Shifting Bottleneck Heuristic
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Shifting Bottleneck Heuristic
The Shifting Bottleneck Heuristic is a procedure intended to minimize the time it takes to do work, or specifically, the makespan in a job shop. The makespan is defined as the amount of time, from start to finish, to complete a set of multi-machine jobs where machine order is pre-set for each job. Assuming that the jobs are actually competing for the same resources (machines) then there will always be one or more resources that act as a 'wikt:bottleneck, bottleneck' in the processing. This heuristic, or 'rule of thumb' procedure minimises the effect of the bottleneck. The Shifting Bottleneck (engineering), Bottleneck Heuristic is intended for job shops with a finite number of jobs and a finite number of machines. Uses The Shifting Bottleneck (engineering), Bottleneck Heuristic is used in manufacturing and service industries that include job shops with constraints on the order that the machines must be used for each job. A good example of a service industry that may use this techniq ...
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Job Shop
Job shops are typically small manufacturing systems that handle job production, that is, custom/bespoke or semi-custom/bespoke manufacturing processes such as small to medium-size customer orders or batch jobs. Job shops typically move on to different jobs (possibly with different customers) when each job is completed. Job shops machines are aggregated in shops by the nature of skills and technological processes involved, each shop therefore may contain different machines, which gives this production system processing flexibility, since jobs are not necessarily constrained to a single machine. In computer science the problem of job shop scheduling is considered strongly NP-hard. A typical example would be a machine shop, which may make parts for local industrial machinery, farm machinery and implements, boats and ships, or even batches of specialized components for the aircraft industry. Other types of common job shops are grinding, honing, jig-boring, gear manufacturing, ...
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Program Evaluation And Review Technique
The program evaluation and review technique (PERT) is a statistical tool used in project management, which was designed to analyze and represent the tasks involved in completing a given project. First developed by the United States Navy in 1958, it is commonly used in conjunction with the critical path method (CPM) that was introduced in 1957. Overview PERT is a method of analyzing the tasks involved in completing a given project, especially the time needed to complete each task, and to identify the minimum time needed to complete the total project. It incorporates uncertainty by making it possible to schedule a project while not knowing precisely the details and durations of all the activities. It is more of an event-oriented technique rather than start- and completion-oriented, and is used more in those projects where time is the major factor rather than cost. It is applied on very large-scale, one-time, complex, non-routine infrastructure and on Research and Developmen ...
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Iteration2
Iteration is the repetition of a process in order to generate a (possibly unbounded) sequence of outcomes. Each repetition of the process is a single iteration, and the outcome of each iteration is then the starting point of the next iteration. In mathematics and computer science, iteration (along with the related technique of recursion) is a standard element of algorithms. Mathematics In mathematics, iteration may refer to the process of iterated function, iterating a function, i.e. applying a function repeatedly, using the output from one iteration as the input to the next. Iteration of apparently simple functions can produce complex behaviors and difficult problems – for examples, see the Collatz conjecture and juggler sequences. Another use of iteration in mathematics is in iterative methods which are used to produce approximate numerical solutions to certain mathematical problems. Newton's method is an example of an iterative method. Manual calculation of a number's s ...
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Single-machine Scheduling
Single-machine scheduling or single-resource scheduling is an optimization problem in computer science and Operations Research, operations research. We are given ''n'' jobs ''J''1, ''J''2, ..., ''Jn'' of varying processing times, which need to be scheduled on a single machine, in a way that optimizes a certain objective, such as the throughput. Single-machine scheduling is a special case of identical-machines scheduling, which is itself a special case of optimal job scheduling. Many problems, which are NP-hard in general, can be solved in polynomial time in the single-machine case. In the standard Optimal job scheduling, three-field notation for optimal job scheduling problems, the single-machine variant is denoted by 1 in the first field. For example, " 1, , \sum C_j" is an single-machine scheduling problem with no constraints, where the goal is to minimize the sum of completion times. The makespan-minimization problem 1, , C_, which is a common objective with multiple machines, ...
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Branch And Bound
Branch and bound (BB, B&B, or BnB) is an algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical optimization. A branch-and-bound algorithm consists of a systematic enumeration of candidate solutions by means of state space search: the set of candidate solutions is thought of as forming a rooted tree with the full set at the root. The algorithm explores ''branches'' of this tree, which represent subsets of the solution set. Before enumerating the candidate solutions of a branch, the branch is checked against upper and lower estimated ''bounds'' on the optimal solution, and is discarded if it cannot produce a better solution than the best one found so far by the algorithm. The algorithm depends on efficient estimation of the lower and upper bounds of regions/branches of the search space. If no bounds are available, the algorithm degenerates to an exhaustive search. The method was first proposed by Ailsa Land and Alison Doig whilst ...
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Graph (discrete Mathematics)
In discrete mathematics, and more specifically in graph theory, a graph is a structure amounting to a Set (mathematics), set of objects in which some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called ''Vertex (graph theory), vertices'' (also called ''nodes'' or ''points'') and each of the related pairs of vertices is called an ''edge'' (also called ''link'' or ''line''). Typically, a graph is depicted in diagrammatic form as a set of dots or circles for the vertices, joined by lines or curves for the edges. Graphs are one of the objects of study in discrete mathematics. The edges may be directed or undirected. For example, if the vertices represent people at a party, and there is an edge between two people if they shake hands, then this graph is undirected because any person ''A'' can shake hands with a person ''B'' only if ''B'' also shakes hands with ''A''. In contrast, if an edge from a person ''A'' to a person ''B'' m ...
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Bottleneck
Bottleneck literally refers to the narrowed portion (neck) of a bottle A bottle is a narrow-necked container made of an impermeable material (such as glass, plastic or aluminium) in various shapes and sizes that stores and transports liquids. Its mouth, at the bottling line, can be sealed with an internal stopp ... near its opening, which limit the volumetric flow rate, rate of outflow, and may describe any object of a similar shape. The literal neck of a bottle was originally used to play what is now known as slide guitar. Metaphorically, the term may also be used as an analogy for any of the following implications of rate limitation or function restriction: Computing * Bottleneck (network), in communication networks using max-min fairness * Bottleneck (software), a software component that severely affects application performance * Internet bottleneck, when high usage slows the performance on the Internet at a particular point * Von Neumann architecture#Von Neumann bottl ...
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