Stochastic Scheduling

	Stochastic Scheduling Stochastic scheduling concerns scheduling problems involving random attributes, such as random processing times, random due dates, random weights, and stochastic machine breakdowns. Major applications arise in manufacturing systems, computer systems, communication systems, logistics and transportation, and machine learning, among others. Introduction The objective of the stochastic scheduling problems can be regular objectives such as minimizing the total flowtime, the makespan In operations research Operations research () (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a branch of applied mathematics that deals with the development and application of analytical methods t ..., or the total tardiness cost of missing the due dates; or can be irregular objectives such as minimizing both earliness and tardiness costs of completing the jobs, or the total cost of scheduling tasks under likely arrival of a disastrous event such as a seve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Scheduling A schedule (, ) or a timetable, as a basic time-management tool, consists of a list of times at which possible tasks, events, or actions are intended to take place, or of a sequence of events in the chronological order in which such things are intended to take place. The process of creating a schedule — deciding how to order these tasks and how to commit resources between the variety of possible tasks — is called scheduling,Ofer Zwikael, John Smyrk, ''Project Management for the Creation of Organisational Value'' (2011), p. 196: "The process is called scheduling, the output from which is a timetable of some form". and a person responsible for making a particular schedule may be called a scheduler. Making and following schedules is an ancient human activity. Some scenarios associate this kind of planning with learning life skills. Schedules are necessary, or at least useful, in situations where individuals need to know what time they must be at a specific location to rece ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Makespan In operations research Operations research () (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a branch of applied mathematics that deals with the development and application of analytical methods to improve management and ..., 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. The term commonly appears in the context of scheduling. Example There is a complex project that is composed of several sub-tasks. We would like to assign tasks to workers, such that the project finishes in the shortest possible time. As an example, suppose the "project" is to feed the goats. There are three goats to feed, one child can only feed on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Bayesian Method Bayesian inference ( or ) is a method of statistical inference in which Bayes' theorem is used to calculate a probability of a hypothesis, given prior evidence, and update it as more information becomes available. Fundamentally, Bayesian inference uses a prior distribution to estimate posterior probabilities. Bayesian inference is an important technique in statistics, and especially in mathematical statistics. Bayesian updating is particularly important in the dynamic analysis of a sequence of data. Bayesian inference has found application in a wide range of activities, including science, engineering, philosophy, medicine, sport, and law. In the philosophy of decision theory, Bayesian inference is closely related to subjective probability, often called "Bayesian probability". Introduction to Bayes' rule Formal explanation Bayesian inference derives the posterior probability as a consequence of two antecedents: a prior probability and a "likelihood function" derived from ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Gittins Index The Gittins index is a measure of the reward that can be achieved through a given stochastic process with certain properties, namely: the process has an ultimate termination state and evolves with an option, at each intermediate state, of terminating. Upon terminating at a given state, the reward achieved is the sum of the probabilistic expected rewards associated with every state from the actual terminating state to the ultimate terminal state, inclusive. The index is a real scalar. Terminology To illustrate the theory we can take two examples from a developing sector, such as from electricity generating technologies: wind power and wave power. If we are presented with the two technologies when they are both proposed as ideas we cannot say which will be better in the long run as we have no data, as yet, to base our judgments on. It would be easy to say that wave power would be too problematic to develop as it seems easier to put up many wind turbines than to make the long floating ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]