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Flow Shop Scheduling
Flow-shop scheduling is an optimization problem in computer science and operations research. It is a variant of optimal job scheduling. In a general job-scheduling problem, we are given ''n'' jobs ''J''1, ''J''2, ..., ''Jn'' of varying processing times, which need to be scheduled on ''m'' machines with varying processing power, while trying to minimize the makespan – the total length of the schedule (that is, when all the jobs have finished processing). In the specific variant known as ''flow-shop scheduling'', each job contains exactly ''m'' operations. The ''i''-th operation of the job must be executed on the ''i''-th machine. No machine can perform more than one operation simultaneously. For each operation of each job, execution time is specified. Flow-shop scheduling is a special case of job-shop scheduling where there is strict order of all operations to be performed on all jobs. Flow-shop scheduling may apply as well to production facilities as to computing de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimization Problem
In mathematics, computer science and economics, an optimization problem is the problem of finding the ''best'' solution from all feasible solutions. Optimization problems can be divided into two categories, depending on whether the variables are continuous or discrete: * An optimization problem with discrete variables is known as a '' discrete optimization'', in which an object such as an integer, permutation or graph must be found from a countable set. * A problem with continuous variables is known as a ''continuous optimization'', in which an optimal value from a continuous function must be found. They can include constrained problems and multimodal problems. Continuous optimization problem The '' standard form'' of a continuous optimization problem is \begin &\underset& & f(x) \\ &\operatorname & &g_i(x) \leq 0, \quad i = 1,\dots,m \\ &&&h_j(x) = 0, \quad j = 1, \dots,p \end where * is the objective function to be minimized over the -variable vector , * are called ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Behnam Malakooti
Behnam Malakooti'' is Professor of Systems Engineering of Department of Electrical Engineering and Computer Science at the (CWRU), OH, USA. He has been affiliated with CWRU since 1982. He is a pioneer researcher in risk, Operations Management, Manufacturing Systems, multiple criteria optimization. He developed artificial neural networks for predicting decision-making behavior for out-of-sample data. He also pioneered the theory of multiple-objective optimization for solving decision making, operations and manufacturing systems, machinability of materials, Artificial Neural Networks, facili ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Job-shop Scheduling
Job-shop scheduling, the job-shop problem (JSP) or job-shop scheduling problem (JSSP) is an optimization problem in computer science and operations research. It is a variant of optimal job scheduling. In a general job scheduling problem, we are given ''n'' jobs ''J''1, ''J''2, ..., ''Jn'' of varying processing times, which need to be scheduled on ''m'' machines with varying processing power, while trying to minimize the makespan – the total length of the schedule (that is, when all the jobs have finished processing). In the specific variant known as ''job-shop scheduling'', each job consists of a set of ''operations'' ''O''1, ''O''2, ..., ''On'' which need to be processed in a specific order (known as ''precedence constraints''). Each operation has a ''specific machine'' that it needs to be processed on and only one operation in a job can be processed at a given time. A common relaxation is the flexible job shop, where each operation can be processed on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Open-shop Scheduling
Open-shop scheduling or open-shop scheduling problem (OSSP) is an optimization problem in computer science and operations research. It is a variant of optimal job scheduling. In a general job-scheduling problem, we are given ''n'' jobs ''J''1, ''J''2, ..., ''Jn'' of varying processing times, which need to be scheduled on ''m'' machines with varying processing power, while trying to minimize the makespan - the total length of the schedule (that is, when all the jobs have finished processing). In the specific variant known as ''open-shop scheduling'', each job consists of a set of ''operations'' ''O''1, ''O''2, ..., ''On'' which need to be processed in an ''arbitrary'' order. The problem was first studied by Teofilo F. Gonzalez and Sartaj Sahni in 1976. In the standard three-field notation for optimal job-scheduling problems, the open-shop variant is denoted by O in the first field. For example, the problem denoted by "O3, p_, C_\max" is a 3-machines job ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Genetic Algorithm
In computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA). Genetic algorithms are commonly used to generate high-quality solutions to optimization and search problems by relying on biologically inspired operators such as mutation, crossover and selection. Some examples of GA applications include optimizing decision trees for better performance, solving sudoku puzzles, hyperparameter optimization, etc. Methodology Optimization problems In a genetic algorithm, a population of candidate solutions (called individuals, creatures, organisms, or phenotypes) to an optimization problem is evolved toward better solutions. Each candidate solution has a set of properties (its chromosomes or genotype) which can be mutated and altered; traditionally, solutions are represented in binary as strings of 0s and 1s, but other encodings are also p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heuristic Algorithm
In mathematical optimization and computer science, heuristic (from Greek εὑρίσκω "I find, discover") is a technique designed for solving a problem more quickly when classic methods are too slow for finding an approximate solution, or when classic methods fail to find any exact solution. This is achieved by trading optimality, completeness, accuracy, or precision for speed. In a way, it can be considered a shortcut. A heuristic function, also simply called a heuristic, is a function that ranks alternatives in search algorithms at each branching step based on available information to decide which branch to follow. For example, it may approximate the exact solution. Definition and motivation The objective of a heuristic is to produce a solution in a reasonable time frame that is good enough for solving the problem at hand. This solution may not be the best of all the solutions to this problem, or it may simply approximate the exact solution. But it is still valuable ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 whil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exact Algorithm
In computer science and operations research, exact algorithms are algorithms that always solve an optimization problem to optimality. Unless P = NP, an exact algorithm for an NP-hard optimization problem cannot run in worst-case polynomial time. There has been extensive research on finding exact algorithms whose running time is exponential with a low base. See also * Approximation-preserving reduction * APX is the class of problems with some constant-factor approximation algorithm * Heuristic algorithm In mathematical optimization and computer science, heuristic (from Greek εὑρίσκω "I find, discover") is a technique designed for solving a problem more quickly when classic methods are too slow for finding an approximate solution, or whe ... * PTAS - a type of approximation algorithm that takes the approximation ratio as a parameter References {{reflist Computational complexity theory Optimization algorithms and methods ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimal Job Scheduling
Optimal job scheduling is a class of optimization problems related to scheduling. The inputs to such problems are a list of ''jobs'' (also called ''processes'' or ''tasks'') and a list of ''machines'' (also called ''processors'' or ''workers''). The required output is a ''schedule'' – an assignment of jobs to machines. The schedule should optimize a certain ''objective function''. In the literature, problems of optimal job scheduling are often called machine scheduling, processor scheduling, multiprocessor scheduling, or just scheduling. There are many different problems of optimal job scheduling, different in the nature of jobs, the nature of machines, the restrictions on the schedule, and the objective function. A convenient notation for optimal scheduling problems was introduced by Ronald Graham, Eugene Lawler, Jan Karel Lenstra and Alexander Rinnooy Kan. It consists of three fields: α, β and γ. Each field may be a comma separated list of words. The α field describes t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (including the design and implementation of hardware and software). Computer science is generally considered an area of academic research and distinct from computer programming. Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and for preventing security vulnerabilities. Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of repositories o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Process (engineering)
In engineering, a process is a series of interrelated tasks that, together, transform inputs into a given output. These tasks may be carried out by people, nature or machines using various resources; an engineering process must be considered in the context of the agents carrying out the tasks and the resource attributes involved.Gilb, p392 Systems engineering normative documents and those related to Maturity Models are typically based on processes, for example, systems engineering processes of the EIA-632 and processes involved in the Capability Maturity Model Integration (CMMI) institutionalization and improvement approach. Constraints imposed on the tasks and resources required to implement them are essential for executing the tasks mentioned. Semiconductor industry Semiconductor process engineers face the unique challenge of transforming raw materials into high-tech devices. Common semiconductor devices include Integrated Circuits (ICs), Light-Emitting Diodes (LEDs), solar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
