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Dynamic scheduling of a multiclass make-to-stock queue
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TLDR
This work considers a scheduling problem for a single server queue that can process a variety of different job classes, and the Brownian control problem is solved, and its solution is interpreted in terms of the queueing system to obtain a scheduling policy.Abstract:
Motivated by make-to-stock production systems, we consider a scheduling problem for a single server queue that can process a variety of different job classes. After jobs are processed, they enter a finished goods inventory that services customer demand. The scheduling problem is to dynamically decide which job class, if any, to serve next in order to minimize the long-run expected average cost incurred per unit of time, which includes linear costs which may differ by class for backordering and holding finished goods inventory. Under the heavy traffic condition that the server must be busy the great majority of the time in order to satisfy customer demand, the scheduling problem is approximated by a dynamic control problem involving Brownian motion. The Brownian control problem is solved, and its solution is interpreted in terms of the queueing system to obtain a scheduling policy. A simulation experiment is performed that demonstrates the policy's effectiveness.read more
Citations
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Convergence of Probability Measures
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
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Control Techniques for Complex Networks
TL;DR: The workload model that is the basis of traditional analysis of the single queue becomes a foundation for workload relaxations used in the treatment of complex networks and Lyapunov functions and dynamic programming equations lead to the celebrated MaxWeight policy.
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Optimal Stock Allocation for a Capacitated Supply System
TL;DR: This work considers a capacitated supply system that produces a single item that is demanded by several classes of customers, and shows that the optimal allocation policy has a simple and intuitive structure.
Journal ArticleDOI
Make-to-order, make-to-stock, or delay product differentiation? A common framework for modeling and analysis
Diwakar Gupta,Saif Benjaafar +1 more
TL;DR: In this article, the authors developed models to compute the costs and benefits of delaying differentiation in series production systems when the order lead times are load dependent, and then used these models to gain insights through analytical and numerical comparisons.
Journal ArticleDOI
Optimal Dynamic Scheduling Policy for a Make-To-Stock Production System
TL;DR: It is shown that it is optimal to produce the product with the larger bµ index when it is backordered if the production times are identically distributed and that a base stock policy coupled with a switching curve is optimal for some initial inventory levels.
References
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Book
Convergence of Probability Measures
TL;DR: Weak Convergence in Metric Spaces as discussed by the authors is one of the most common modes of convergence in metric spaces, and it can be seen as a form of weak convergence in metric space.
Journal ArticleDOI
Convergence of Probability Measures
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
Book
Brownian motion and stochastic flow systems
TL;DR: Brownian Motion as discussed by the authors : Brownian Motion is a model of buffered flow, and it can be used to control flow system performance, as shown in Fig. 1 : Optimal Control of Brownain Motion.
Journal ArticleDOI
A Review of Production Scheduling
TL;DR: The intent of this paper is to present a broad classification for various scheduling problems, to review important theoretical developments for these problem classes, and to contrast the currently available theory with the practice of production scheduling.
Journal ArticleDOI
Open Queueing Networks in Heavy Traffic
TL;DR: These limit theorems state that properly normalized sequences of queue length and sojourn time processes converge weakly to a certain diffusion as the network traffic intensity converges to unity.