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Notation For Theoretic Scheduling Problems
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 the ... [...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 ine ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform-machines Scheduling
Uniform machine scheduling (also called uniformly-related machine scheduling or related machine scheduling) is an optimization problem in computer science and operations research. It is a variant of optimal job scheduling. We are given ''n'' jobs ''J''1, ''J''2, ..., ''Jn'' of varying processing times, which need to be scheduled on ''m'' different machines. The goal is to minimize the makespan - the total time required to execute the schedule. The time that machine ''i'' needs in order to process job j is denoted by ''pi,j''. In the general case, the times ''pi,j'' are unrelated, and any matrix of positive processing times is possible. In the specific variant called ''uniform machine scheduling'', some machines are ''uniformly'' faster than others. This means that, for each machine ''i'', there is a speed factor ''si'', and the run-time of job ''j'' on machine ''i'' is ''pi,j'' = ''pj'' / ''si''. In the standard three-field notation for optimal job scheduling problems, the uniform-m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multi-objective Optimization
Multi-objective optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, multiattribute optimization or Pareto optimization) is an area of multiple criteria decision making that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously. Multi-objective optimization has been applied in many fields of science, including engineering, economics and logistics where optimal decisions need to be taken in the presence of trade-offs between two or more conflicting objectives. Minimizing cost while maximizing comfort while buying a car, and maximizing performance whilst minimizing fuel consumption and emission of pollutants of a vehicle are examples of multi-objective optimization problems involving two and three objectives, respectively. In practical problems, there can be more than three objectives. For a nontrivial multi-objective optimization problem, no single solutio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Earliness (scheduling)
In scheduling, tardiness is a measure of a delay in executing certain operations and earliness is a measure of finishing operations before due time. The operations may depend on each other and on the availability of equipment to perform them. Typical examples include job scheduling in manufacturing and data delivery scheduling in data processing networks. In manufacturing environment, inventory management considers both tardiness and earliness undesirable. Tardiness involves backlog issues such as customer compensation for delays and loss of goodwill. Earliness incurs expenses for storage of the manufactured items and ties up capital. Mathematical formulations In an environment with multiple jobs, let the deadline be d_i and the completion time be C_i of job i. Then for job i * lateness is L_i=C_i-d_i, * earliness is E_i = \max(0, d_i-C_i), * tardiness is T_i = \max(0, C_i-d_i). In scheduling common objective functions are C_\max, L_\max, E_\max, T_\max, \sum C_i, \sum L_i, \s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tardiness (scheduling)
In scheduling, tardiness is a measure of a delay in executing certain operations and earliness is a measure of finishing operations before due time. The operations may depend on each other and on the availability of equipment to perform them. Typical examples include job scheduling in manufacturing and data delivery scheduling in data processing networks. In manufacturing environment, inventory management considers both tardiness and earliness undesirable. Tardiness involves backlog issues such as customer compensation for delays and loss of goodwill. Earliness incurs expenses for storage of the manufactured items and ties up capital. Mathematical formulations In an environment with multiple jobs, let the deadline be d_i and the completion time be C_i of job i. Then for job i * lateness is L_i=C_i-d_i, * earliness is E_i = \max(0, d_i-C_i), * tardiness is T_i = \max(0, C_i-d_i). In scheduling common objective functions are C_\max, L_\max, E_\max, T_\max, \sum C_i, \sum L_i, \s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Throughput
Network throughput (or just throughput, when in context) refers to the rate of message delivery over a communication channel, such as Ethernet or packet radio, in a communication network. The data that these messages contain may be delivered over physical or logical links, or through network nodes. Throughput is usually measured in bits per second (bit/s or bps), and sometimes in data packets per second (p/s or pps) or data packets per time slot. The system throughput or aggregate throughput is the sum of the data rates that are delivered to all terminals in a network. Throughput is essentially synonymous to digital bandwidth consumption; it can be determined numerically by applying the queueing theory, where the load in packets per time unit is denoted as the arrival rate (), and the drop in packets per unit time is denoted as the departure rate (). The throughput of a communication system may be affected by various factors, including the limitations of the underlying analog ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lateness (scheduling)
In scheduling (other), scheduling, tardiness is a measure of a delay in executing certain operations and earliness is a measure of finishing operations before due time. The operations may depend on each other and on the availability of equipment to perform them. Typical examples include Scheduling (production processes), job scheduling in manufacturing and data delivery scheduling in data processing networks. In manufacturing environment, inventory management considers both tardiness and earliness undesirable. Tardiness involves backlog issues such as customer compensation for delays and loss of goodwill. Earliness incurs expenses for storage of the manufactured items and ties up capital. Mathematical formulations In an environment with multiple jobs, let the deadline be d_i and the completion time be C_i of job i. Then for job i * lateness is L_i=C_i-d_i, * earliness is E_i = \max(0, d_i-C_i), * tardiness is T_i = \max(0, C_i-d_i). In scheduling common objective funct ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Makespan
In operations research, the makespan of a project is the length of time that elapses from the start of work to the end. This type of multi-mode resource constrained project scheduling problem (MRCPSP) seeks to create the shortest logical project schedule, by efficiently using project resources, adding the lowest number of additional resources as possible to achieve the minimum makespan. ', Afshar-Nadjafi, B, ''in Applied Computing and Informatics (2014) The term commonly appears in the context of |
Parallel Task Scheduling
Parallel task scheduling (also called parallel job scheduling or parallel processing 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 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 ''parallel-task scheduling'', all machines are identical. Each job ''j'' has a ''length'' parameter ''pj'' and a ''size'' parameter ''q''j, and it must run for exactly ''pj'' time-steps on exactly ''q''j machines in ''parallel''. Veltman et al. and Drozdowski denote this problem by P, size_j, C_ in the three-field notation introduced by Graham et al. P means that there are several identical machines running in parallel; ''sizej'' means tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Competitive Analysis (online Algorithm)
Competitive analysis is a method invented for analyzing online algorithms, in which the performance of an online algorithm (which must satisfy an unpredictable sequence of requests, completing each request without being able to see the future) is compared to the performance of an optimal ''offline algorithm'' that can view the sequence of requests in advance. An algorithm is ''competitive'' if its ''competitive ratio''—the ratio between its performance and the offline algorithm's performance—is bounded. Unlike traditional worst-case analysis, where the performance of an algorithm is measured only for "hard" inputs, competitive analysis requires that an algorithm perform well both on hard and easy inputs, where "hard" and "easy" are defined by the performance of the optimal offline algorithm. For many algorithms, performance is dependent not only on the size of the inputs, but also on their values. For example, sorting an array of elements varies in difficulty depending on the ... [...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] |
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] |
