Theory of Constraints and Queuing Theory Essay Example

or compelled to avoid or perform some action. Goldratt’s (1990) take on a constraint is that it is anything that limits a system from achieving higher performance verses its goal. As it applies to TOC, Bates (n. d. ) states that a constraint is defined in three ways:

* A process or process step that limits throughput. * Anything that limits a system from achieving higher performance versus its goal. A constraint is a factor that limits the system from getting more of whatever it strives. In order to limit these constraints in today’s rapidly changing environment businesses must understand that to improve means to change (AGI-Goldratt Institute, n. d. ). To make this happen AGI-Goldratt Institute states that for companies to improve means that they must:

* Provide products and services that solve customers’ problems. * Release products and services consistent with market demand. Reduce variability in our processes. * Have measurements that indicate success relative to achieving our goal. * Reward people for their contribution. Rather than reacting to external change, or being subjected to random internal change, many organizations have concluded that a process of on-going improvement is an absolute necessity. Bates (n. d. ) states that the core idea of the Theory of Constraints is that every real system such as a profit-making enterprise must have at least one constraint limiting output.

The major component is the methodology that is known as the TOC Thinking Processes (Cox and Spencer, 1998). This system of thinking processes layout logic trees that provide a roadmap for change. They address the three basic questions of what to change, what to change to,

and how to cause the change (AGI-Goldratt Institute, n. d. ). They help the users navigate a decision making process of problem structuring, identifying the problem, building the solution, identifying barriers to be overcome, and implementing the solution (Goldratt and Cox, 1992).

The trees make recourse to a set of logic rules, called the Categories of Legitimate Reservation (CLR), which set out to check for and correct common flaws in our logic, and provide the analytical rigor usually associated with philosophy or hard scientific approaches (Cox and Spencer, 1998). Business Application Fagan (2009) looked into a Smail Collision Center in Greensburg, Pa and how they have been actively implementing the Theory of Constraints for more than a year. The findings were staggering with regards to the positive impact that was realized throughout company.

Fagan (2009) stated that Smail was able to reduce its cycle times by 64 percent, making them twice as fast as their previous operating model. Their flat rate productivity went from 120 percent to 190 percent. Sales grew by 12. 8 percent and net growth was 36. 7 percent in 2007 and increased by an additional 26 percent in 2008 which resulted in a net increase of 50 percent. With these astounding results digging further into the TOC process becomes a very attractive option for many businesses to explore. Taking a step back, Bates (n. d. ) examines how TOC helps companies.

He states that TOC allows companies to focus improvement efforts where they will have the greatest immediate impact on bottom line as well as providing a reliable process that insists on follow through. AGI-Goldratt Institute (n. d.

) asks the question as to how can any generic solution have such a broad applicability? They answer this question with a powerful analogy: just as the strength of a chain is dictated by its weakest link, the performance of any value-chain is dictated by its constraint. Recognizing this, Bates (n. d. ) lists the five steps in the road map for a business to accomplish this:

* Identify a system’s constraints. Decide to exploit the system’s constraints. * Subordinate everything else to the above decision. * Evaluate/elevate the system’s constraints. * If in the previous steps a constraint has been broken, go back to step 1. That is, find a new constraint. These five steps provide a simple, yet extremely effective way for companies to maximize efficiencies and improve quality. Stepping through the process, Boone (n. d. ) walks through Intel’s use of TOC, how it improved their cycle times, and how it was later implemented throughout other areas of production.

Intel, the world’s largest maker of computer chips, was facing challenges with both the length and variability of order cycle times – from the time the order was dropped to the warehouse until the time it was shipped. This added to overall complexity, made order promising to customers difficult, and increased the time of the promised ship date to customers. The TOC-based analysis identified that one step in the process – the packing operation – was the overall system constraint. Order picking and consolidation steps before the packing operation, and shipment preparation after packing, could all operate at much higher rates per hour.

This meant that the fulfillment system as

a whole could only process as many orders per hour as the packing station no matter how many orders could be picked before packing or processed on the back end. This situation also resulted in picked orders being staged ahead of the packing operating at levels that created complexity and variability - too much “buffer” inventory. This complexity also meant that frequently the constrained packing area operated at lower than its maximum capacity, further limiting total throughout.

Typically, to improve total output/throughput, a company using TOC would seek to improve the processing capability of the constraint (Goldratt and Cox, 1992). However, in Intel’s case that was not really possible. Physical limitations in the distribution area, and no budget to add any sort of automation, meant the packing process throughput would have to stay static for now (Boone, n. d. ). In Intel’s case, the constraint has to be fed consistently – if it isn’t, and the constrained process can’t reach its limit, then total system throughput will be lower. It is important to note that you don’t want too much buffer inventory.

This can clog up the operation, and actually again reduce the output of the constrained process. That was exactly what was happening at Intel. You need to monitor the process and send feedback upstream to pull enough work-in-process (in Intel’s case picked and staged bulk product) to keep the constrained packing operation fully utilized, but not awash in product. Edwards said Intel used several tools to send the demand signals, including low tech but effective tools such as walkie-talkies, as well as electronic signals based on scanning activity by pickers with

Radio Frequency devices.

When the new process was implemented, results were seen almost immediately, and eventually delivered substantial improvements in many areas across eight Intel DCs: * Average order cycle times decreased by 75%. * Variability in cycle times decreased at a similar level. * Total throughput actually increased somewhat, as the constrained packing area was more fully utilized by better buffer management. These improvements were achieved with no investment other than travel costs to facilities. At the beginning, Intel used a three-hour buffer before the packing stations, but over time was able to reduce it to just a one hour planned buffer.

A planned buffer under one hour sometimes led to the packing stations not having work. According to AGI-Goldratt Institute (n. d. ) the TOC process is described in the use of three simple questions: * What to change? * What to change to? * How to cause the change? Bates (n. d. ) states that often times company’s over think the process and how to make it more efficient. By answering these three questions companies are given a simple roadmap to finding the answers to issues that may improve their efficiency and overall performance.

Queueing Theory Queueing theory was born in the early 1900s with the work of A. K. Erlang of the Copenhagen Telephone Company, who derived several important formulas for teletraffic engineering that today bear his name (Cooper, 2000). According to Cooper (2000), the range of applications has grown to include not only telecommunications and computer science, but also manufacturing, air traffic control, military logistics, design of theme parks, and many other areas that involve service systems whose

demands are random. Queueing theory is considered to be one of the standard methodologies (together with linear programming, simulation, etc. of operations research and management science, and is standard fare in academic programs in industrial engineering, manufacturing engineering, etc. , as well as in programs in telecommunications, computer engineering, and computer science (Hirayama, Hong, & Krunz, 2004).

Leonard Kleinrock, which is known as the “father of the internet”, used queuing theory along with his development of mathematical theory of packet networks to create the technology underpinning the internet (Macao Polytechnic Institute, n. . ). There are dozens of books and thousands of papers on queueing theory, and they continue to be published at an ever-increasing rate. But, despite its apparent simplicity (customers arrive, request service, and leave or wait until they get it), the subject is one of some depth and subtlety. A queue is a waiting line, like customers waiting at a supermarket checkout counter. Queueing theory is a mathematical theory of waiting lines (Reilly, Ralston, & Hemmendinger, 2000).

Forming a queue being a social phenomenon, it is beneficial to the society if it can be managed so that both the unit that waits and the one that serves get the most benefit (Hirayama, Hong, & Krunz, 2004). For instance, there was a time when in airline terminals passengers formed separate queues in front of check-in counters (Cooper, 2000). But now we see invariably only one line feeding into several counters. This is because of the realization that a single line policy serves better for the passengers as well as the airline management.

Such a conclusion has come from analyzing the

mode by which a queue is formed and the service is provided. Cooper (2000) states that the analysis is based on building a mathematical model representing the process of arrival of passengers who join the queue, the rules by which they are allowed into service, and the time it takes to serve the passengers. Queueing theory embodies the full gamut of such models covering all perceivable systems which incorporate characteristics of a queue. We identify the unit demanding service, whether it is human or otherwise, as customer (Hirayama, Hong, & Krunz, 2004).

The unit providing service is known as the server. This terminology of customers and servers is used in a generic sense regardless of the nature of the physical context. Hirayama, Hong, & Krunz (2004) provide some examples: * In communication systems, voice or data traffic queue up for lines for transmission. A simple example is the telephone exchange. * In a manufacturing system with several work stations, units completing work in one station wait for access to the next. * Vehicles requiring service wait for their turn in a garage. * Patients arrive at a doctor’s clinic for treatment.

Numerous examples of this type are of everyday occurrence. While analyzing them we can identify some basic elements of the systems (Hirayama, Hong, & Krunz, 2004). The Input process, service mechanism, system capacity, and queue discipline. Hirayama, Hong, & Krunz, (2004) state that during the input process, if the occurrence of arrivals and the offer of service are strictly according to schedule, a queue can be avoided. But in practice this does not happen. In most cases the arrivals are the product

of external factors (Cooper, 2000).

Therefore, the best one can do is to describe the input process in terms of random variables which can represent either the number arriving during a time interval or the time interval between successive arrivals (Reilly, Ralston, & Hemmendinger, 2000). If customers arrive in groups, their size can be a random variable as well. The uncertainties involved in the service mechanism are the number of servers, the number of customers getting served at any time, and the duration and mode of service (Hirayama, Hong, & Krunz, 2004).

Networks of queues consist of more than one servers arranged in series and/or parallel. Random variables are used to represent service times, and the number of servers, when appropriate. If service is provided for customers in groups, their size can also be a random variable. System capacity represents how many customers can wait at a time in a queueing system and is a significant factor for consideration (Hirayama, Hong, & Krunz, 2004).

If the waiting room is large, one can assume that for all practical purposes, it is infinite. But our everyday experience with the telephone systems tells us that the size of the buffer that accommodates our call while waiting to get a free line is important as well (Cooper, 2004). All other factors regarding the rules of conduct of the queue can be pooled under queue discipline (Hirayama, Hong, & Krunz, 2004). One of these is the rule followed by the server in accepting customers for service.

Cooper (2004) states that rules such as “first-come, first-served” (FCFS), “last-come, first-served” (LCFS), and “random selection for service” (RS) are

self-explanatory and are methods of directing queues. In many situations customers in some classes get priority in service over others. There are many other queue disciplines which have been introduced for the efficient operation of computers and communication systems. Also, there are other factors of customer behavior such as balking, reneging, and jockeying that require consideration as well (Reilly, Ralston, & Hemmendinger, 2000).