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Setting basestock levels in multiproduct systems with setups and random yield (Working paper, Olin School of Business
, 2004
"... This paper shows how to set basestock levels in a multiproduct system with setups and random yield. The system is represented by a polling model and the inventory level of each product is controlled using a basestock policy. When the queue is empty, the inventory level is equal to the basestock leve ..."
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This paper shows how to set basestock levels in a multiproduct system with setups and random yield. The system is represented by a polling model and the inventory level of each product is controlled using a basestock policy. When the queue is empty, the inventory level is equal to the basestock level, thus the server will continue to serve the queue until it is empty. If the capacity of the queue is equal to the inventory allocated to the item, then when the queue is full, inventory is fully depleted and new demand is either backlogged, lost or expedited. Defects are routed to temporary storage queues associated with each item, and then routed back to the original queue for service during the next cycle. For a system with backlogging, we provide a cost function that is minimized by solving N single item newsvendor problems. For a system with lost sales or expediting, we introduce a cost function and provide a heuristic for finding the basestock levels. The effectiveness of the heuristic and accuracy of the cost approximation are validated through numerical tests.
PRECONDITIONING FOR STOCHASTIC AUTOMATA NETWORKS
, 2002
"... Many very large Markov chains can be modeled efficiently as Stochastic Automata Networks (SANs). A SAN is composed of individual automata that, for the most part, act independently, requiring only infrequent interaction. SANs represent the generator matrix Q of the underlying Markov chain compactly ..."
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Many very large Markov chains can be modeled efficiently as Stochastic Automata Networks (SANs). A SAN is composed of individual automata that, for the most part, act independently, requiring only infrequent interaction. SANs represent the generator matrix Q of the underlying Markov chain compactly as the sum of Kronecker products of smaller matrices. Thus, storage savings are immediate. The benefit of a SAN’s compact representation, known as the descriptor, is often outweighed by its tendency to make analysis of the underlying Markov chain tough. Although iterative or projection methods have been used to solve the system πQ = 0, the convergence to the stationary solution π is still unsatisfactory. SAN’s compact representation has made the next logical research step of preconditioning thorny. Several preconditioners for SANs have been proposed and tested, yet each has enjoyed little or no success. Encouraged by the recent success of approximate inverses as preconditioners, we have explored their potential as SAN preconditioners. One promising finding on approximate inverse preconditioner is the nearest Kronecker product (NKP) approximation introduced by Pitsianis and Van Loan [46]. In this dissertation, we approximate Q by the nearest Kronecker product for a SAN with a Kronecker product, A1 ⊗ A2 ⊗ ·· · ⊗ AN. Then, we take M = A −1 1 ⊗ A−1
Testing the nearest Kronecker product preconditioner on Markov chains and stochastic automata networks
 Informs Journal on Computing
"... informs ® doi 10.1287/ijoc.1030.0041 © 2004 INFORMS This paper is the experimental followup to Langville and Stewart (2002), where the theoretical background for the nearest Kronecker product (NKP) preconditioner was developed. Here we test the NKP preconditioner on both Markov chains (MCs) and sto ..."
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informs ® doi 10.1287/ijoc.1030.0041 © 2004 INFORMS This paper is the experimental followup to Langville and Stewart (2002), where the theoretical background for the nearest Kronecker product (NKP) preconditioner was developed. Here we test the NKP preconditioner on both Markov chains (MCs) and stochastic automata networks (SANs). We conclude that the NKP preconditioner is not appropriate for general MCs, but is very effective for a MC stored as a SAN.
Simulation Optimization for the Stochastic Economic Lot Scheduling Problem with SequenceDependent Setup Times
"... We consider the stochastic economic lot scheduling problem (SELSP) with lost sales and random demand, where switching between products is subject to sequencedependent setup times. We propose a solution based on simulation optimization using an iterative twostep procedure which combines global poli ..."
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We consider the stochastic economic lot scheduling problem (SELSP) with lost sales and random demand, where switching between products is subject to sequencedependent setup times. We propose a solution based on simulation optimization using an iterative twostep procedure which combines global policy search with local search heuristics for the traveling salesman sequencing subproblem. To optimize the production cycle, we compare two criteria: minimizing total setup times and evenly distributing setups to obtain a more regular production cycle. Based on a numerical study, we find that a policy with a balanced production cycle outperforms other policies with unbalanced cycles.
Autonomous Solution Methods for Large Markov Chains
"... One of the roadblocks to greater application of Markov chains is that nonnumerically sophisticated users possess the detailed domain knowledge needed to construct a large Markov chain but may have a difficult time deciding which numerical solution method might be best suited to their applications. ..."
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One of the roadblocks to greater application of Markov chains is that nonnumerically sophisticated users possess the detailed domain knowledge needed to construct a large Markov chain but may have a difficult time deciding which numerical solution method might be best suited to their applications. A realistic Markov chain model can easily contain hundreds of thousands of states, yet users may severely restrict their models to keep them small enough to fit within the constraints of certain software packages or solution methods. By making judgments about the Markov chain, an experienced researcher or practitioner can sometimes propose a solution technique in a short amount of time. This research examines methods to obtain a proposed solution technique without the services of an expert and with little or no intervention from the novice user. We take advantage of information readily available in the Markov chain to aid in the selection and execution of a solution method. This can be done without the user being an expert in the various solution techniques and their respective areas of applicability.
Autonomous Solution Methods for LargeScale Markov Chains
"... 1 Introduction Since their introduction in the early 1900s, Markov chains have been proposed as a means of modeling a variety of stochastic processes, including weather forecasting, voting patterns, and demographic trends. Markov chains have even been suggested as a model to predict and guide usage ..."
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1 Introduction Since their introduction in the early 1900s, Markov chains have been proposed as a means of modeling a variety of stochastic processes, including weather forecasting, voting patterns, and demographic trends. Markov chains have even been suggested as a model to predict and guide usage of the World Wide Web [13]. In his book, Modeling and Analysis of Stochastic Systems [10], Kulkarni provides some details on how applications in genetics, sociology, manpower planning, and telecommunications could be modeled as Markov chains. In most scenarios, the models are kept very small, usually less than several hundred states, in order to be kept tractable. Only in the areas of telecommunications and computer systems performance modeling have larger models been used successfully, and this because of the detailed knowledge of numerical solution algorithms possessed by the researchers working in these areas.
A System Dynamics Model for a SingleStage MultiProduct Kanban Production System
"... Abstract: The actual socioeconomic dynamics and the aggressive competition on a global scale lead companies to frequent revision of their organizational structure, strategic objectives and decisionmaking processes. Organizations need, therefore, some methods that can provide for an innovative appr ..."
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Abstract: The actual socioeconomic dynamics and the aggressive competition on a global scale lead companies to frequent revision of their organizational structure, strategic objectives and decisionmaking processes. Organizations need, therefore, some methods that can provide for an innovative approach to their investigations to business problems. Even if the publishing storm around JIT may have subsided to a certain degree in recent years and many analytical methods have been published for its analysis, most of the academic papers concerning pull production suggest Discrete Event Simulation (DES) for systems management. Only little attention has been paid to System Dynamics (SD) applications. In this paper a SD model for a SingleStage MultiProduct Kanban system will be proposed and tested under different demand patterns.
Applications of polling systems M.A.A. Boon∗
, 2011
"... Since the first paper on polling systems, written by Mack in 1957, a huge number of papers on this topic has been written. A typical polling system consists of a number of queues, attended by a single server. In several surveys, the most notable ones written by Takagi, detailed and comprehensive des ..."
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Since the first paper on polling systems, written by Mack in 1957, a huge number of papers on this topic has been written. A typical polling system consists of a number of queues, attended by a single server. In several surveys, the most notable ones written by Takagi, detailed and comprehensive descriptions of the mathematical analysis of polling systems are provided. The goal of the present survey paper is to complement these papers by putting the emphasis on applications of polling models. We discuss not only the capabilities, but also the limitations of polling models in representing various applications. The present survey is directed at both academicians and practitioners.
SCHEDULING POLICIES IN MULTIPRODUCT MANUFACTURING SYSTEMS WITH SEQUENCEDEPENDENT SETUP TIMES
"... Multiproduct production systems with sequencedependent setup times are typical in manufacturing of semiconductor chips and other electronic products. In such systems, the scheduling policies to coordinate the production of multiple product types play an important role. In this paper, we study a mu ..."
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Multiproduct production systems with sequencedependent setup times are typical in manufacturing of semiconductor chips and other electronic products. In such systems, the scheduling policies to coordinate the production of multiple product types play an important role. In this paper, we study a multiproduct manufacturing system with finite buffers, sequencedependent setup times and various scheduling policies. Using continuous time Markov chain models, we evaluate the performance of such systems under seven scheduling policies, i.e., cyclic, shortest queue, shortest processing time, shortest overall time (including setup time and processing time), longest queue, longest processing time, and longest overall time. The impact of these policies on system throughput are compared, and the conditions characterizing the superiority of each policy are investigated. The results of this work can provide production engineers and supervisors practical guidance to operate multiproduct manufacturing systems with sequencedependent setups. 1
Autonomous Solution Methods for LargeScale Markov Chains
"... One of the roadblocks to greater application of Markov chains is that nonnumerically sophisticated users possess the detailed domain knowledge needed to construct a large Markov chain but may have a difficult time deciding which numerical solution method might be best suited to their applications. ..."
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One of the roadblocks to greater application of Markov chains is that nonnumerically sophisticated users possess the detailed domain knowledge needed to construct a large Markov chain but may have a difficult time deciding which numerical solution method might be best suited to their applications. A realistic Markov chain model can easily contain hundreds of thousands of states, yet users may severely restrict their models to keep them small enough to fit within the constraints of certain software packages or solution methods. Even after selecting a solution method, implementation details imposed by compact storage schemes and the nature of the solution method itself may pose additional barriers. By making judgments about the Markov chain, an experienced researcher or practitioner can sometimes propose a solution technique in a short amount of time. This research examines methods to obtain a proposed solution technique without the services of an expert and with little or no intervention from the novice user. We take advantage of information readily available in the Markov chain to aid in the selection and execution of a solution method. We test a computer tool with a graphical user interface (GUI) and embedded expert system to make largescale Markov chain analysis more accessible. The computer tool receives a user’s Markov chain, examines the chain, determines its primary characteristics, and then gives the user useful information and recommendations about how to analyze the model. This can be done without the user being an expert in the various solution techniques and their respective areas of applicability. 1.