Scheduling Theory. Single-Stage Systems
Total and Maximal Cost. Ordered Sets of Jobs.
Priority-Generating Functions. Elimination Conditions. Tree-like Order. Series-Parallel Order.
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General Case. Convergence Conditions. Reducibility of the Partition Problem. Reducibility of the 3-Partition Problem. Reducibility of the Vertex Covering Problem. Reducibility of the Clique Problem. Reducibility of the Linear Arrangement Problem. Bibliographic Notes. Approximation Algorithms. Additional References.
Scheduling Theory. Single-Stage Systems : Vyacheslav S. Tanaev :
Du kanske gillar. Permanent Record Edward Snowden Inbunden. Lifespan David Sinclair Inbunden. Scheduling Theory. Spara som favorit. Skickas inom vardagar. Skickas inom vardagar specialorder. Scheduling theory is an important branch of operations research. Problems studied within the framework of that theory have numerous applications in various fields of human activity.
As an independent discipline scheduling theory appeared in the middle of the fifties, and has attracted the attention of researchers in many countries. In the Soviet Union, research in this direction has been mainly related to production scheduling, especially to the development of automated systems for production control.
In Nauka "Science" Publishers, Moscow, issued two books providing systematic descriptions of scheduling theory. The first one was the Russian translation of the classical book Theory of Scheduling by American mathematicians R. The natural extension of Smith's rule is also optimal to the above stochastic model. In general, the rule that assigns higher priority to jobs with shorter expected processing time is optimal for the flowtime objective under the following assumptions: when all the job processing time distributions are exponential;  when all the jobs have a common general processing time distribution with a nondecreasing hazard rate function;  and when job processing time distributions are stochastically ordered.
Multi-armed bandit models form a particular type of optimal resource allocation usually working with time assignment , in which a number of machines or processors are to be allocated to serve a set of competing projects termed as arms. In the typical framework, the system consists of a single machine and a set of stochastically independent projects, which will contribute random rewards continuously or at certain discrete time points, when they are served.
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The objective is to maximize the expected total discounted rewards over all dynamically revisable policies. The first version of multi-bandit problems was formulated in the area of sequential designs by Robbins In this early model, each arm is modeled by a Markov or semi-Markov process in which the time points of making state transitions are decision epochs. The machine can at each epoch pick an arm to serve with a reward represented as a function of the current state of the arm being processed, and the solution is characterized by allocation indices assigned to each state that depends only on the states of the arms.
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These indices are therefore known as Gittins indices and the optimal policies are usually called Gittins index policies, due to his reputable contributions. Soon after the seminal paper of Gittins, the extension to branching bandit problem to model stochastic arrivals also known as the open bandit or arm acquiring bandit problem was investigated by Whittle Models in this class are concerned with the problems of designing optimal service disciplines in queueing systems, where the jobs to be completed arrive at random epochs over time, instead of being available at the start.
The main class of models in this setting is that of multiclass queueing networks MQNs , widely applied as versatile models of computer communications and manufacturing systems. The simplest types of MQNs involve scheduling a number of job classes in a single server.
follow link Similarly as in the two model categories discussed previously, simple priority-index rules have been shown to be optimal for a variety of such models. More general MQN models involve features such as changeover times for changing service from one job class to another Levy and Sidi, ,  or multiple processing stations, which provide service to corresponding nonoverlapping subsets of job classes.
Due to the intractability of such models, researchers have aimed to design relatively simple heuristic policies which achieve a performance close to optimal. However, there are circumstances where the information is only partially available. Examples of scheduling with incomplete information can be found in environmental clean-up,  project management,  petroleum exploration,  sensor scheduling in mobile robots,  and cycle time modeling,  among many others.
As a result of incomplete information, there may be multiple competing distributions to model the random variables of interest. An effective approach is developed by Cai et al. A key concern in decision making is how to utilize the updated information to refine and enhance the decisions.
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When the scheduling policy is static in the sense that it does not change over time, optimal sequences are identified to minimize the expected discounted reward and stochastically minimize the number of tardy jobs under a common exponential due date. From Wikipedia, the free encyclopedia.
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Optimal Stochastic Scheduling. Springer US. In Floudas, C. Encyclopedia of Optimization. US: Springer.
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