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Posts Tagged ‘Theory’

Tommy and Angelica have to divide a dozen cookies between themselves. Tommy’s parents have given Angelica the responsibility of choosing how to split them. The catch: if Tommy doesn’t like the offer, he can reject it and leave both children with nothing. How do they rationally work through their situation? This video also serves as a soft introduction to forward introduction–note that we must guess what sort of offers the first player will make and then check to see how the second player will respond.

Product Description
Queueing Theory deals with systems where there is contention for resources, but the demands are only known probabilistically. This book can be considered to be a monograph or a textbook, and thus is aimed at two audiences: those who already know Queueing Theory but would like to know more of the Linear Algebraic Approach; and as a rst course for students who don’t already have a strong background in probability, and feel more comfortable with algebraic arguments. A… More >>

Queueing Theory: A Linear Algebraic Approach

Product Description
High Quality Content by WIKIPEDIA articles! In queueing theory, a queueing model is used to approximate a real queueing situation or system, so the queueing behaviour can be analysed mathematically. Queueing models allow a number of useful steady state performance measures to be determined, including: * the average number in the queue, or the system, * the average time spent in the queue, or the system, * the statistical distribution of those numbers or… More >>

Queing Model: Queueing Theory, Kendall’s Notation, Markov Property, Erlang Distribution, Degenerate Distribution, Phase-Type Distribution, Markov Chain, Stochastic

We Have a Problem!
There was no doubt that improvements were needed at Brown Fintube. No systematic method of planning or scheduling was in place and jobs were accepted without  regard to capacity or loading. Consequently, we were not able to accurately predict shipment dates for contracts and never knew when a job was going to be late until it  was late. Our on-time delivery performance to meet original promise dates was dismal (in the low 40% range). Designs and drawings were too often late getting to the shop  because we were unable to provide Mechanical Engineering and Drafting with real need dates. There was confusion on the shop floor about how to prioritize jobs. In order to  compensate for problems and still attempt to meet ship dates, overtime and intense expediting was necessary. Each month began from scratch. By the end of the month,  the floor was clean and there was no new work in progress.

Because we couldn’t accurately anticipate or account for variation in the process, we were unable to correctly predict revenue or forecast late shipment of jobs for any  current month. We were able to meet customer needs, but only through last minute, heroic efforts by the organization. We realized that, like so many long-time  manufacturers, our order fulfillment process was out of sync. In order to bring our system under control, planning and execution needed improvement. The operations group  proposed implementation of a formal scheduling system using drum-buffer-rope (DBR), a Theory of Constraints (ToC) solution.

We were aware of the Theory of Constraints and thought it held promise, but realized there much was much to do before we could harness it successfully. We decided to  cultivate a clear understanding of the Theory of Constraints among Brown Fintube personnel and develop an effective methodology for applying it.

We were still uncertain on how to apply the Theory of Constraints to our business because most texts on the subject addressed machine shops and our business consists  of fabrication and welding with some assembly. The difference is not trivial; capacity at most machine shops is based on machine availability and our capacity is based on  labor skill availability. We researched whether or not Theory of Constraints – based scheduling software could help our business by discussing it with others who had  implemented it. Each of them confirmed our original thinking – they advised us not to implement the software without first establishing a thorough organizational  understanding of the Theory of Constraints. They also strongly advised us to use DBR manually before moving to the software phase.

We hired a respected theory of constraints consultant and together, we devised a plan for implementation of Drum Buffer Rope scheduling in our fabrication shop.  Our  implementation was not intended to be just a production solution; it was intended to be a complete turnaround for all of Brown Fintube. The goals of the implementation  were to improve on-time delivery to a sustainable level of performance greater than 95%, improve our ability to accurately predict monthly revenue amounts, and provide a  method to predict man-hour loading and capacity requirements.

The Implementation
We set the implementation in motion immediately, focusing the first group of changes where the greatest impact could be achieved. The idea behind the implementation  was to gain control of operations in increments of time. First, a few days were controlled, then a week, then a month. Finally, an implementation of a medium-range sales  and operations planning process that would manage the next several months after that, was established.

We then proceeded to train our employees in Theory of Constraints concepts. Every  shop floor employee was given an introduction, as were engineers, project managers, and key support people. Once training was complete, our shop supervisors were  excited and dedicated to making the implementation a success.

The most significant step towards bringing production under control came with the introduction of a full time scheduler. The scheduler has responsibility for generating the  production schedule, handling day-to-day reconciliation of demand to capacity, promising deliveries and overseeing the components (released and unreleased  manufacturing orders) of schedule execution. Although controversial at the time, by giving responsibility and accountability to a single person, premature release of  materials into the shop was prevented, halting misallocation of capacity and preventing late arrival of components to the constraint. We selected a drum (constraint)  resource and created a workable, daily schedule. This step was significant because the decision making processes for the entire company would now center on this  resource. No capacity, sales, or order delivery decisions would be made, from this point forward, without considering their impact on this resource. To formalize the  decision, procedures and policies were written and people were trained how to apply them. One of the tools created was the “lead time report.” This report from the  scheduler gave Sales a tool to accurately promise customer deliveries.

We then separated normal process variation from unnecessary variation (that had been introduced by lack of plant synchronization). Unwanted fluctuations were  compensated for through the addition of an effective planning and execution management process that included time buffers.

Daily “buffer management” meetings were initiated to synchronize the different departments; paying sharp attention to the constraint and to what orders were shipping – two  of the most important factors in operations. This process ensured that the constraint resource always had at least a one-day queue of parts from which to work, thereby  eliminating month end spikes in shipments and leveling our shipping rates. It also served to smooth out the flow of work in the plant by reducing spikes in capacity load.
On-time delivery performance started improving immediately. Within 90 days, we improved on-time delivery performance from 40% to more than 90%, and since February  2002, we have consistently performed on time at or above 95%. We felt we were better organized as a result of systematically planning business activity.

Our first two goals were fully accomplished and proved to be an unqualified success. Our accuracy in predicting monthly revenue is now very high. Our accuracy in the  area of “available to promise” is close to 100%. Revenue has increased while the number of direct labor employees has declined (through attrition) and it has been  unnecessary to replace them. Over 18 months, our average annual revenue per shop employee increased by $72,000.

Benefits realized inside Brown Fintube include a more responsive shop and shorter lead times. The process analysis, policy and procedure development, and execution  management means that all steps taken now work together to culminate in process improvement. For example, we are now able to determine which orders to pursue  based, not on which will cost the least per unit to make, but on which will yield the greatest profit per minute.

Results
Rather than fighting fires, we are now able to focus on anticipating and preventing tomorrow’s problems as well as planning future growth. Due to our vastly improved  reliability in predicting delivery times, we have also been able to increase the amount of premium-priced business for which we are able to provide “rush” turnaround.

Dramatic results achieved from the time of initial planning through implementation of  our Theory of Constraints scheduling initiative include:
•    Sales growth of 35% ($1.7mm per month to $2.3mm)
•    Inventory turns have increased from two to 10
•    Productivity improvement of $72,000 per employee
•    20% reduction in overtime
•    Consistent 95% or better on-time delivery

We are convinced that our reliability on ship dates gives us a definite competitive edge. As customers become more and more accustomed to our vastly improved service,  we easily win business over competition that is still merely promising.

Product Description
Queueing Theory with Applications to Packet Telecommunication is an efficient introduction to fundamental concepts and principles underlying the behavior of queueing systems and its application to the design of packet-oriented electrical
communication systems. In addition to techniques and approaches found in earlier works, the author presents a thoroughly modern computational approach based on Schur decomposition. This approach facilitates solution of broad clas… More >>

Queueing Theory with Applications to Packet Telecommunication

Product Description
This book explores how developing solutions with heuristic tools offers two major advantages: shortened development time and more robust systems. It begins with an overview of modern heuristic techniques and goes on to cover specific applications of heuristic approaches to power system problems, such as security assessment, optimal power flow, power system scheduling and operational planning, power generation expansion planning, reactive power planning, transmission… More >>

Modern Heuristic Optimization Techniques: Theory and Applications to Power Systems

Why would a suspect admit to committing murder when there’s a lack of evidence against them? Let’s check out the prisoner’s dilemma and find out. www.michaelanuzis.com

The necessary condition for using the theory of a “trick” is that players are to have insufficient information about each other. In this case the “trick” consists in guessing the intentions of the adversary on condition of hiding one’s own intentions: a positive “trick” and a negative “trick”. The tactics of every player is to be very flexible, and one and the same “trick” should not be used for many times, otherwise it will become “tactics” and will revert, like a boomerang, back to its user. The player should strive to modify his game according to the reaction of his adversary by making the most successful choice for this situation: hence comes the probability of probabilities.

Oscar Morgenstern (born in 1902) gave an example of a successful choice in the situation unsuccessful by itself. The example was based on one of the stories about Sherlock Holmes. Being chased by professor Moriarty, he took a train heading from London to Dover through Canterbury. But while getting on the train, he noticed that Moriarty has also taken this train. Holmes knew that if he set off simultaneously with Moriarty, he would certainly be killed. He had to get to Dover alone, in order to embark on the steamer that crossed the channel. This was his objective. The following variants are possible:

a) Holmes gets off in Dover;

b) Holmes gets off in Canterbury;

c) Moriarty gets off in Canterbury;

d) Moriarty gets off in Dover. The outcome, in Holmes’ opinion, can be:

1) complete success: ас

2) partial success: bd

3) failure: ad or bс.

These three outcomes, in the point of view of Holmes’ preferences, sequentially decrease as those worthy of the choice, the last one being the worst. Moriarty’s system of preferences is opposite to that of Holmes. Immediately evident is the difficulty of choice due to lack of information. The decision both for Holmes and Moriarty is the result of a random choice that plays the role of a defensive tactics. Both of them are well-prepared, and both alertly wait for the smallest neglect of the adversary in order to attack at once. But apart from this possible (accidental) mistake, the chance rules the game. Thus we get what G. von Neuman (born in 1903) revealed.

We can mathematically express the game before its beginning by introducing probabilistic preferences of both players: for instance, Pr(a) = p; Pr(b) = l – p Pr(c) = q; Pr(d) = l – q.

Then the probabilities of various outcomes (moves) are calculated with the help of rules of compound possibilities: Рr(ас) = р * q; Pr(bc) = (1 – р) * q;

Pr(ad) = р(1 – q); Pr(bd) = (1 – р) * (1 – q),where Pr(ad or bc) = р(1 – q) + q(1 – р) = p + q – 2pq.

But these probabilities are initially unknown to players. For example, Holmes does not know q, but even if he knew q, his choice would not become less probabilistic. Every player acts, meditating on the possible move of the adversary, and at the moment previous calculations represent the problem well, making an instant estimation of probabilities for p and q.

The practical value of the threshold d, for which the alternative of “success” with probability d and death with probability 1 – d is preferred to ”certain defeat”, depends on the boldness of the famous English detective.

The game theory finds application also in the economic life for strategic calculations. But the problems that arise in this case are quite difficult… © Copyright 2006-2007 www.bonus-map.com

Mathematicians and life scientists say they have identified the signal that the brain sends to the rest of the body to control biological rhythms, a finding that overturns a long-held theory about our internal clock.

View full post on ScienceDaily: Mathematical Modeling News