Harrell Ghosh Bowden cap4

Harrell−Ghosh−Bowden: Simulation Using ProModel, Second Edition

I. Study Chapters 2. System Dynamics © The McGraw−Hill Companies, 2004

C H A P T E R

2 SYSTEM DYNAMICS

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“A fool with a tool is still a fool.”—Unknown

2.1 IntroductionKnowing how to do simulation doesn’t make someone a good systems designerany more than knowing how to use a CAD system makes one a good product de-signer. Simulation is a tool that is useful only if one understands the nature of theproblem to be solved. It is designed to help solve systemic problems that are op-erational in nature. Simulation exercises fail to produce useful results more oftenbecause of a lack of understanding of system dynamics than a lack of knowinghow to use the simulation software. The challenge is in understanding how thesystem operates, knowing what you want to achieve with the system, and beingable to identify key leverage points for best achieving desired objectives. Toillustrate the nature of this challenge, consider the following actual scenario:

The pipe mill for the XYZ Steel Corporation was an important profit center, turningsteel slabs selling for under $200/ton into a product with virtually unlimited demandselling for well over $450/ton. The mill took coils of steel of the proper thickness andwidth through a series of machines that trimmed the edges, bent the steel into acylinder, welded the seam, and cut the resulting pipe into appropriate lengths, all on acontinuously running line. The line was even designed to weld the end of one coil tothe beginning of the next one “on the fly,” allowing the line to run continually for dayson end.

Unfortunately the mill was able to run only about 50 percent of its theoretical ca-pacity over the long term, costing the company tens of millions of dollars a year in lostrevenue. In an effort to improve the mill’s productivity, management studied each stepin the process. It was fairly easy to find the slowest step in the line, but additionalstudy showed that only a small percentage of lost production was due to problems atthis “bottleneck” operation. Sometimes a step upstream from the bottleneck would



24 Part I Study Chapters

have a problem, causing the bottleneck to run out of work, or a downstream stepwould go down temporarily, causing work to back up and stop the bottleneck. Some-times the bottleneck would get so far behind that there was no place to put incoming,newly made pipe. In this case the workers would stop the entire pipe-making processuntil the bottleneck was able to catch up. Often the bottleneck would then be idle wait-ing until the newly started line was functioning properly again and the new pipe had achance to reach it. Sometimes problems at the bottleneck were actually caused by im-proper work at a previous location.

In short, there was no single cause for the poor productivity seen at this plant.Rather, several separate causes all contributed to the problem in complex ways. Man-agement was at a loss to know which of several possible improvements (additional orfaster capacity at the bottleneck operation, additional storage space between stations,better rules for when to shut down and start up the pipe-forming section of the mill,better quality control, or better training at certain critical locations) would have themost impact for the least cost. Yet the poor performance of the mill was costing enor-mous amounts of money. Management was under pressure to do something, but whatshould it be?

This example illustrates the nature and difficulty of the decisions that anoperations manager faces. Managers need to make decisions that are the “best” insome sense. To do so, however, requires that they have clearly defined goals andunderstand the system well enough to identify cause-and-effect relationships.

While every system is different, just as every product design is different,the basic elements and types of relationships are the same. Knowing how theelements of a system interact and how overall performance can be improved areessential to the effective use of simulation. This chapter reviews basic systemdynamics and answers the following questions:

• What is a system?

• What are the elements of a system?

• What makes systems so complex?

• What are useful system metrics?

• What is a systems approach to systems planning?

• How do traditional systems analysis techniques compare with simulation?

2.2 System DefinitionWe live in a society that is composed of complex, human-made systems thatwe depend on for our safety, convenience, and livelihood. Routinely we rely ontransportation, health care, production, and distribution systems to provide neededgoods and services. Furthermore, we place high demands on the quality, conve-nience, timeliness, and cost of the goods and services that are provided by thesesystems. Remember the last time you were caught in a traffic jam, or waited forwhat seemed like an eternity in a restaurant or doctor’s office? Contrast that ex-perience with the satisfaction that comes when you find a store that sells qualitymerchandise at discount prices or when you locate a health care organization that



Chapter 2 System Dynamics 25

provides prompt and professional service. The difference is between a system thathas been well designed and operates smoothly, and one that is poorly planned andmanaged.

A system, as used here, is defined as a collection of elements that functiontogether to achieve a desired goal (Blanchard 1991). Key points in this definitioninclude the fact that (1) a system consists of multiple elements, (2) these elementsare interrelated and work in cooperation, and (3) a system exists for the purposeof achieving specific objectives. Examples of systems are traffic systems, politicalsystems, economic systems, manufacturing systems, and service systems. Ourmain focus will be on manufacturing and service systems that process materials,information, and people.

Manufacturing systems can be small job shops and machining cells or largeproduction facilities and assembly lines. Warehousing and distribution as well asentire supply chain systems will be included in our discussions of manufacturingsystems. Service systems cover a wide variety of systems including health carefacilities, call centers, amusement parks, public transportation systems, restau-rants, banks, and so forth.

Both manufacturing and service systems may be termed processing systemsbecause they process items through a series of activities. In a manufacturing sys-tem, raw materials are transformed into finished products. For example, a bicyclemanufacturer starts with tube stock that is then cut, welded, and painted to pro-duce bicycle frames. In service systems, customers enter with some service needand depart as serviced (and, we hope, satisfied) customers. In a hospital emer-gency room, for example, nurses, doctors, and other staff personnel admit andtreat incoming patients who may undergo tests and possibly even surgical proce-dures before finally being released. Processing systems are artificial (they arehuman-made), dynamic (elements interact over time), and usually stochastic (theyexhibit random behavior).

2.3 System ElementsFrom a simulation perspective, a system can be said to consist of entities, activi-ties, resources, and controls (see Figure 2.1). These elements define the who,what, where, when, and how of entity processing. This model for describing a

Resources Controls

Incoming entities Outgoing entities

System

Activities

FIGURE 2.1Elements of a system.




system corresponds closely to the well-established ICAM definition (IDEF)process model developed by the defense industry (ICAM stands for an early AirForce program in integrated computer-aided manufacturing). The IDEF modelingparadigm views a system as consisting of inputs and outputs (that is, entities), ac-tivities, mechanisms (that is, resources), and controls.

2.3.1 Entities

Entities are the items processed through the system such as products, customers,and documents. Different entities may have unique characteristics such as cost,shape, priority, quality, or condition. Entities may be further subdivided into thefollowing types:

• Human or animate (customers, patients, etc.).

• Inanimate (parts, documents, bins, etc.).

• Intangible (calls, electronic mail, etc.).

For most manufacturing and service systems, the entities are discrete items.This is the case for discrete part manufacturing and is certainly the case for nearlyall service systems that process customers, documents, and others. For some pro-duction systems, called continuous systems, a nondiscrete substance is processedrather than discrete entities. Examples of continuous systems are oil refineries andpaper mills.

2.3.2 Activities

Activities are the tasks performed in the system that are either directly orindirectly involved in the processing of entities. Examples of activities includeservicing a customer, cutting a part on a machine, or repairing a piece of equip-ment. Activities usually consume time and often involve the use of resources.Activities may be classified as

• Entity processing (check-in, treatment, inspection, fabrication, etc.).

• Entity and resource movement (forklift travel, riding in an elevator, etc.).

• Resource adjustments, maintenance, and repairs (machine setups, copymachine repair, etc.).

2.3.3 Resources

Resources are the means by which activities are performed. They provide thesupporting facilities, equipment, and personnel for carrying out activities. Whileresources facilitate entity processing, inadequate resources can constrain process-ing by limiting the rate at which processing can take place. Resources havecharacteristics such as capacity, speed, cycle time, and reliability. Like entities,resources can be categorized as

• Human or animate (operators, doctors, maintenance personnel, etc.).

• Inanimate (equipment, tooling, floor space, etc.).

• Intangible (information, electrical power, etc.).




Resources can also be classified as being dedicated or shared, permanent orconsumable, and mobile or stationary.

2.3.4 Controls

Controls dictate how, when, and where activities are performed. Controls imposeorder on the system. At the highest level, controls consist of schedules, plans, andpolicies. At the lowest level, controls take the form of written procedures and ma-chine control logic. At all levels, controls provide the information and decisionlogic for how the system should operate. Examples of controls include

• Routing sequences.

• Production plans.

• Work schedules.

• Task prioritization.

• Control software.

• Instruction sheets.

2.4 System ComplexityElements of a system operate in concert with one another in ways that often resultin complex interactions. The word complex comes from the Latin complexus,meaning entwined or connected together. Unfortunately, unaided human intuitionis not very good at analyzing and understanding complex systems. EconomistHerbert Simon called this inability of the human mind to grasp real-worldcomplexity “the principle of bounded rationality.” This principle states that “thecapacity of the human mind for formulating and solving complex problems isvery small compared with the size of the problem whose solution is required forobjectively rational behavior in the real world, or even for a reasonable approxi-mation to such objective rationality” (Simon 1957).

While the sheer number of elements in a system can stagger the mind (thenumber of different entities, activities, resources, and controls can easily exceed100), the interactions of these elements are what make systems so complex and

Bounded rationality—our limited ability to graspreal-world complexity.




Number of interdependenciesand random variables

Deg

ree

of a

naly

tical

diffi

culty

FIGURE 2.2Analytical difficultyas a function of thenumber ofinterdependencies andrandom variables.

difficult to analyze. System complexity is primarily a function of the followingtwo factors:

1. Interdependencies between elements so that each element affects otherelements.

2. Variability in element behavior that produces uncertainty.

These two factors characterize virtually all human-made systems and makesystem behavior difficult to analyze and predict. As shown in Figure 2.2, the de-gree of analytical difficulty increases exponentially as the number of interdepen-dencies and random variables increases.

2.4.1 Interdependencies

Interdependencies cause the behavior of one element to affect other elements inthe system. For example, if a machine breaks down, repair personnel are put intoaction while downstream operations become idle for lack of parts. Upstreamoperations may even be forced to shut down due to a logjam in the entity flowcausing a blockage of activities. Another place where this chain reaction ordomino effect manifests itself is in situations where resources are shared between

Interdependencies Variability Complexity




two or more activities. A doctor treating one patient, for example, may be unableto immediately respond to another patient needing his or her attention. This delayin response may also set other forces in motion.

It should be clear that the complexity of a system has less to do with thenumber of elements in the system than with the number of interdependent rela-tionships. Even interdependent relationships can vary in degree, causing more orless impact on overall system behavior. System interdependency may be eithertight or loose depending on how closely elements are linked. Elements that aretightly coupled have a greater impact on system operation and performance thanelements that are only loosely connected. When an element such as a worker ormachine is delayed in a tightly coupled system, the impact is immediately felt byother elements in the system and the entire process may be brought to a screech-ing halt.

In a loosely coupled system, activities have only a minor, and often delayed,impact on other elements in the system. Systems guru Peter Senge (1990) notesthat for many systems, “Cause and effect are not closely related in time andspace.” Sometimes the distance in time and space between cause-and-effect rela-tionships becomes quite sizable. If enough reserve inventory has been stockpiled,a truckers’ strike cutting off the delivery of raw materials to a transmission plantin one part of the world may not affect automobile assembly in another part of theworld for weeks. Cause-and-effect relationships are like a ripple of water that di-minishes in impact as the distance in time and space increases.

Obviously, the preferred approach to dealing with interdependencies is toeliminate them altogether. Unfortunately, this is not entirely possible for mostsituations and actually defeats the purpose of having systems in the first place.The whole idea of a system is to achieve a synergy that otherwise would be un-attainable if every component were to function in complete isolation. Severalmethods are used to decouple system elements or at least isolate their influenceso disruptions are not felt so easily. These include providing buffer inventories,implementing redundant or backup measures, and dedicating resources to sin-gle tasks. The downside to these mitigating techniques is that they often lead toexcessive inventories and underutilized resources. The point to be made hereis that interdependencies, though they may be minimized somewhat, are sim-ply a fact of life and are best dealt with through effective coordination andmanagement.

2.4.2 Variability

Variability is a characteristic inherent in any system involving humans andmachinery. Uncertainty in supplier deliveries, random equipment failures, unpre-dictable absenteeism, and fluctuating demand all combine to create havoc in plan-ning system operations. Variability compounds the already unpredictable effect ofinterdependencies, making systems even more complex and unpredictable. Vari-ability propagates in a system so that “highly variable outputs from one worksta-tion become highly variable inputs to another” (Hopp and Spearman 2000).




TABLE 2.1 Examples of System Variability

Type of Variability Examples

Activity times Operation times, repair times, setup times, move times Decisions To accept or reject a part, where to direct a particular customer, which

task to perform nextQuantities Lot sizes, arrival quantities, number of workers absentEvent intervals Time between arrivals, time between equipment failuresAttributes Customer preference, part size, skill level

Table 2.1 identifies the types of random variability that are typical of most manu-facturing and service systems.

The tendency in systems planning is to ignore variability and calculate sys-tem capacity and performance based on average values. Many commercial sched-uling packages such as MRP (material requirements planning) software work thisway. Ignoring variability distorts the true picture and leads to inaccurate perfor-mance predictions. Designing systems based on average requirements is likedeciding whether to wear a coat based on the average annual temperature or pre-scribing the same eyeglasses for everyone based on average eyesight. Adults havebeen known to drown in water that was only four feet deep—on the average!Wherever variability occurs, an attempt should be made to describe the nature orpattern of the variability and assess the range of the impact that variability mighthave on system performance.

Perhaps the most illustrative example of the impact that variability can haveon system behavior is the simple situation where entities enter into a single queueto wait for a single server. An example of this might be customers lining up infront of an ATM. Suppose that the time between customer arrivals is exponen-tially distributed with an average time of one minute and that they take an averagetime of one minute, exponentially distributed, to transact their business. In queu-ing theory, this is called an M/M/1 queuing system. If we calculate system per-formance based solely on average time, there will never be any customers waitingin the queue. Every minute that a customer arrives the previous customer finisheshis or her transaction. Now if we calculate the number of customers waiting inline, taking into account the variation, we will discover that the waiting line growsto infinity (the technical term is that the system “explodes”). Who would guessthat in a situation involving only one interdependent relationship that variationalone would make the difference between zero items waiting in a queue and an in-finite number in the queue?

By all means, variability should be reduced and even eliminated whereverpossible. System planning is much easier if you don’t have to contend with it.Where it is inevitable, however, simulation can help predict the impact it will haveon system performance. Likewise, simulation can help identify the degree ofimprovement that can be realized if variability is reduced or even eliminated. For




example, it can tell you how much reduction in overall flow time and flow timevariation can be achieved if operation time variation can be reduced by, say,20 percent.

2.5 System Performance MetricsMetrics are measures used to assess the performance of a system. At the highestlevel of an organization or business, metrics measure overall performance interms of profits, revenues, costs relative to budget, return on assets, and so on.These metrics are typically financial in nature and show bottom-line performance.Unfortunately, such metrics are inherently lagging, disguise low-level operationalperformance, and are reported only periodically. From an operational standpoint,it is more beneficial to track such factors as time, quality, quantity, efficiency, andutilization. These operational metrics reflect immediate activity and are directlycontrollable. They also drive the higher financially related metrics. Key opera-tional metrics that describe the effectiveness and efficiency of manufacturing andservice systems include the following:

• Flow time—the average time it takes for an item or customer to beprocessed through the system. Synonyms include cycle time, throughputtime, and manufacturing lead time. For order fulfillment systems, flowtime may also be viewed as customer response time or turnaround time.A closely related term in manufacturing is makespan, which is the timeto process a given set of jobs. Flow time can be shortened by reducingactivity times that contribute to flow time such as setup, move, operation,and inspection time. It can also be reduced by decreasing work-in-processor average number of entities in the system. Since over 80 percent ofcycle time is often spent waiting in storage or queues, elimination ofbuffers tends to produce the greatest reduction in cycle time. Anothersolution is to add more resources, but this can be costly.

• Utilization—the percentage of scheduled time that personnel, equipment,and other resources are in productive use. If a resource is not beingutilized, it may be because it is idle, blocked, or down. To increaseproductive utilization, you can increase the demand on the resource orreduce resource count or capacity. It also helps to balance work loads. In asystem with high variability in activity times, it is difficult to achieve highutilization of resources. Job shops, for example, tend to have low machineutilization. Increasing utilization for the sake of utilization is not a goodobjective. Increasing the utilization of nonbottleneck resources, forexample, often only creates excessive inventories without creatingadditional throughput.

• Value-added time—the amount of time material, customers, and so forthspend actually receiving value, where value is defined as anything forwhich the customer is willing to pay. From an operational standpoint,




value-added time is considered the same as processing time or time spentactually undergoing some physical transformation or servicing. Inspectiontime and waiting time are considered non-value-added time.

• Waiting time—the amount of time that material, customers, and so onspend waiting to be processed. Waiting time is by far the greatestcomponent of non-value-added time. Waiting time can be decreased byreducing the number of items (such as customers or inventory levels) inthe system. Reducing variation and interdependencies in the system canalso reduce waiting times. Additional resources can always be added, butthe trade-off between the cost of adding the resources and the savings ofreduced waiting time needs to be evaluated.

• Flow rate—the number of items produced or customers serviced per unitof time (such as parts or customers per hour). Synonyms includeproduction rate, processing rate, or throughput rate. Flow rate can beincreased by better management and utilization of resources, especiallythe limiting or bottleneck resource. This is done by ensuring that thebottleneck operation or resource is never starved or blocked. Once systemthroughput matches the bottleneck throughput, additional processing orthroughput capacity can be achieved by speeding up the bottleneckoperation, reducing downtimes and setup times at the bottleneck operation,adding more resources to the bottleneck operation, or off-loading workfrom the bottleneck operation.

• Inventory or queue levels—the number of items or customers in storageor waiting areas. It is desirable to keep queue levels to a minimum whilestill achieving target throughput and response time requirements. Wherequeue levels fluctuate, it is sometimes desirable to control the minimumor maximum queue level. Queuing occurs when resources are unavailablewhen needed. Inventory or queue levels can be controlled either bybalancing flow or by restricting production at nonbottleneck operations.JIT (just-in-time) production is one way to control inventory levels.

• Yield—from a production standpoint, the percentage of productscompleted that conform to product specifications as a percentage of thetotal number of products that entered the system as raw materials. If 95out of 100 items are nondefective, the yield is 95 percent. Yield can alsobe measured by its complement—reject or scrap rate.

• Customer responsiveness—the ability of the system to deliver products ina timely fashion to minimize customer waiting time. It might be measuredas fill rate, which is the number of customer orders that can be filledimmediately from inventory. In minimizing job lateness, it may bedesirable to minimize the overall late time, minimize the number orpercentage of jobs that are late, or minimize the maximum tardiness ofjobs. In make-to-stock operations, customer responsiveness can beassured by maintaining adequate inventory levels. In make-to-order,customer responsiveness is improved by lowering inventory levels so thatcycle times can be reduced.




• Variance—the degree of fluctuation that can and often does occur in anyof the preceding metrics. Variance introduces uncertainty, and thereforerisk, in achieving desired performance goals. Manufacturers and serviceproviders are often interested in reducing variance in delivery and servicetimes. For example, cycle times and throughput rates are going to havesome variance associated with them. Variance is reduced by controllingactivity times, improving resource reliability, and adhering to schedules.

These metrics can be given for the entire system, or they can be broken down byindividual resource, entity type, or some other characteristic. By relating thesemetrics to other factors, additional meaningful metrics can be derived that areuseful for benchmarking or other comparative analysis. Typical relational metricsinclude minimum theoretical flow time divided by actual flow time (flow timeefficiency), cost per unit produced (unit cost), annual inventory sold divided byaverage inventory (inventory turns or turnover ratio), or units produced per cost orlabor input (productivity).

2.6 System VariablesDesigning a new system or improving an existing system requires more than sim-ply identifying the elements and performance goals of the system. It requires anunderstanding of how system elements affect each other and overall performanceobjectives. To comprehend these relationships, you must understand three typesof system variables:

1. Decision variables

2. Response variables

3. State variables

2.6.1 Decision Variables

Decision variables (also called input factors in SimRunner) are sometimes re-ferred to as the independent variables in an experiment. Changing the values of asystem’s independent variables affects the behavior of the system. Independentvariables may be either controllable or uncontrollable depending on whether theexperimenter is able to manipulate them. An example of a controllable variable isthe number of operators to assign to a production line or whether to work one ortwo shifts. Controllable variables are called decision variables because the deci-sion maker (experimenter) controls the values of the variables. An uncontrollablevariable might be the time to service a customer or the reject rate of an operation.When defining the system, controllable variables are the information about thesystem that is more prescriptive than descriptive (see section 2.9.3).

Obviously, all independent variables in an experiment are ultimatelycontrollable—but at a cost. The important point here is that some variables areeasier to change than others. When conducting experiments, the final solution is




often based on whether the cost to implement a change produces a higher returnin performance.

2.6.2 Response Variables

Response variables (sometimes called performance or output variables) measurethe performance of the system in response to particular decision variable settings.A response variable might be the number of entities processed for a given period,the average utilization of a resource, or any of the other system performance met-rics described in section 2.5.

In an experiment, the response variable is the dependent variable, which de-pends on the particular value settings of the independent variables. The experi-menter doesn’t manipulate dependent variables, only independent or decisionvariables. Obviously, the goal in systems planning is to find the right values or set-tings of the decision variables that give the desired response values.

2.6.3 State Variables

State variables indicate the status of the system at any specific point in time. Ex-amples of state variables are the current number of entities waiting to beprocessed or the current status (busy, idle, down) of a particular resource. Re-sponse variables are often summaries of state variable changes over time. For ex-ample, the individual times that a machine is in a busy state can be summed overa particular period and divided by the total available time to report the machineutilization for that period.

State variables are dependent variables like response variables in that theydepend on the setting of the independent variables. State variables are often ig-nored in experiments since they are not directly controlled like decision variablesand are not of as much interest as the summary behavior reported by responsevariables.

Sometimes reference is made to the state of a system as though a system it-self can be in a particular state such as busy or idle. The state of a system actuallyconsists of “that collection of variables necessary to describe a system at a partic-ular time, relative to the objectives of the study” (Law and Kelton 2000). If westudy the flow of customers in a bank, for example, the state of the bank for agiven point in time would include the current number of customers in the bank,the current status of each teller (busy, idle, or whatever), and perhaps the time thateach customer has been in the system thus far.

2.7 System OptimizationFinding the right setting for decision variables that best meets performanceobjectives is called optimization. Specifically, optimization seeks the best com-bination of decision variable values that either minimizes or maximizes someobjective function such as costs or profits. An objective function is simply a




response variable of the system. A typical objective in an optimization problem fora manufacturing or service system might be minimizing costs or maximizing flowrate. For example, we might be interested in finding the optimum number of per-sonnel for staffing a customer support activity that minimizes costs yet handles thecall volume. In a manufacturing concern, we might be interested in maximizingthe throughput that can be achieved for a given system configuration. Optimizationproblems often include constraints, limits to the values that the decision variablescan take on. For example, in finding the optimum speed of a conveyor such thatproduction cost is minimized, there would undoubtedly be physical limits to howslow or fast the conveyor can operate. Constraints can also apply to response vari-ables. An example of this might be an objective to maximize throughput but sub-ject to the constraint that average waiting time cannot exceed 15 minutes.

In some instances, we may find ourselves trying to achieve conflictingobjectives. For example, minimizing production or service costs often conflictswith minimizing waiting costs. In system optimization, one must be careful toweigh priorities and make sure the right objective function is driving the deci-sions. If, for example, the goal is to minimize production or service costs, theobvious solution is to maintain only a sufficient workforce to meet processingrequirements. Unfortunately, in manufacturing systems this builds up work-in-process and results in high inventory carrying costs. In service systems, longqueues result in long waiting times, hence dissatisfied customers. At the otherextreme, one might feel that reducing inventory or waiting costs should be theoverriding goal and, therefore, decide to employ more than an adequate numberof resources so that work-in-process or customer waiting time is virtually elimi-nated. It should be obvious that there is a point at which the cost of adding anotherresource can no longer be justified by the diminishing incremental savings inwaiting costs that are realized. For this reason, it is generally conceded that abetter strategy is to find the right trade-off or balance between the number ofresources and waiting times so that the total cost is minimized (see Figure 2.3).

Number of resources

Optimum

Cos

t

Total costResource costs

Waiting costs

FIGURE 2.3Cost curves showingoptimum number ofresources to minimizetotal cost.




As shown in Figure 2.3, the number of resources at which the sum of theresource costs and waiting costs is at a minimum is the optimum number ofresources to have. It also becomes the optimum acceptable waiting time.

In systems design, arriving at an optimum system design is not alwaysrealistic, given the almost endless configurations that are sometimes possible andlimited time that is available. From a practical standpoint, the best that can beexpected is a near optimum solution that gets us close enough to our objective,given the time constraints for making the decision.

2.8 The Systems ApproachDue to departmentalization and specialization, decisions in the real world are oftenmade without regard to overall system performance. With everyone busy mindinghis or her own area of responsibility, often no one is paying attention to the bigpicture. One manager in a large manufacturing corporation noted that as many as99 percent of the system improvement recommendations made in his companyfailed to look at the system holistically. He further estimated that nearly 80 per-cent of the suggested changes resulted in no improvement at all, and many of thesuggestions actually hurt overall performance. When attempting to make systemimprovements, it is often discovered that localized changes fail to produce theoverall improvement that is desired. Put in technical language: Achieving a localoptimum often results in a global suboptimum. In simpler terms: It’s okay to actlocally as long as one is thinking globally. The elimination of a problem in one areamay only uncover, and sometimes even exacerbate, problems in other areas.

Approaching system design with overall objectives in mind and consideringhow each element relates to each other and to the whole is called a systems orholistic approach to systems design. Because systems are composed of interde-pendent elements, it is not possible to accurately predict how a system willperform simply by examining each system element in isolation from the whole.To presume otherwise is to take a reductionist approach to systems design, whichfocuses on the parts rather than the whole. While structurally a system may be di-visible, functionally it is indivisible and therefore requires a holistic approach tosystems thinking. Kofman and Senge (1995) observe

The defining characteristic of a system is that it cannot be understood as a function ofits isolated components. First, the behavior of the system doesn’t depend on whateach part is doing but on how each part is interacting with the rest. . . . Second, to un-derstand a system we need to understand how it fits into the larger system of which itis a part. . . . Third, and most important, what we call the parts need not be taken asprimary. In fact, how we define the parts is fundamentally a matter of perspective andpurpose, not intrinsic in the nature of the “real thing” we are looking at.

Whether designing a new system or improving an existing system, it is impor-tant to follow sound design principles that take into account all relevant variables.The activity of systems design and process improvement, also called systems




Identify problemsand opportunities.

Select andimplement thebest solution.

Developalternativesolutions.

Evaluate thesolutions.

FIGURE 2.4Four-step iterativeapproach to systemsimprovement.

engineering, has been defined as

The effective application of scientific and engineering efforts to transform an opera-tional need into a defined system configuration through the top-down iterative processof requirements definition, functional analysis, synthesis, optimization, design, testand evaluation (Blanchard 1991).

To state it simply, systems engineering is the process of identifying problems orother opportunities for improvement, developing alternative solutions, evaluatingthe solutions, and selecting and implementing the best solutions (see Figure 2.4).All of this should be done from a systems point of view.

2.8.1 Identifying Problems and Opportunities

The importance of identifying the most significant problem areas and recognizingopportunities for improvement cannot be overstated. Performance standardsshould be set high in order to look for the greatest improvement opportunities.Companies making the greatest strides are setting goals of 100 to 500 percentimprovement in many areas such as inventory reduction or customer lead time re-duction. Setting high standards pushes people to think creatively and often resultsin breakthrough improvements that would otherwise never be considered. Con-trast this way of thinking with one hospital whose standard for whether a patienthad a quality experience was whether the patient left alive! Such lack of visionwill never inspire the level of improvement needed to meet ever-increasingcustomer expectations.

2.8.2 Developing Alternative Solutions

We usually begin developing a solution to a problem by understanding the prob-lem, identifying key variables, and describing important relationships. This helps




identify possible areas of focus and leverage points for applying a solution.Techniques such as cause-and-effect analysis and pareto analysis are useful here.

Once a problem or opportunity has been identified and key decision variablesisolated, alternative solutions can be explored. This is where most of the designand engineering expertise comes into play. Knowledge of best practices for com-mon types of processes can also be helpful. The designer should be open to allpossible alternative feasible solutions so that the best possible solutions don’t getoverlooked.

Generating alternative solutions requires creativity as well as organizationaland engineering skills. Brainstorming sessions, in which designers exhaust everyconceivably possible solution idea, are particularly useful. Designers should useevery stretch of the imagination and not be stifled by conventional solutionsalone. The best ideas come when system planners begin to think innovatively andbreak from traditional ways of doing things. Simulation is particularly helpful inthis process in that it encourages thinking in radical new ways.

2.8.3 Evaluating the Solutions

Alternative solutions should be evaluated based on their ability to meet the criteriaestablished for the evaluation. These criteria often include performance goals,cost of implementation, impact on the sociotechnical infrastructure, and consis-tency with organizational strategies. Many of these criteria are difficult to measurein absolute terms, although most design options can be easily assessed in terms ofrelative merit.

After narrowing the list to two or three of the most promising solutions usingcommon sense and rough-cut analysis, more precise evaluation techniques mayneed to be used. This is where simulation and other formal analysis tools comeinto play.

2.8.4 Selecting and Implementing the Best Solution

Often the final selection of what solution to implement is not left to the analyst, butrather is a management decision. The analyst’s role is to present his or her evalua-tion in the clearest way possible so that an informed decision can be made.

Even after a solution is selected, additional modeling and analysis are oftenneeded for fine-tuning the solution. Implementers should then be careful to makesure that the system is implemented as designed, documenting reasons for anymodifications.

2.9 Systems Analysis TechniquesWhile simulation is perhaps the most versatile and powerful systems analysistool, other available techniques also can be useful in systems planning. These al-ternative techniques are usually computational methods that work well for simplesystems with little interdependency and variability. For more complex systems,




these techniques still can provide rough estimates but fall short in producing theinsights and accurate answers that simulation provides. Systems implementedusing these techniques usually require some adjustments after implementation tocompensate for inaccurate calculations. For example, if after implementing a sys-tem it is discovered that the number of resources initially calculated is insufficientto meet processing requirements, additional resources are added. This adjustmentcan create extensive delays and costly modifications if special personnel trainingor custom equipment is involved. As a precautionary measure, a safety factor issometimes added to resource and space calculations to ensure they are adequate.Overdesigning a system, however, also can be costly and wasteful.

As system interdependency and variability increase, not only does systemperformance decrease, but the ability to accurately predict system performancedecreases as well (Lloyd and Melton 1997). Simulation enables a planner to ac-curately predict the expected performance of a system design and ultimately makebetter design decisions.

Systems analysis tools, in addition to simulation, include simple calculations,spreadsheets, operations research techniques (such as linear programming andqueuing theory), and special computerized tools for scheduling, layout, and soforth. While these tools can provide quick and approximate solutions, they tend tomake oversimplifying assumptions, perform only static calculations, and are lim-ited to narrow classes of problems. Additionally, they fail to fully account forinterdependencies and variability of complex systems and therefore are not as ac-curate as simulation in predicting complex system performance (see Figure 2.5).They all lack the power, versatility, and visual appeal of simulation. They do pro-vide quick solutions, however, and for certain situations produce adequate results.They are important to cover here, not only because they sometimes provide agood alternative to simulation, but also because they can complement simulationby providing initial design estimates for input to the simulation model. They also

100%

50%

0%Low HighMedium

System complexity

Withsimulation

Withoutsimulation

Call centersDoctor's officesMachining cells

BanksEmergency roomsProduction lines

AirportsHospitalsFactories

Sys

tem

pre

dic

tab

ility

FIGURE 2.5Simulation improvesperformancepredictability.




can be useful to help validate the results of a simulation by comparing them withresults obtained using an analytic model.

2.9.1 Hand Calculations

Quick-and-dirty, pencil-and-paper sketches and calculations can be remark-ably helpful in understanding basic requirements for a system. Many importantdecisions have been made as the result of sketches drawn and calculations per-formed on a napkin or the back of an envelope. Some decisions may be so basicthat a quick mental calculation yields the needed results. Most of these calcula-tions involve simple algebra, such as finding the number of resource units (such asmachines or service agents) to process a particular workload knowing the capacityper resource unit. For example, if a requirement exists to process 200 items perhour and the processing capacity of a single resource unit is 75 work itemsper hour, three units of the resource, most likely, are going to be needed.

The obvious drawback to hand calculations is the inability to manually per-form complex calculations or to take into account tens or potentially even hun-dreds of complex relationships simultaneously.

2.9.2 Spreadsheets

Spreadsheet software comes in handy when calculations, sometimes involvinghundreds of values, need to be made. Manipulating rows and columns of numberson a computer is much easier than doing it on paper, even with a calculator handy.Spreadsheets can be used to perform rough-cut analysis such as calculatingaverage throughput or estimating machine requirements. The drawback to spread-sheet software is the inability (or, at least, limited ability) to include variability inactivity times, arrival rates, and so on, and to account for the effects of inter-dependencies.

What-if experiments can be run on spreadsheets based on expected values(average customer arrivals, average activity times, mean time between equipmentfailures) and simple interactions (activity A must be performed before activity B).This type of spreadsheet simulation can be very useful for getting rough perfor-mance estimates. For some applications with little variability and component in-teraction, a spreadsheet simulation may be adequate. However, calculations basedon only average values and oversimplified interdependencies potentially can bemisleading and result in poor decisions. As one ProModel user reported, “We justcompleted our final presentation of a simulation project and successfully savedapproximately $600,000. Our management was prepared to purchase an addi-tional overhead crane based on spreadsheet analysis. We subsequently built aProModel simulation that demonstrated an additional crane will not be necessary.The simulation also illustrated some potential problems that were not readily ap-parent with spreadsheet analysis.”

Another weakness of spreadsheet modeling is the fact that all behavior isassumed to be period-driven rather than event-driven. Perhaps you have tried to




figure out how your bank account balance fluctuated during a particular periodwhen all you had to go on was your monthly statements. Using ending balancesdoes not reflect changes as they occurred during the period. You can know the cur-rent state of the system at any point in time only by updating the state variables ofthe system each time an event or transaction occurs. When it comes to dynamicmodels, spreadsheet simulation suffers from the “curse of dimensionality” be-cause the size of the model becomes unmanageable.

2.9.3 Operations Research Techniques

Traditional operations research (OR) techniques utilize mathematical models tosolve problems involving simple to moderately complex relationships. Thesemathematical models include both deterministic models such as mathematicalprogramming, routing, or network flows and probabilistic models such as queuingand decision trees. These OR techniques provide quick, quantitative answerswithout going through the guesswork process of trial and error. OR techniquescan be divided into two general classes: prescriptive and descriptive.

Prescriptive TechniquesPrescriptive OR techniques provide an optimum solution to a problem, such asthe optimum amount of resource capacity to minimize costs, or the optimumproduct mix that will maximize profits. Examples of prescriptive OR optimiza-tion techniques include linear programming and dynamic programming. Thesetechniques are generally applicable when only a single goal is desired for mini-mizing or maximizing some objective function—such as maximizing profits orminimizing costs.

Because optimization techniques are generally limited to optimizing for asingle goal, secondary goals get sacrificed that may also be important. Addition-ally, these techniques do not allow random variables to be defined as input data,thereby forcing the analyst to use average process times and arrival rates that canproduce misleading results. They also usually assume that conditions are constantover the period of study. In contrast, simulation is capable of analyzing muchmore complex relationships and time-varying circumstances. With optimizationcapabilities now provided in simulation, simulation software has even taken on aprescriptive roll.

Descriptive TechniquesDescriptive techniques such as queuing theory are static analysis techniques thatprovide good estimates for basic problems such as determining the expectedaverage number of entities in a queue or the average waiting times for entities ina queuing system. Queuing theory is of particular interest from a simulationperspective because it looks at many of the same system characteristics and issuesthat are addressed in simulation.

Queuing theory is essentially the science of waiting lines (in the UnitedKingdom, people wait in queues rather than lines). A queuing system consists of




Arriving entities Server Departing entitiesQueue

.

..

.

FIGURE 2.6Queuing systemconfiguration.

one or more queues and one or more servers (see Figure 2.6). Entities, referred toin queuing theory as the calling population, enter the queuing system and eitherare immediately served if a server is available or wait in a queue until a server be-comes available. Entities may be serviced using one of several queuing disci-plines: first-in, first-out (FIFO); last-in, first-out (LIFO); priority; and others. Thesystem capacity, or number of entities allowed in the system at any one time, maybe either finite or, as is often the case, infinite. Several different entity queuing be-haviors can be analyzed such as balking (rejecting entry), reneging (abandoningthe queue), or jockeying (switching queues). Different interarrival time distribu-tions (such as constant or exponential) may also be analyzed, coming from eithera finite or infinite population. Service times may also follow one of several distri-butions such as exponential or constant.

Kendall (1953) devised a simple system for classifying queuing systems inthe form A/B/s, where A is the type of interarrival distribution, B is the type ofservice time distribution, and s is the number of servers. Typical distribution typesfor A and B are

M for Markovian or exponential distributionG for a general distributionD for a deterministic or constant value

An M/D/1 queuing system, for example, is a system in which interarrival times areexponentially distributed, service times are constant, and there is a single server.

The arrival rate in a queuing system is usually represented by the Greek letterlambda (λ) and the service rate by the Greek letter mu (µ). The mean interarrivaltime then becomes 1/λ and the mean service time is 1/µ. A traffic intensity factorλ/µ is a parameter used in many of the queuing equations and is represented bythe Greek letter rho (ρ).

Common performance measures of interest in a queuing system are based onsteady-state or long-term expected values and include

L = expected number of entities in the system (number in the queue and inservice)

Lq = expected number of entities in the queue (queue length)




W = expected time in the system (flow time)Wq = expected time in the queue (waiting time)Pn = probability of exactly n customers in the system (n = 0, 1, . . .)

The M/M/1 system with infinite capacity and a FIFO queue discipline is perhapsthe most basic queuing problem and sufficiently conveys the procedure for -analyzing queuing systems and understanding how the analysis is performed. Theequations for calculating the common performance measures in an M/M/1 are

L = ρ

(1 − ρ)= λ

(µ − λ)

Lq = L − ρ = ρ2

(1 − ρ)

W = 1

µ − λ

Wq = λ

µ(µ − λ)

Pn = (1 − ρ)ρn n = 0, 1, . . .

If either the expected number of entities in the system or the expected waitingtime is known, the other can be calculated easily using Little’s law (1961):

L = λW

Little’s law also can be applied to the queue length and waiting time:

Lq = λWq

Example: Suppose customers arrive to use an automatic teller machine (ATM) at aninterarrival time of 3 minutes exponentially distributed and spend an average of2.4 minutes exponentially distributed at the machine. What is the expected number ofcustomers the system and in the queue? What is the expected waiting time for cus-tomers in the system and in the queue?

λ = 20 per hour

µ = 25 per hour

ρ = λ

µ= .8

Solving for L:

L = λ

(µ − λ)

= 20

(25 − 20)

= 20

5= 4




Solving for Lq:

Lq = ρ2

(1 − ρ)

= .82

(1 − .8)

= .64

.2

= 3.2

Solving for W using Little’s formula:

W = L

λ

= 4

20

= .20 hrs

= 12 minutes

Solving for Wq using Little’s formula:

Wq = Lq

λ

= 3.2

20

= .16 hrs

= 9.6 minutes

Descriptive OR techniques such as queuing theory are useful for the mostbasic problems, but as systems become even moderately complex, the problemsget very complicated and quickly become mathematically intractable. In contrast,simulation provides close estimates for even the most complex systems (assum-ing the model is valid). In addition, the statistical output of simulation is notlimited to only one or two metrics but instead provides information on all per-formance measures. Furthermore, while OR techniques give only average per-formance measures, simulation can generate detailed time-series data andhistograms providing a complete picture of performance over time.

2.9.4 Special Computerized Tools

Many special computerized tools have been developed for forecasting, schedul-ing, layout, staffing, and so on. These tools are designed to be used for narrowlyfocused problems and are extremely effective for the kinds of problems they areintended to solve. They are usually based on constant input values and are com-puted using static calculations. The main benefit of special-purpose decision toolsis that they are usually easy to use because they are designed to solve a specifictype of problem.




2.10 SummaryAn understanding of system dynamics is essential to using any tool for planningsystem operations. Manufacturing and service systems consist of interrelatedelements (personnel, equipment, and so forth) that interactively function to pro-duce a specified outcome (an end product, a satisfied customer, and so on).Systems are made up of entities (the objects being processed), resources (the per-sonnel, equipment, and facilities used to process the entities), activities (theprocess steps), and controls (the rules specifying the who, what, where, when, andhow of entity processing).

The two characteristics of systems that make them so difficult to analyze areinterdependencies and variability. Interdependencies cause the behavior of oneelement to affect other elements in the system either directly or indirectly. Vari-ability compounds the effect of interdependencies in the system, making systembehavior nearly impossible to predict without the use of simulation.

The variables of interest in systems analysis are decision, response, and statevariables. Decision variables define how a system works; response variablesindicate how a system performs; and state variables indicate system conditions atspecific points in time. System performance metrics or response variables are gen-erally time, utilization, inventory, quality, or cost related. Improving system per-formance requires the correct manipulation of decision variables. System opti-mization seeks to find the best overall setting of decision variable values thatmaximizes or minimizes a particular response variable value.

Given the complex nature of system elements and the requirement to makegood design decisions in the shortest time possible, it is evident that simulationcan play a vital role in systems planning. Traditional systems analysis techniquesare effective in providing quick but often rough solutions to dynamic systemsproblems. They generally fall short in their ability to deal with the complexity anddynamically changing conditions in manufacturing and service systems. Simula-tion is capable of imitating complex systems of nearly any size and to nearly anylevel of detail. It gives accurate estimates of multiple performance metrics andleads designers toward good design decisions.

2.11 Review Questions1. Why is an understanding of system dynamics important to the use of

simulation?

2. What is a system?

3. What are the elements of a system from a simulation perspective? Givean example of each.

4. What are two characteristics of systems that make them so complex?

5. What is the difference between a decision variable and a response variable?

6. Identify five decision variables of a manufacturing or service systemthat tend to be random.




7. Give two examples of state variables.

8. List three performance metrics that you feel would be important for acomputer assembly line.

9. List three performance metrics you feel would be useful for a hospitalemergency room.

10. Define optimization in terms of decision variables and response variables.

11. Is maximizing resource utilization a good overriding performanceobjective for a manufacturing system? Explain.

12. What is a systems approach to problem solving?

13. How does simulation fit into the overall approach of systems engineering?

14. In what situations would you use analytical techniques (like handcalculations or spreadsheet modeling) over simulation?

15. Assuming you decided to use simulation to determine how many lifttrucks were needed in a distribution center, how might analytical modelsbe used to complement the simulation study both before and after?

16. What advantages does simulation have over traditional OR techniquesused in systems analysis?

17. Students come to a professor’s office to receive help on a homeworkassignment every 10 minutes exponentially distributed. The time to helpa student is exponentially distributed with a mean of 7 minutes. What arethe expected number of students waiting to be helped and the averagetime waiting before being helped? For what percentage of time is itexpected there will be more than two students waiting to be helped?

ReferencesBlanchard, Benjamin S. System Engineering Management. New York: John Wiley & Sons,

1991.Hopp, Wallace J., and M. Spearman. Factory Physics. New York: Irwin/McGraw-Hill,

2000, p. 282.Kendall, D. G. “Stochastic Processes Occurring in the Theory of Queues and Their

Analysis by the Method of Imbedded Markov Chains.” Annals of MathematicalStatistics 24 (1953), pp. 338–54.

Kofman, Fred, and P. Senge. Communities of Commitment: The Heart of LearningOrganizations. Sarita Chawla and John Renesch, (eds.), Portland, OR. ProductivityPress, 1995.

Law, Averill M., and David W. Kelton. Simulation Modeling and Analysis. New York:McGraw-Hill, 2000.

Little, J. D. C. “A Proof for the Queuing Formula: L = λW.” Operations Research 9, no. 3(1961), pp. 383–87.

Lloyd, S., and K. Melton. “Using Statistical Process Control to Obtain More PreciseDistribution Fitting Using Distribution Fitting Software.” Simulators InternationalXIV 29, no. 3 (April 1997), pp. 193–98.

Senge, Peter. The Fifth Discipline. New York: Doubleday, 1990.Simon, Herbert A. Models of Man. New York: John Wiley & Sons, 1957, p. 198.

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