by Collin Wheeler | Jun 15, 2021 | White Papers

ABSTRACT

Chain conveyors are a specific type of conveyor often used in a variety of manufacturing and production applications, such as body and paint shops. These conveyors must typically interface with other types of conveyors such as cross-transfer conveyors, and also with other material-handling equipment such as lift tables and hold tables. Micromodeling of chain conveyors and their equipment interfaces requires close attention to numerous details. These details include not only static and operational properties of the chain conveyors themselves, but also the particulars of dimensional and operational interfaces of the conveyors and the equipment served by the conveyors, such as lift tables and the conveyor acceleration and deceleration ramps.

In this paper, we first delineate the situations in which micromodeling of material-handling equipment is appropriate. We then present an overview of conveyor types and terminology. Next, we describe the challenges of modeling chain conveyors accurately, and our recommendations for meeting these challenges within the framework of typical modeling tools and simulation-study contexts. As an example, we present details of these recommendations relative to the AutoMod modeling tool. In conclusion, we summarize these recommendations and indicate promising directions for further development of modeling techniques and enhancement of model-building tools.

1 MACRO- VS. MICRO-MODELING

Macro models are, by definition, overview models with a “coarse” level of detail. In contrast, micro models incorporate a “fine” (high) level of detail (Ülgen, Shore, and Grajo 1994). The appropriate level of detail for a particular model within a simulation study, and hence the decision of whether to build a macro or a micro model, properly depends on the objectives of the study, availability of data, credibility concerns, and constraints of model-development and computer-run time available (Law and McComas 1991). In view of this credibility concern, the modeler making the “micro model versus macro model” decision properly anticipates the task of validation by asking “Will our modeling team be able to use the model – in place of the system – to make the decisions required by the study objectives?” (Ruch and Kellert 1995).

Simulation may be applied to the study of material handling systems during any or all of four project phases: the conceptual phase, the detailed design phase, the launching phase, and the fully-operational phase (Ülgen and Upendram 1995). In the context of modeling material-handling systems, typical indications calling for development of a micromodel are requirements to minimize both global and local work-in-process levels and maximize utilization of material-handling equipment, plus availability of detailed dimensional, cycle-time, and downtime data relative to individual pieces of equipment, such as the aerial gravity conveyors and motorized roller conveyors compared in (Cerda 1995). Such modeling is frequently required due to the mathematical intractibility of operational questions involving material-handling equipment. For example, (Tsai 1995) verifies the “NP-hard” status of minimizing the likelihood of conveyor stoppage to complete assembly-station work, via mixed-model sequencing, when a conveyor serves even a single station with arbitrary processing times. In such a context, detailed modeling of conveyors becomes vital to address decision-making policy relative to both line balancing and product sequencing. The motivation to model conveyors, in particular, at a high level of detail increases in studies undertaken to assess competing conveyor management strategies, such as dynamic allocation of workpieces to conveyors which alternately merge with each other, diverge again, and must serve widely dispersed, dissimilar work cells (Laughery 1995). Macro models are frequently analyzed to optimize conveyor and overall system performance via selection of a workpiece to convey, selection of a conveyor, choice of waiting discipline among conveyors, or choice of waiting discipline among jobs awaiting a conveyor. Micro models of conveyor performance furnish required input to such macro models (Backers and Steffens 1983).

2 DEFINITIONS AND TERMINOLOGY OF CONVEYORS AND INTERFACE EQUIPMENT

Conveyors can transport a high volume of items over a fixed path at adjustable speed with little manual intervention. Many varieties of conveyors are in use, such as belt conveyors (endless belt), chute conveyors (metal slides), screw conveyors (large spiral contained in confining trough or tube), chain conveyors (endless chain), and roller conveyors (load carried on transverse rollers which are either gravity- or power-driven) (Sule 1988). For example, belt or roller conveyors can be readily configured to transport small, odd-shaped items (Gould 1994). Chain-driven conveyors with roller surfaces, the type of conveyor considered in this paper, are occasionally non-powered (gravity) or, more usually, powered (live). Such conveyors are relatively inexpensive, readily assembled and adjusted, and well suited for a wide range of loads, provided the materials being transported have, or are mounted on, a rigid riding surface (Allegri 1992). These chain-driven conveyors may accumulate material by use of slip or clutch mechanisms built into the rollers. The “roller flight” variety typically uses two parallel sections of chain supporting rollers on non-rotating shafts. Those rollers can turn under the material, permitting its accumulation (Gould 1993). Additionally, acceleration and deceleration sections may be appended to powered roller conveyors when precise material control is required, as at interface points, through inclines or declines, or around curves (K. W. Tunnell Company, Incorporated 1995). Recent advances in designs and materials have markedly increased speeds and decreased operating noise of powered roller conveyors, hence increasing their economic appeal (Witt 1995).

These conveyors characteristically interact with other material-handling equipment such as lift tables and hold tables. Lift tables provide a working or material-transfer surface at heights and positions chosen for ergonomic and operational advantage (Tompkins and White 1984). Hold tables are a passive variant of lift tables; unlike a lift table, a hold table cannot move a load perpendicularly to the direction of travel of a downstream conveyor to align the load for placement on that conveyor.

3 CHALLENGES OF MODELING CHAIN CONVEYORS

As predicted in (Muth and White 1979), work in conveyor modeling comprises both analytical models (limited to a low level of complexity but quantifying fundamental relationships among important conveyor parameters) and simulation models (allowing tradeoff studies during design and analysis of operational problems of existing conveyors). Numerous studies illustrate the wide applicability of simulation to the analysis of conveyor systems, such as designing and implementing a power-and-free conveyor system (Good and Bauner 1984), comparative macro evaluations of accumulating and non-accumulating conveyor systems (Henriksen and Schriber 1986), layout and flow path analysis of overhead conveyors (Foote et al. 1988), micromodeling of conveyors transporting extremely fragile workpieces forbidden to touch one another (Hopings 1988), and rapid assessments of proposed modifications to a power and free conveyor system in an automotive paint shop (Graehl 1992).

Chain conveyors are widely used in automotive assembly plants. High volume production requires cycle times in the order of a few seconds. For example, for a conveyor running at fifteen feet per minute and for pallets of length fifteen feet, a time loss of two seconds amounts to two jobs per hour and forty jobs per day over two ten-hour shifts. Depending on the sales price of a car, such a loss might be somewhere from $500,000 to $1,200,000 in lost revenue per day. On the other hand, the types of material handling equipment required to support such production might be very costly to install, operate, and maintain. Therefore, the system design must strive for balance between high throughput capacity and low redundancy in material handling equipment requirements. Consequently, it is necessary that simulation models of such material handling systems should represent sufficient detail of the parts movement to make accurate assessments of the adequacy of those systems and the overall production systems of which they are a component. Output results from micromodels of conveyor configuration and performance can then guide experimentation with macromodels of the manufacturing system.

A typical vehicle assembly plant would have an abundance of various kinds of conveyors. Chain conveyors constitute one of the most commonly used types of material handling equipment in many assembly plants. Modeling of those conveyors can be a challenging task. The following is a discussion of some of the issues in modeling of chain conveyors and the supporting material handling equipment that can be found in a typical assembly plant.

3.1 Production and Transfer Conveyors

These conveyor sections move pallets through production operations. They are also used for buffer storage purposes, holding pallets between production departments or during off-shift activities such as clean-ups. Furthermore, pallets are accumulated in a bank of conveyors before they are sequenced for the next operation.

There are essentially two types of chain conveyors: accumulating and non-accumulating. Accumulating conveyors, also referred to as roller flight conveyors, have the ability to hold pallets without stopping the power chain. A non-accumulating conveyor allows the pallets to stop only when the entire conveyor chain stops. In a typical setup, non-accumulating conveyors are used to move pallets through production processes (paint booths, wash rooms, etc.). Accumulating conveyors are used for other purposes mentioned previously (e.g., temporary storage, delivery, and resequencing). Regardless of the accumulation capabilities, most conveyors have special head and tail sections (speed-up sections) that are used to accelerate and decelerate pallets, respectively. Those sections are needed to adjust the speed of pallets as they move onto and off the conveyors, which typically have much lower chain speeds than the equipment with which they interface.

Pallets move on chain conveyors with a specified minimum distance between them. Depending on the speed of the conveyor, this distance may be different on various conveyors of a typical production setup. On an accumulating conveyor, the spacing between pallets might be different in accumulation from that between moving pallets. Also, once in accumulation, a pallet does not start moving again until the preceding pallet moves away to a distance defined as the moving space.

Most simulation software provides built-in constructs to model accumulating and non-accumulating conveyors. Simulation software that does not provide such constructs might require substantial amounts of overhead code to account for the operational characteristics of either type of conveyors for a typical production system. Even with built-in conveyor constructs, some of the operational characteristics might be challenging modeling tasks. A speed-up section, for example, consists of several smaller sections of the same conveyor that run at different speeds (from low to high speed or vice versa along the direction of travel). A pallet changes its speed when its center of gravity shifts from one portion of the speed-up section to the next. As there might be pallets of different lengths moving through the system, the time to get onto and off a conveyor differs among pallets. Some simulation software (such as AutoMod) allows precise calculation of these time delays by providing mechanisms to define such small sections of conveyor, the pallet size, and locations for speed changes. In other packages, the same effect can be achieved by calculating such delays prior to simulation and by explicitly representing them in the model. A further complication to modeling speed-up sections is the requirement that no accumulation be allowed on those sections, even on accumulating conveyors.

3.2 Cross Transfer Conveyors

Cross transfers are fast-moving chain conveyors with no accumulation capability. These conveyors are used to move pallets between different sections of production and transfer conveyors. A cross transfer conveyor typically interfaces several production and transfer conveyors. Incoming pallets are moved to one of several conveyors served by the cross transfer conveyor. There is a series of hold and lift tables along those conveyor sections to compensate for the lack of accumulation capability. Hold tables are used only for temporary storage purposes. Lift tables also act as the interface between the cross transfer and production conveyors, as they have the capability to push the pallets perpendicularly. Pallets move sideways on a cross transfer. A pallet moves along a cross transfer from one hold/lift table to another, stopping as necessary. A pallet stops on a table if the next table is occupied by another pallet. Once stopped at a table, the pallet is raised off (disengaged from) the conveyor chain to prevent its moving further (as the chain runs continuously on a cross transfer). Once the next table becomes available, the table lowers the pallet back onto (into reengagement with) the chain and the pallet starts moving along the conveyor again. Only after a pallet reaches the next table or clears a limit switch placed at a distance from the table, can another pallet move onto the table. Such control is required because cross transfer conveyors typically move at higher speeds and serve several chain conveyors. Typical simulation software constructs for conveyors provide no built-in support for such control logic. There is a clear need to model such logic to represent cross transfer conveyors accurately.

3.3 Lift and Hold Tables

These special tables are used along cross transfer conveyors. The main purpose of a lift table is to move pallets onto and off the cross transfer. A lift table has powered rolls to move pallets in a direction perpendicular to the direction of travel on the cross transfer. These rolls are used to move the pallets from/to production and transfer conveyors. A hold table is typically used to provide temporary storage on the conveyor to allow accumulation (cross transfers otherwise have no accumulation capability). Either type of table raises pallets from the conveyor chain to stop them from moving. Once the pallet is ready to move forward, the table lowers the pallet back onto the chain, and upon contact with the chain, the pallet starts moving again, as described in the previous subsection. Pallets do not stop at a table if they can continue to move forward (i.e., if the next table on the chain is available) and do not experience the cycle of going up and down at that table.

Availability of a table is usually signaled by the last pallet to visit the table. There is a clear limit switch placed at a distance from the table. This switch may be on the cross transfer conveyor, on an adjacent table, or on a production/transfer conveyor served by the cross transfer. Once the pallet reaches a clear switch, it sets the switch “off,” indicating that it is now safe for its successor pallet to move onto the conveyor. Accordingly, any pallet waiting to get clearance to move onto the table sets the switch “on,” flagging that the table is now assigned to its use.

In a simulation model, cross transfer conveyors can be treated as non-accumulating conveyors with discrete segments between hold/lift tables. Simulation packages with built-in conveyor constructs provide adequate support to model the movement between tables. However, additional steps should be taken to account for the up-down cycle of tables. Also, the model should replicate the logic to control the access to the tables. This effect can be achieved by treating the tables as resources and by capturing and releasing them at appropriate points.

3.4 Powered Roll Beds

Powered-roll beds are relatively short conveyor sections which use powered rolls for high-speed transfer of pallets. They are typically used between production/transfer conveyors and other higher-speed transfer equipment such as lift tables, turntables, and lifts (Sims 1992). They also provide buffer storage space for one pallet at a time. Those conveyors run at higher speeds than the others described above. Consequently, during transfers from/to power-roll beds, pallets experience speed changes. As indicated earlier, due to different sizes of pallets, the time to clear a power-roll bed differs among pallets. Consequently, a simulation model needs to represent the clearance time by accounting for the travel distances and the length of the pallets. With simulation languages such as AutoMod, it is possible to address such detail by utilizing built-in capabilities. With some other languages, up-front calculations are required for each power roll bed to determine the time it takes to move onto and off that power roll bed.

3.5 Turntables

Turntables are short conveyor tread sections mounted on a bearing surface; they can rotate around a vertical axis to reorient pallets in transit (Cahill 1985). Some production processes require the parts to be in a certain orientation. Movement on conveyors and cross transfers between them changes the pallet orientation. Also, transfer/production conveyor segments are sometimes at angles to each other. Consequently, in a typical production setup utilizing chain conveyors, there would be several turntables with different amounts of rotation (e.g., 45, 90, 180 degree turns). Once a pallet moves onto it, a turntable rotates and aligns itself with the new path that the pallet will follow. In most cases, a turntable does not start its rotation back to its loading position before the pallet clears a limit switch. Once the pallet clears the limit switch, the table rotates back to the loading position. The rotation time is typically proportional to the angle of rotation. Clearly, a simulation model should make sure that a pallet does not attempt to move onto a turntable before the turntable returns to the loading position. Turntables can be modeled in most simulation languages by using resources and by capturing and releasing those resources at appropriate points in time.

3.6 Lifts

In a typical production facility, there will be conveyors and production processes at different floors. Lifts (elevators) are used for transferring pallets vertically between different floors. Apart from the vertical travel time, there are delays in loading and unloading of lifts (Hudson 1954). Also, in most cases, there will be clearance limits for enabling/ disabling access to lifts. Due to various pallet sizes, those delays will differ among pallets. Consequently, the model should have either an explicit (in-travel distances, pallet sizes, and locations of clear limits) or an implicit (in-time delays and signals) representation of the delays that occur in the load-travel-unload-return cycle of lifts.

4 AN AUTOMOD EXAMPLE OF CHAIN CONVEYORS

AutoMod is an industrial simulation system combining the convenience of CAD-like drawing tools, an engineering-oriented modeling language, and accurate capture of distances, sizes, speeds, and accelerations as aids to building accurate simulation models supported by three-dimensional animation (Rohrer 1994a).

The example model is a small portion of a large body shop simulation built for an automobile manufacturer. Although small in scale, this example demonstrates some of the components mentioned above. Figure 1 depicts a CAD layout of the portion of the body shop, including three accumulating chain conveyors, two cross transfer conveyors, and several lift and hold tables.

AutoMod has detailed built-in constructs for modeling conveyors. The CAD drawing of the layout is imported into AutoMod as a static background and a conveyor system is superimposed upon it. Figure 2 displays the conveyor system used for this portion of the system. As Figure 2 shows, to capture the details of transfers between equipment running at different speeds, smaller conveyor pieces were slightly extended over the gaps between the actual conveyors. An “X” represents locations where loads stop and/or either set or reset clear switches. Also, the speed-up sections on chain conveyors are represented as separate conveyor pieces appended to the end/tail of conveyor segments. Furthermore, multiple stations were defined to represent the locations where the speed of a pallet changes. The stations in AutoMod are defined with a load alignment attribute that determines when a load is considered to be at that location. For example, if a station has a “trailing edge” alignment, then the load will be considered to have arrived at that station when the trailing edge of the load reaches it. Consequently, travel speeds and distances can be accurately captured in the model by appropriately laying out stations and selecting their alignment attributes accordingly.

The lift tables interfacing with conveyor segments are represented as smaller conveyor sections attached directly to the end of a chain conveyor segment. The cross transfer conveyors are also represented as separate conveyor segments laid atop the segments that represent lift/hold tables. To model transitions between lift/hold tables and the cross transfer conveyors, two stations are created at the same coordinates. One of the stations is then attached to the conveyor segment that represents the hold/lift table; the other, to the conveyor segment representing the cross transfer line. Then, by using the “move” command at appropriate points, the load representing the pallet is instantaneously transferred from one segment to the other, displaying a smooth movement in animation. The time delays in lowering and raising the load to/from the chain are explicitly represented in the model by using the “wait” command.

Clear limit switches are represented in the model as conveyor stations. Once a load reaches a station representing a clear switch, it releases a resource that corresponds to the area that the switch controls. Clearly, most of those stations have a “trailing edge” alignment. Loads trying to enter the area wait to capture the resource and start moving as soon as the previous pallet clears the area. For each lift table and each hold table, there is a corresponding resource in the model.

5 ANALYSIS AND RESULTS OF AUTOMOD EXAMPLE

The complete simulation model of the body shop contained many more conveyors, processing times at stations, and downtimes associated with processes and some of the material handling equipment. Analysis of this model was conveniently undertaken with AutoStat. AutoStat, working in conjunction with AutoMod, provides determination of initial transients, management of scenarios as a database, and a “Design of Experiments” feature (Rohrer 1994b).

Analyses performed with the base model indicated that the system as designed could not meet the target production. Detailed analyses showed that the portion of the system shown in Figure 1 was one of several problem areas. Part of the problem was due to the distance between the first and second lift tables on the cross transfer (right side of drawing). As indicated earlier, on a cross transfer conveyor, pallets do not move until the next lift/hold table is cleared by the previous pallet. In this case, because of the long distance, each pallet experienced a delay exceeding the maximum allowable cycle time. The problem was remedied by placing a clear limit switch at a distance sufficiently removed from the lift table to avoid collisions. Consequently, the cycle time at the table was considerably reduced, thereby increasing the throughput.

Another part of the problem was due to the flow of pallets through the area. Normal flow of pallets required that the pallets go up on the cross transfer to the first conveyor, and proceed to the cross transfer (right side of Figure 1). The top two conveyors were to be used as temporary storage only when the pallets could not be sent (e.g., due to equipment down time) to the next set of conveyors that are beyond the top part of the drawing. However, simulations showed that the system would back up faster because once the first conveyor is blocked, there was no other way to utilize the middle conveyor for temporary storage. An alternative to this routing scheme was to send the pallets to the last conveyor at the top of the surge as the normal flow and then to accumulate pallets on the bottom two conveyors. Again, the model runs showed that this routing scheme worked better than the original and improved the overall throughput of the system.

Similarly, the complete model helped to identify several other problems with the conveyor system. By facilitating quick evaluation of the alternatives, the simulation model not only played a significant role in the detailed design of the system, but also provided quantitative support for managerial capital-investment decisions constrained by a tight project timetable.

In all these ways, results from micromodeling of conveyors, when included in macromodels of the production system, helped assess the degree to which material handling improvements spawned improvements in overall system performance.

6 SUMMARY

Particularly at the micromodeling level of detail, the accurate representation of conveyors and the equipment interfacing with them comprises numerous challenges. Meeting these challenges requires close attention to operational specifications and detail of the equipment, plus keen awareness of the capabilities of the simulation modeling tool chosen for use. This paper surveys these challenges and specific examples of them pertinent to a model including chain conveyors, cross transfer conveyors, lift and hold tables, and clear switches.

ACKNOWLEDGMENTS

Dr. Onur M. Ülgen, Professor, Department of Industrial & Systems Engineering, University of Michigan – Dearborn, and president, Production Modeling Corporation, has made valuable suggestions helpful to the presentation, organization, and clarity of this paper. Additionally, the cogent criticisms of two anonymous referees were especially helpful in these regards.

A preliminary version of this paper was presented at the June 1996 AutoSimulations annual users’ group meeting (AutoSimulations Symposium ’96 Mountain Rendezvous Proceedings, pages 313-319).

APPENDIX: TRADEMARKS

AutoMod and AutoStat are registered trademarks of AutoSimulations, Incorporated.

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AUTHOR BIOGRAPHIES

ALI K. GUNAL is a Systems Consultant at Production Modeling Corporation. He received his Ph.D. degree in Industrial Engineering from Texas Tech University in 1991. Prior to joining PMC, he worked as an Operations Research Specialist for the State of Washington, where he developed a simulation system for modeling and analysis of civil lawsuit litigation. At PMC, he is involved in consulting services for the analysis of manufacturing systems using simulation and other Industrial Engineering tools. He is familiar with several simulation systems including AutoMod, ARENA, QUEST, ROBCAD, and IGRIP. He is a member of the Institute for Operations Research and the Management Sciences [INFORMS], the Institute of Industrial Engineers [IIE], and the Society of Manufacturing Engineers [SME].

SHIGERU SADAKANE holds a bachelor’s degree in Industrial & Systems Engineering (University of Michigan – Dearborn, 1994). He is an Applications Engineer at Production Modeling Corporation, and highly familiar with simulation and facilities-layout optimization systems including AutoMod, WITNESS, LayOPT, QUEST, IGRIP, and SIMAN. He is a member of the Institute of Industrial Engineers [IIE] and the Society of Manufacturing Engineers [SME].

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], and the Society of Manufacturing Engineers [SME]. He serves on the editorial board of the International Journal of Industrial Engineering – Applications and Practice.

PMC White Paper | Simulation Attacks Manufacturing Challenges

by Collin Wheeler | Dec 21, 2014 | White Papers

SIMULATION ATTACKS MANUFACTURING CHALLENGES

Edward J. Williams

PMC

15726 Michigan Avenue Dearborn, MI 48126 USA

ABSTRACT

All during the past half-century, the environment of computing applications has evolved from large, comparatively slow mainframes with storage small and expensive by today’s standards to desktops, laptops, cloud computing, fast computation, graphical capabilities, and capacious flash drives carried in pocket or purse. All this time, discrete-event process simulation has steadily grown in power, ease of application, availability of expertise, and breadth of applications to business challenges in manufacturing, supply chain operations, health care, call centers, retailing, transport networks, and more. Manufacturing applications were among the first, and are now among the most frequent and most beneficial, applications of simulation. In this paper, the road, from newcomer to simulation in manufacturing to contented beneficiary of its regular and routine use, is mapped and signposted.

INTRODUCTION

As the world becomes conceptually smaller and more tightly integrated in the economic sense, the challenges of designing, staffing, equipping, and operating a manufacturing process or plant intensify. These challenges include, but are surely not limited to, process design and configuration, selection of personnel (staffing levels and skill levels), selection of machines, sizing and placement of buffers, production scheduling, capacity planning, implementation of material handling, and choices for ongoing process revision and improvement (Jacobs et al. 2011). During its fifty-year history of application to manufacturing operations, simulation has successfully addressed all of these and more (Rohrer 1998). Additionally, simulation correctly used is a powerful force for organizational learning (Stansfield, Massey, and Jamison 2014).

Therefore, let us next examine typical reasons and motivations frequently set forth to initiate a manufacturing-context simulation project:

• We already know the system design we are determined to use, but upper management won’t let us spend the money until we do a simulation providing good news about that design. (Definitely contraindicated!)
• We have a design (or several) sketched “on a cocktail napkin,” and expect simulation to give insight as to its (their) potential capability and indicate points amenable to
• Our system is already operational, but not satisfactorily; several improvements have been suggested – indeed, have been hotly We need to investigate their merits, both individually and in combination.
• Our system is already operational, and we need to have contingency plans in place for reasons such as increased product demand, increased economic pressures, wider variety of product mix, and/or other plausible changes.

Observe the zero prefacing the first motivation.   Beginning a simulation project with this motivation is setting foot on the road to ruin – the simulation results will inevitably be irretrievably contaminated by bias. The next motivation is the one with the greatest potential return on investment (ROI) relative to the cost of the simulation.   Many examples exist of a 10:1 ROI, occasionally reaching 100:1 ROI (Murty et al. 2005). In this situation, estimating all needed input data required for the simulation will surely be a challenge – after all, the system does not yet exist! The power of sensitivity analysis (to be explained below) is then extremely valuable. In the last two situations, input data for the existing system, to be modeled as a baseline, will be more readily (not necessarily easily) available. Very possibly, suggested improvement A will be of little value, suggested improvement B will be of little value, yet implementation of both A and B will be of great value. Statistical analysis of the output can expose such valuable insights. “Unsatisfactory operation” may refer to any or all of low throughput, low utilization of expensive resources, excessive in-process inventory, or long makespan (likely including long waits in queues). As examples of such applications, Habanicht and Mönch (2007) achieved improvements to long makespan in a wafer fabrication facility; Khalili and Zahedi (2013) used simulation to prepare a mattress production line for anticipated demand increases over a five-year planning horizon.

THE FOUNDATION – WHERE ARE WE GOING?

First, and vitally, when a simulation project is to be started, the following questions must be asked and answered:

• What is to be modeled?
• What questions shall the model and output analysis of it answer, and what decisions will the results guide?
• When are results needed?
• Who will do the work, if it is to be done at all?

Let us explore likely answers to these questions. For question #1, and especially for a first or early foray into simulation usage (which management may be approaching charily), the preferred answer is a small one.   Extensive experience strongly suggests that an answer such as “the milling department” or “the XYZ line” augurs much better for eventual success than an answer such as “the whole factory,” or, worse, “the whole factory plus inbound and outbound shipments.” For question #2, example answers (note that these answers are themselves questions) might be:

1. Of the three proposed alternatives for production line expansion, which one will produce the greatest throughput per hour?
2. Will a specific proposal for line design be able to produce at least 55 jobs per hour?
3. What level of staffing of machine repairpersons will ensure that the total value of in-line inventory will not exceed $40,000 at any time during one month of scheduled production?
4. Will the utilization of a particular critical and expensive piece of equipment be between 80% and 90%?
5. Which of several proposed designs, if any, will ensure that no part waits more than 8 minutes to enter the brazing oven?

Raising and documenting these questions accomplishes several vital tasks. First, these questions will in due course provide an unequivocal basis for answering the final question “Has the simulation project successfully met its objectives?” Second, the questions guide decisions concerning the answer to question #4 above, the level of detail to be incorporated into the model (this level should be as low as possible consistent with answering the chosen questions), guide data collection efforts, and help guide the choice of simulation software. Third, for question #3, typical example answers are:

1. The simulation modeling and analysis must be complete by August 24 for review. Management will make an irrevocable decision on system design on August 31. Results available later than August 24 will be useless and ignored.
2. The sooner results are available, the sooner the company can start earning greater profits via an improved system. It would be nice if results are available by June 27, in time for discussion at the quarterly management review

In the first case, the project plan will almost surely require modification. Possible modifications include canceling the project (yes!), reducing its scope, adding headcount to the project at its inception (quite dangerous, c.f. “we need the baby in three months, not nine, so three women will be assigned to produce it”), or adding headcount to the project after it is underway (even more dangerous). The last alternative is likely to crash into the figurative iceberg so aptly described by Brooks: “Adding headcount to a late project makes it later” (Brooks 1995). The second case is much more amenable to favoring quality over speed. Fourth, relative to the last question, reasonable alternatives are:

1. Doing the simulation modeling and analysis in-house.
2. Contracting with a service vendor to do this and all future simulation
3. Contracting with a service vendor to do this project, instructing us meanwhile so future projects can be done internally (perhaps with external guidance from specialists).

Now, if the project is to proceed, it’s time for data collection.

DATA COLLECTION AND ANALYSIS

Data collection is notoriously the hardest and most tedious, time-consuming, and pitfall-prone phase of a simulation project (Sadowski and Grabau 2000). First, consider the wide variety of data typically needed for a manufacturing simulation:

• Cycle times of automatic or semi-automatic machines; process time on manually operated
• Changeover times of machines, whether occasioned by product change (“next one is green, not red”), cycle count (after making 55th part, sharpen the drill bit), working time (“after polishing for 210 minutes, replenish the abrasive”), or elapsed time (“it’s been 3 hours since we last recharged the battery”).
• Frequency and durations of downtimes; whether downtimes are predicted by operating time, total elapsed time, or number of operations undertaken; whether a downtime ruins or damages a work item in
• Travel time, load time, unload time, routes, and availability of material-handling equipment (conveyors, tug-trains, AGVs, forklifts….); whether travel time differs for loaded versus unloaded vehicles; accelerations and decelerations may also be significant and
• Frequency of defective product; whether the defective product is scrapped or
• Operating schedule – number of shifts run, their
• Workers – their schedule, number and type of workers available (operators, repair persons, material-handling workers…), duties, travel time between duties, absenteeism
• Buffer locations and
• Availability and frequency of delivery of raw

The author has yet to undertake a manufacturing-simulation project in which the client added nothing to this generic list.

Next, be careful of misunderstandings, such as:

• The client spokesperson said “Cycle time of this machine is 6 minutes.” Actually, the operator is needed for 45 seconds to load the machine, which then runs automatically for 4½ minutes, then the operator is needed for 45 seconds to unload the machine; during the 4½ minutes, the operator can travel to/from and perform other tasks. Indeed, the term “cycle time” has no one standard
• The person collecting data reported “The workers work 8am-5pm, with fifteen-minute breaks starting at 10am and 2:30pm and a half-hour lunch at noon.” Actually correct, the workers spend 10 minutes (8:00am-8:10am) donning protective clothing and equipment, which they take off from 4:50pm to 5pm.
• The person collecting data reported “The drill press was down for a whole hour, from 9:20am to 10:20am.” Actually, the drill press was in working order, but idle, during that time – a problem upstream prevented any work from reaching it.
• The person assigned to collect data during the 4pm-midnight afternoon shift reported the milling machine suffered a 20-minute downtime beginning at 11:40pm. The person assigned to collect data during the midnight-8am night shift reported the milling machine suffered a 20-minute downtime ending at 12:20am. Actually, the milling machine suffered one downtime of 40 minutes’

Forewarned by these examples (all from experience), the reader and practitioner will be alert to others. Further, downtime data are particularly difficult to gather (Williams 1994). Too often, production personnel are reluctant to report downtimes, perhaps fearing that such reports would cast aspersions on the rigor with which maintenance policies and procedures are followed. As another example, a 30-minute downtime might need to be subdivided as (a) the machine was down for 5 minutes before the malfunction was noticed and reported, (b) it took the repair expert 10 minutes to gather needed tools and travel to the machine, and (c) it then took her 15 minutes to effect the repair.   Neglecting (a) overestimates the demands on the repairperson.

Next, the input data must be analyzed for best inclusion in the model. For ease of checking and updating the data, practitioners routinely and strongly urge that constant values be kept in spreadsheets (e.g., Microsoft Excel®) and imported into the model (all modern simulation software enables this task), not hard-coded in the model. When data is thus imported into the model, it can be updated without the necessity of updating the model itself. Eliminating this task eliminates the errors introduced by the overconfidence of “I don’t know this simulation software very well, but it can’t be that hard to open the model and just change a cycle time.”

Furthermore, the modeler or analyst must decide whether to use the data directly (i.e., sample from an empirical distribution formed by the data points collected) or fit a closed-form distribution (e.g., exponential, gamma, Erlang, Weibull…) to the data (using readily available software) and sample from this distribution. The latter approach has two significant advantages: (a) it realistically permits sampling values in the simulation which are outside the range of actual data points collected, and (b) it eases the drawing of conclusions concerning the model and its results, since formulas are readily available for common closed-form distributions. However, realizing these advantages is contingent upon finding a closed-form distribution which fits the empirical data well – and that may be impossible. For example, it will be impossible if the empirical distribution is conspicuously bimodal (or multimodal). In that case, re- examine the data. For example, the data set, seemingly “cycle times of the lathe,” may really be two data sets: “cycle time of the lathe on x-type parts” and “cycle time of the lathe on y-type parts.” In such a case, subdivide the data set and re-analyze each subset. Valuable further detail on distribution-fitting analyses is available in Cheng (1993) and in chapter 6 of Kelton, Smith, and Sturrock (2013). For example, the assessment of how well or poorly the proposed closed-form distribution fits the empirical data may be based upon any or all of the chi-square (also “chi squared”), Anderson-Darling, Cramérvon Mises, or Kolmogorov-Smirnov statistical tests.

Furthermore, looking ahead to the next step, data should be used in the model-under-construction as it is collected. The sooner the data actually enters a model (even one in early stages of development), the sooner significant errors in the data, or misunderstandings involving its collection, will come to light.

MODEL BUILDING, VERIFICATION, AND VALIDATION

The task of building the simulation model now waxes large – indeed, in actual practice, data collection and the building of the model should be, and are, undertaken largely concurrently. The choice of software to build the model may be clear if previous simulation projects have been done using that software; here, let us assume that it is not the case (first foray into simulation). Then various considerations might direct the choice of software:

• Use package x because its salesperson gave us the flashiest demonstration and made the rosiest (Definitely contraindicated!)
• Use package x because one or several of our employees have received instruction in its use (perhaps in a university course).
• Use package x because our analysts attended a conference where competing packages were exhibited, and those analysts undertook a detailed comparative examination of competing packages relative to our modeling
• Use package x because a consultant whom we trust, and who demonstrably has no vested interest in recommending x, and who can clearly articulate substantive reasons for choosing x, recommends it.
• Use package x because of assurance that support (including both software documentation and vendor support) will be timely and of high quality.

The analyst choosing the software must ensure that it accommodates any modeling needs specific to the system to be modeled. Examples of such specific needs might be:

• Ability to model shifts of work, perhaps including situations where parts of the facility run one shift and other parts run two, very likely including situations involving coffee breaks and/or meal
• Ability to model changeover times, perhaps including situations where more than one cause of changeover (as discussed in data collection) exist.
• Ability to model downtimes whose occurrence is based on any or all of elapsed working time, elapsed total time, or number of cycles executed.
• Ability to model repair operations whose undertaking may be contingent on the availability of a repair person with a specialized skill and/or the availability of specific repair
• Ability to model bridge cranes, perhaps including multiple cranes and “bump-away” priorities in one
• Ability to model conveyors, accumulating and/or non-accumulating, perhaps including configurations in which the conveyors have curves in which travel speed is reduced.
• Ability to model material-handling operations including equipment such as tug trains, forklifts, high-lows, and/or automatic guided vehicles.
• Ability to model situations in which several parts are joined together permanently in a
• Ability to model situations in which expected remaining cycle time suddenly changes because a piece of equipment suddenly becomes (un)available; for example, two polishers working together need ½ hour more to complete a job, one breaks down, and the estimated remaining cycle time suddenly becomes 1 hour.
• Ability to model situations in which parts are inspected, with some being judged “good” (ready for shipment or use in an assembly), some being judged “needing rework,” after which they may become “good,” and some being judged “scrap” to be rejected.
• Ability to model situations in which several parts are joined temporarily; for example, to travel together on a
• Ability to model situations in which several parts are joined permanently, for shipment or for further assembly
• Ability to model situations in which raw material or parts are
• Ability to interface conveniently with relational database software (e.g., Microsoft Access®).

The task of verification should be concurrent with the task of building the model. Verification, conceptually equivalent with “debugging” in the context of computer software coding, seeks to find and extirpate all errors (“bugs”) in the model by testing the model. As clearly stated (Myers 1979), a successful test is one that exposes an error. The analyst should not build the entire model and then begin verification – errors in the model are then difficult to expose and isolate for correction.   Rather, the analyst should build the model piecemeal, pausing to verify each component (e.g., another segment of the production line) before building the next component. Verification methods include stepwise examination of the animation (are entities [items] in the model going where they should?) and code or model walkthroughs (the model-builder explains the construction and operation of the model to a willing listener, often becoming aware of an error in doing so).

Validation is fundamentally distinct from verification. Whereas verification answers the question “Is the model built right?”, validation answers the question “Did we build the right model?” The right model is one that accurately mirrors the real or proposed system in all ways important to the client, and does so as simply as possible. Therefore, validation requires the participation of the client more than verification does. Powerful methods of validation include (Sargent 1992):

• Comparing model output with observed values of the current system – if the current system Here, a Turing test can be especially valuable. Put similarly formatted reports of model output and of actual system output (e.g., utilizations, throughput, queue lengths and residence times) side-by-side and ask the client “Which is which?” If the client is uncertain, congratulations! The model has passed the Turing test. If the client confidently and correctly says, for example, “The one on the left is the model output,” the model fails the Turing test. Ask “How could you tell?” An example answer might be “It has a shorter queue upstream from the milling machine than we’ve ever seen in practice.” Such an explanation provides valuable information for correcting the model and adding to its realism.
• Temporarily replacing all randomness in the model with constants and checking results against spreadsheet computations (also useful in verification).
• Allowing only one entity [item] into the model and examining the output results (also useful in verification).
• Undertaking directional tests: g., increasing arrival rates should increase queue lengths, queue residence times, and machine utilizations.
• Checking for face validity: g., a chronically long queue directly upstream from a machine with low utilization is suspicious and merits close examination.

The ultimate goal of verification and validation is model credibility. A credible model is one the client trusts to guide managerial decision-making..

MODEL EXECUTION AND OUTPUT ANALYSIS

After verification and validation are complete, and the model has achieved credibility in the opinion of the client, it must be executed to evaluate and assess the merits of the system design(s) under investigation. Key questions to ask and answer at this stage of the simulation project are:

1. How much warm-up time is appropriate?
2. How long should the replications be?
3. How many replications should be run?

Warm-up time refers to the simulated time during which the model runs to achieve typical system conditions, as opposed to the time-zero “empty and idle” default condition of the model. To select the warm-up time, the analyst must first decide whether the simulation is “terminating” or “steady-state.” A terminating simulation models a system which itself begins “empty and idle,” such as a bank. A steady- state simulation models a system which does not periodically empty and shut down, such as a hospital emergency room or a telephone exchange. Most manufacturing systems are steady-state – even if operations pause over the weekend, for example, work very probably resumes Monday morning where it left off Friday afternoon.   Whereas terminating systems need and should have zero warm-up time, a model of a manufacturing system must be run for sufficient warm-up time to reach typical long-term conditions before the simulation software is instructed to begin gathering output statistics and performance metrics. Statistical tests are available to help the analyst choose the appropriate warm-up time (Goldsman and Tokol 2000).

The length of a replication (i.e., the simulated time it represents) is likewise a delicate statistical question. The longer each replication is, the more confidence both the analyst and the client can have that the replication will accurately capture representative reality in the system being modeled. One useful rule of thumb is that even the rarest of events (for example, a conveyor breakdown) should have a chance to happen “half a dozen” times during the replication. The analyst does well to remember that the rarest events may be interactions. For example, if each of two particular machines fails occasionally and independently, both machines may be simultaneously “down” very occasionally – yet information on system performance during that situation may be extremely important to have. As an additional convenience, the length of a replication should be an integer multiple of a canonical work period. For example, suppose performance metrics on the actual system are (or will be) gathered on a basis of 24- hour intervals. If the foregoing considerations guide the analyst to a replication length of 450 hours, the replication length might well be increased to 480 hours, representing twenty days.

From a statistical viewpoint, each replication represents another experimental data point – “another throw of the dice” (using different random numbers generated by the simulation software). Therefore, successive replications are statistically independent, permitting the use of standard statistical formulas (for example, those pertaining to the Student-t distribution) for calculation of confidence intervals for the performance metrics of interest. These formulas provide confidence intervals whose width varies inversely as the square root of n (= number of replications), not inversely as n. Therefore, for example, if the width of these intervals needs to be halved to give the client sufficient confidence when making decisions based on the simulation analysis, it is insufficient to double the number of replications. The number of replications must be quadrupled. Furthermore, the analyst must avoid the mistake of making one extremely long run (for example, using the previous numbers, 9600 hours) and mentally dividing it into 20 “replications” of 480 hours each. Such misconstrued replications are not statistically independent – for example, conditions in the system at 955 hours (near the end of one subdivision) and conditions at 965 hours (near the beginning of the next) are very similar, the result of positive correlation. With independence thus foregone, the foundations underpinning the computation of confidence intervals for the performance metrics are therefore severely compromised. Indeed, breaking a “long” run (replication) into pieces can be done, using the technique of batch means and taking care to ensure the batches are as nearly independent as possible (Sanchez 1999).

When only a very few alternatives are to be compared (e.g., a, b, and c), the analyst can reasonably build confidence intervals for all comparisons needed (here, a relative to b, a relative to c, and b relative to c). However, much greater statistical power is available for the typical situation of multiple comparisons on multiple factors. For example, the analyst may need to investigate a situation such as:

1. Conveyor currently in use versus a faster
2. Current material-handling equipment versus one more fork
3. Current repair staff level versus one more repair

In situations such as this, the analyst can and should use Design of Experiments (DOE). This powerful statistical methodology, using designs such as one- or two-way analysis of variance, a full factorial design, a fractional factorial design, or others, can readily analyze the alternatives collectively. A significant advantage of DOE is its ability to detect interactions.   In this example, it may be the case that a faster conveyor, by itself, will yield almost no improvement and an additional fork truck, by itself, will yield almost no improvement – yet making both changes will yield a significant improvement.

ACKNOWLEDGMENTS

The author gratefully acknowledges the help and encouragement of Professors Onur M. Ülgen (PMC and University of Michigan – Dearborn) and Y. Ro (University of Michigan – Dearborn). Furthermore, two anonymous referees have provided valuable and explicit suggestions to improve this paper.

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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 Motor Company in 1972, where he worked until retirement in December 2001 as a computer software analyst supporting statistical and simulation software. After retirement from Ford, he joined PMC, Dearborn, Michigan, as a senior simulation analyst. Also, since 1980, he has taught classes at the University of Michigan – Dearborn, including both undergraduate and graduate simulation classes using GPSS/H™, SLAM II™, SIMAN™, ProModel®, SIMUL8®, Arena®, and Simio®.   He is a member of the Institute of Industrial Engineers [IIE], the Society for Computer Simulation International [SCS], and the Michigan Simulation Users Group [MSUG]. He has served on the editorial board of the International Journal of Industrial Engineering – Applications and Practice. During the last several years, he has given invited plenary addresses on simulation and statistics at conferences in Monterrey, México; İstanbul, Turkey; Genova, Italy; Rīga, Latvia; Jyväskylä, Finland; and Winnipeg, Canada. He served as a co-editor of Proceedings of the International Workshop on Harbour, Maritime and Multimodal Logistics Modelling & Simulation 2003, a conference held in Rīga, Latvia. Likewise, he served the Summer Computer Simulation Conferences of 2004, 2005, and 2006 as Proceedings co-editor. He was the Simulation Applications track coordinator for the 2011 Winter Simulation Conference and the 2014 Institute of Industrial Engineers Conference.