Misplaced Pages

#524475

58-557: Much of the PMBOK Guide is unique to project management such as critical path method and work breakdown structure (WBS). The PMBOK Guide also overlaps with general management regarding planning, organising, staffing, executing and controlling the operations of an organisation. Other management disciplines which overlap with the PMBOK Guide include financial forecasting , organisational behaviour , management science , budgeting and other planning methods. Earlier versions of

116-595: A binary search algorithm (with cost ⁠ O ( log ⁡ n ) {\displaystyle O(\log n)} ⁠ ) outperforms a sequential search (cost ⁠ O ( n ) {\displaystyle O(n)} ⁠ ) when used for table lookups on sorted lists or arrays. The analysis, and study of algorithms is a discipline of computer science . Algorithms are often studied abstractly, without referencing any specific programming language or implementation. Algorithm analysis resembles other mathematical disciplines as it focuses on

174-580: A computation . Algorithms are used as specifications for performing calculations and data processing . More advanced algorithms can use conditionals to divert the code execution through various routes (referred to as automated decision-making ) and deduce valid inferences (referred to as automated reasoning ). In contrast, a heuristic is an approach to solving problems that do not have well-defined correct or optimal results. For example, although social media recommender systems are commonly called "algorithms", they actually rely on heuristics as there

232-468: A flowchart offers a way to describe and document an algorithm (and a computer program corresponding to it). It has four primary symbols: arrows showing program flow, rectangles (SEQUENCE, GOTO), diamonds (IF-THEN-ELSE), and dots (OR-tie). Sub-structures can "nest" in rectangles, but only if a single exit occurs from the superstructure. It is often important to know how much time, storage, or other cost an algorithm may require. Methods have been developed for

290-494: A step function is more applicable. Originally, the critical path method considered only logical dependencies between terminal elements. Since then, it has been expanded to allow for the inclusion of resources related to each activity, through processes called activity-based resource assignments and resource optimization techniques such as Resource Leveling and Resource smoothing . A resource-leveled schedule may include delays due to resource bottlenecks (i.e., unavailability of

348-680: A computer-executable form, but are also used to define or document algorithms. There are many possible representations and Turing machine programs can be expressed as a sequence of machine tables (see finite-state machine , state-transition table , and control table for more), as flowcharts and drakon-charts (see state diagram for more), as a form of rudimentary machine code or assembly code called "sets of quadruples", and more. Algorithm representations can also be classified into three accepted levels of Turing machine description: high-level description, implementation description, and formal description. A high-level description describes qualities of

406-719: A computing machine or a human who could only carry out specific elementary operations on symbols . Most algorithms are intended to be implemented as computer programs . However, algorithms are also implemented by other means, such as in a biological neural network (for example, the human brain performing arithmetic or an insect looking for food), in an electrical circuit , or a mechanical device. Step-by-step procedures for solving mathematical problems have been recorded since antiquity. This includes in Babylonian mathematics (around 2500 BC), Egyptian mathematics (around 1550 BC), Indian mathematics (around 800 BC and later),

464-414: A critical path is the sequence of project network activities that adds up to the longest overall duration, regardless of whether that longest duration has float or not. This determines the shortest time possible to complete the project. "Total float" (unused time) can occur within the critical path. For example, if a project is testing a solar panel and task 'B' requires 'sunrise', a scheduling constraint on

522-479: A final ending state. The transition from one state to the next is not necessarily deterministic ; some algorithms, known as randomized algorithms , incorporate random input. Around 825 AD, Persian scientist and polymath Muḥammad ibn Mūsā al-Khwārizmī wrote kitāb al-ḥisāb al-hindī ("Book of Indian computation") and kitab al-jam' wa'l-tafriq al-ḥisāb al-hindī ("Addition and subtraction in Indian arithmetic"). In

580-525: A programmer can write structured programs using only these instructions; on the other hand "it is also possible, and not too hard, to write badly structured programs in a structured language". Tausworthe augments the three Böhm-Jacopini canonical structures : SEQUENCE, IF-THEN-ELSE, and WHILE-DO, with two more: DO-WHILE and CASE. An additional benefit of a structured program is that it lends itself to proofs of correctness using mathematical induction . By themselves, algorithms are not usually patentable. In

638-484: A project or its various phases. A Guide to the Project Management Body of Knowledge — Sixth Edition provides guidelines for managing individual projects and defines project management related concepts. It also describes the project management life cycle and its related processes, as well as the project life cycle. and for the first time it includes an "Agile Practice Guide". The PMBOK as described in

SECTION 10

#1732772792525

696-415: A regular basis, CPM allows continuous monitoring of the schedule, which allows the project manager to track the critical activities, and alerts the project manager to the possibility that non-critical activities may be delayed beyond their total float, thus creating a new critical path and delaying project completion. In addition, the method can easily incorporate the concepts of stochastic predictions, using

754-430: A resource at the required time), and may cause a previously shorter path to become the longest or most "resource critical" path while a resource-smoothed schedule avoids impacting the critical path by using only free and total float. A related concept is called the critical chain , which attempts to protect activity and project durations from unforeseen delays due to resource constraints. Since project schedules change on

812-477: A sequence of operations", which would include all computer programs (including programs that do not perform numeric calculations), and any prescribed bureaucratic procedure or cook-book recipe . In general, a program is an algorithm only if it stops eventually —even though infinite loops may sometimes prove desirable. Boolos, Jeffrey & 1974, 1999 define an algorithm to be an explicit set of instructions for determining an output, that can be followed by

870-416: Is a method or mathematical process for problem-solving and engineering algorithms. The design of algorithms is part of many solution theories, such as divide-and-conquer or dynamic programming within operation research . Techniques for designing and implementing algorithm designs are also called algorithm design patterns, with examples including the template method pattern and the decorator pattern. One of

928-581: Is a more specific classification of algorithms; an algorithm for such problems may fall into one or more of the general categories described above as well as into one of the following: One of the simplest algorithms finds the largest number in a list of numbers of random order. Finding the solution requires looking at every number in the list. From this follows a simple algorithm, which can be described in plain English as: High-level description: (Quasi-)formal description: Written in prose but much closer to

986-420: Is a term referring to the shortest possible time for which an activity can be scheduled. It can be achieved by shifting more resources towards the completion of that activity, resulting in decreased time spent and often a reduced quality of work, as the premium is set on speed. Crash duration is typically modeled as a linear relationship between cost and activity duration, but in many cases, a convex function or

1044-419: Is generally recognized as a good practice. 'Generally recognized' means the knowledge and practices described are applicable to most projects most of the time and there is a consensus about their value and usefulness. 'Good practice' means there is a general agreement that the application of the knowledge, skills, tools, and techniques can enhance the chance of success over many projects." This means that sometimes

1102-460: Is no truly "correct" recommendation. As an effective method , an algorithm can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function . Starting from an initial state and initial input (perhaps empty ), the instructions describe a computation that, when executed , proceeds through a finite number of well-defined successive states, eventually producing "output" and terminating at

1160-532: Is not realized precisely, as estimations are used to calculate times: if one mistake is made, the results of the analysis may change. This could cause an upset in the implementation of a project if the estimates are blindly believed, and if changes are not addressed promptly. However, the structure of critical path analysis is such that the variance from the original schedule caused by any change can be measured, and its impact either ameliorated or adjusted for. Indeed, an important element of project postmortem analysis

1218-438: Is the 'as built critical path' (ABCP), which analyzes the specific causes and impacts of changes between the planned schedule and eventual schedule as actually implemented. Algorithm In mathematics and computer science , an algorithm ( / ˈ æ l ɡ ə r ɪ ð əm / ) is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform

SECTION 20

#1732772792525

1276-453: Is useful for uncovering unexpected interactions that affect performance. Benchmarks may be used to compare before/after potential improvements to an algorithm after program optimization. Empirical tests cannot replace formal analysis, though, and are non-trivial to perform fairly. To illustrate the potential improvements possible even in well-established algorithms, a recent significant innovation, relating to FFT algorithms (used heavily in

1334-1107: The Entscheidungsproblem (decision problem) posed by David Hilbert . Later formalizations were framed as attempts to define " effective calculability " or "effective method". Those formalizations included the Gödel – Herbrand – Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church 's lambda calculus of 1936, Emil Post 's Formulation 1 of 1936, and Alan Turing 's Turing machines of 1936–37 and 1939. Algorithms can be expressed in many kinds of notation, including natural languages , pseudocode , flowcharts , drakon-charts , programming languages or control tables (processed by interpreters ). Natural language expressions of algorithms tend to be verbose and ambiguous and are rarely used for complex or technical algorithms. Pseudocode, flowcharts, drakon-charts, and control tables are structured expressions of algorithms that avoid common ambiguities of natural language. Programming languages are primarily for expressing algorithms in

1392-629: The Jacquard loom , a precursor to Hollerith cards (punch cards), and "telephone switching technologies" led to the development of the first computers. By the mid-19th century, the telegraph , the precursor of the telephone, was in use throughout the world. By the late 19th century, the ticker tape ( c.  1870s ) was in use, as were Hollerith cards (c. 1890). Then came the teleprinter ( c.  1910 ) with its punched-paper use of Baudot code on tape. Telephone-switching networks of electromechanical relays were invented in 1835. These led to

1450-687: The PMBOK Guide were recognized as standards by the American National Standards Institute (ANSI) which assigns standards in the United States (ANSI/PMI 99-001-2008) and the Institute of Electrical and Electronics Engineers (IEEE 1490–2011). The evolution of the PMBOK Guide is reflected in editions of the Guide. The PMBOK Guide is intended to be a "subset of the project management body of knowledge" that

1508-466: The critical chain developers and followers (e.g. Eliyahu M. Goldratt and Lawrence P. Leach ), as opposed to critical path method adherents. The PMBOK Guide section on Project Time Management does indicate Critical Chain as an alternative method to Critical Path. A second strand of criticism originates in Lean Construction . This approach emphasises the lack of two way communication in

1566-412: The longest path of planned activities to logical end points or to the end of the project, and the earliest and latest that each activity can start and finish without making the project longer. This process determines which activities are "critical" (i.e., on the longest path) and which have no float/slack or "total float" zero (i.e., can be delayed without making the project longer). In project management,

1624-631: The "latest" project management trends, often promoted by consultants, may not be part of the latest version of The PMBOK Guide . However, the 6th Edition of the PMBOK Guide now includes an "Agile Practice Guide" The PMBOK Guide is process-based, meaning it describes work as being accomplished by processes. This approach is consistent with other management standards such as ISO 9000 and the Software Engineering Institute 's CMMI . Processes overlap and interact throughout

1682-496: The Guide recognizes 49 processes that fall into five basic process groups and ten knowledge areas that are typical of most projects, most of the time. The five process groups are: The ten knowledge areas , each of which contains some or all of the project management processes, are: Each of the ten knowledge areas contains the processes that need to be accomplished within its discipline in order to achieve effective project management. Each of these processes also falls into one of

1740-792: The Ifa Oracle (around 500 BC), Greek mathematics (around 240 BC), and Arabic mathematics (around 800 AD). The earliest evidence of algorithms is found in ancient Mesopotamian mathematics. A Sumerian clay tablet found in Shuruppak near Baghdad and dated to c.  2500 BC describes the earliest division algorithm . During the Hammurabi dynasty c.  1800  – c.  1600 BC , Babylonian clay tablets described algorithms for computing formulas. Algorithms were also used in Babylonian astronomy . Babylonian clay tablets describe and employ algorithmic procedures to compute

1798-506: The PERT and event chain methodology . Currently, there are several software solutions available in industry that use the CPM method of scheduling; see list of project management software . The method currently used by most project management software is based on a manual calculation approach developed by Fondahl of Stanford University. A schedule generated using the critical path techniques often

Project Management Body of Knowledge - Misplaced Pages Continue

1856-472: The PMBOK model and offers an alternative which emphasises a language/action perspective and continual improvement in the planning process. Critical path method The critical path method ( CPM ), or critical path analysis ( CPA ), is an algorithm for scheduling a set of project activities. A critical path is determined by identifying the longest stretch of dependent activities and measuring

1914-533: The United States, a claim consisting solely of simple manipulations of abstract concepts, numbers, or signals does not constitute "processes" (USPTO 2006), so algorithms are not patentable (as in Gottschalk v. Benson ). However practical applications of algorithms are sometimes patentable. For example, in Diamond v. Diehr , the application of a simple feedback algorithm to aid in the curing of synthetic rubber

1972-454: The algorithm itself, ignoring how it is implemented on the Turing machine. An implementation description describes the general manner in which the machine moves its head and stores data in order to carry out the algorithm, but does not give exact states. In the most detail, a formal description gives the exact state table and list of transitions of the Turing machine. The graphical aid called

2030-588: The algorithm's properties, not implementation. Pseudocode is typical for analysis as it is a simple and general representation. Most algorithms are implemented on particular hardware/software platforms and their algorithmic efficiency is tested using real code. The efficiency of a particular algorithm may be insignificant for many "one-off" problems but it may be critical for algorithms designed for fast interactive, commercial or long life scientific usage. Scaling from small n to large n frequently exposes inefficient algorithms that are otherwise benign. Empirical testing

2088-403: The analysis of algorithms to obtain such quantitative answers (estimates); for example, an algorithm that adds up the elements of a list of n numbers would have a time requirement of ⁠ O ( n ) {\displaystyle O(n)} ⁠ , using big O notation . The algorithm only needs to remember two values: the sum of all the elements so far, and its current position in

2146-407: The critical path (and near-critical path activities if desired) as a cascading waterfall that flows from the project's start (or current status date) to the selected logical end point. Although the activity-on-arrow diagram (PERT chart) is still used in a few places, it has generally been superseded by the activity-on-node diagram, where each activity is shown as a box or node and the arrows represent

2204-410: The critical path" (i.e., shortening the durations of critical path activities by adding resources ). Critical path drag analysis has also been used to optimize schedules in processes outside of strict project-oriented contexts, such as to increase manufacturing throughput by using the technique and metrics to identify and alleviate delaying factors and thus reduce assembly lead time. "Crash duration"

2262-694: The developers of the PERT, which was developed at about the same time by Booz Allen Hamilton and the U.S. Navy . The precursors of what came to be known as critical path were developed and put into practice by DuPont between 1940 and 1943 and contributed to the success of the Manhattan Project . Critical path analysis is commonly used with all forms of projects, including construction, aerospace and defense, software development, research projects, product development, engineering, and plant maintenance, among others. Any project with interdependent activities can apply this method of mathematical analysis. CPM

2320-521: The earliest codebreaking algorithm. Bolter credits the invention of the weight-driven clock as "the key invention [of Europe in the Middle Ages ]," specifically the verge escapement mechanism producing the tick and tock of a mechanical clock. "The accurate automatic machine" led immediately to "mechanical automata " in the 13th century and "computational machines"—the difference and analytical engines of Charles Babbage and Ada Lovelace in

2378-523: The early 12th century, Latin translations of said al-Khwarizmi texts involving the Hindu–Arabic numeral system and arithmetic appeared, for example Liber Alghoarismi de practica arismetrice , attributed to John of Seville , and Liber Algorismi de numero Indorum , attributed to Adelard of Bath . Hereby, alghoarismi or algorismi is the Latinization of Al-Khwarizmi's name; the text starts with

Project Management Body of Knowledge - Misplaced Pages Continue

2436-427: The field of image processing), can decrease processing time up to 1,000 times for applications like medical imaging. In general, speed improvements depend on special properties of the problem, which are very common in practical applications. Speedups of this magnitude enable computing devices that make extensive use of image processing (like digital cameras and medical equipment) to consume less power. Algorithm design

2494-476: The five process groups, creating a matrix structure such that every process can be related to one knowledge area and one process group. While the PMBOK Guide is meant to offer a general guide to manage most projects most of the time, there are currently three official extensions: The PMBOK is a widely accepted standard in project management, however there are alternatives to the PMBOK standard, and PMBOK does have its critics. One thrust of critique has come from

2552-450: The input list. If the space required to store the input numbers is not counted, it has a space requirement of ⁠ O ( 1 ) {\displaystyle O(1)} ⁠ , otherwise ⁠ O ( n ) {\displaystyle O(n)} ⁠ is required. Different algorithms may complete the same task with a different set of instructions in less or more time, space, or ' effort ' than others. For example,

2610-490: The invention of the digital adding device by George Stibitz in 1937. While working in Bell Laboratories, he observed the "burdensome" use of mechanical calculators with gears. "He went home one evening in 1937 intending to test his idea... When the tinkering was over, Stibitz had constructed a binary adding device". In 1928, a partial formalization of the modern concept of algorithms began with attempts to solve

2668-416: The logical relationships going from predecessor to successor as shown here in the "Activity-on-node diagram". In this diagram, Activities A, B, C, D, and E comprise the critical or longest path, while Activities F, G, and H are off the critical path with floats of 15 days, 5 days, and 20 days respectively. Whereas activities that are off the critical path have float and are therefore not delaying completion of

2726-429: The mid-19th century. Lovelace designed the first algorithm intended for processing on a computer, Babbage's analytical engine, which is the first device considered a real Turing-complete computer instead of just a calculator . Although a full implementation of Babbage's second device was not realized for decades after her lifetime, Lovelace has been called "history's first programmer". Bell and Newell (1971) write that

2784-627: The most important aspects of algorithm design is resource (run-time, memory usage) efficiency; the big O notation is used to describe e.g., an algorithm's run-time growth as the size of its input increases. Per the Church–Turing thesis , any algorithm can be computed by any Turing complete model. Turing completeness only requires four instruction types—conditional GOTO, unconditional GOTO, assignment, HALT. However, Kemeny and Kurtz observe that, while "undisciplined" use of unconditional GOTOs and conditional IF-THEN GOTOs can result in " spaghetti code ",

2842-479: The overall project. In other words, individual tasks on the critical path prior to the constraint might be able to be delayed without elongating the critical path; this is the total float of that task, but the time added to the project duration by the constraint is actually critical path drag , the amount by which the project's duration is extended by each critical path activity and constraint. A project can have several, parallel, near-critical paths, and some or all of

2900-564: The phrase Dixit Algorismi , or "Thus spoke Al-Khwarizmi". Around 1230, the English word algorism is attested and then by Chaucer in 1391, English adopted the French term. In the 15th century, under the influence of the Greek word ἀριθμός ( arithmos , "number"; cf. "arithmetic"), the Latin word was altered to algorithmus . One informal definition is "a set of rules that precisely defines

2958-505: The project, those on the critical path will usually have critical path drag, i.e., they delay project completion. The drag of a critical path activity can be computed using the following formula: These results, including the drag computations, allow managers to prioritize activities for the effective management of project, and to shorten the planned critical path of a project by pruning critical path activities, by "fast tracking" (i.e., performing more activities in parallel), and/or by "crashing

SECTION 50

#1732772792525

3016-481: The tasks could have free float and/or total float. An additional parallel path through the network with the total durations shorter than the critical path is called a subcritical or noncritical path. Activities on subcritical paths have no drag, as they are not extending the project's duration. CPM analysis tools allow a user to select a logical end point in a project and quickly identify its longest series of dependent activities (its longest path). These tools can display

3074-399: The testing activity could be that it would not start until the scheduled time for sunrise. This might insert dead time (total float) into the schedule on the activities on that path prior to the sunrise due to needing to wait for this event. This path, with the constraint-generated total float, would actually make the path longer, with total float being part of the shortest possible duration for

3132-422: The time required to complete them from start to finish. It is commonly used in conjunction with the program evaluation and review technique (PERT). The CPM is a project-modeling technique developed in the late 1950s by Morgan R. Walker of DuPont and James E. Kelley Jr. of Remington Rand . Kelley and Walker related their memories of the development of CPM in 1989. Kelley attributed the term "critical path" to

3190-675: The time and place of significant astronomical events. Algorithms for arithmetic are also found in ancient Egyptian mathematics , dating back to the Rhind Mathematical Papyrus c.  1550 BC . Algorithms were later used in ancient Hellenistic mathematics . Two examples are the Sieve of Eratosthenes , which was described in the Introduction to Arithmetic by Nicomachus , and the Euclidean algorithm , which

3248-449: Was deemed patentable. The patenting of software is controversial, and there are criticized patents involving algorithms, especially data compression algorithms, such as Unisys 's LZW patent . Additionally, some cryptographic algorithms have export restrictions (see export of cryptography ). Another way of classifying algorithms is by their design methodology or paradigm . Some common paradigms are: For optimization problems there

3306-692: Was first described in Euclid's Elements ( c.  300 BC ). Examples of ancient Indian mathematics included the Shulba Sutras , the Kerala School , and the Brāhmasphuṭasiddhānta . The first cryptographic algorithm for deciphering encrypted code was developed by Al-Kindi , a 9th-century Arab mathematician, in A Manuscript On Deciphering Cryptographic Messages . He gave the first description of cryptanalysis by frequency analysis ,

3364-561: Was used for the first time in 1966 for the major skyscraper development of constructing the former World Trade Center Twin Towers in New York City. Although the original CPM program and approach is no longer used, the term is generally applied to any approach used to analyze a project network logic diagram. The essential technique for using CPM is to construct a model of the project that includes: Using these values, CPM calculates

#524475