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Rescheduling manufacturing systems: A framework of strategies, policies, and methods
 Journal of Scheduling
, 2003
"... Manymanufacturing facilities generate and update production schedules, which are plans that state when certain controllable activities (e.g., processing of jobs byresources) should take place. Production schedules help managers and supervisors coordinate activities to increase productivityand reduce ..."
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Cited by 80 (5 self)
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Manymanufacturing facilities generate and update production schedules, which are plans that state when certain controllable activities (e.g., processing of jobs byresources) should take place. Production schedules help managers and supervisors coordinate activities to increase productivityand reduce operating costs. Because a manufacturing system is dynamic and unexpected events occur, rescheduling is necessary to update a production schedule when the state of the manufacturing system makes it infeasible. Rescheduling updates an existing production schedule in response to disruptions or other changes. Though manystudies discuss rescheduling, there are no standard definitions or classification of the strategies, policies, and methods presented in the rescheduling literature. This paper presents definitions appropriate for most applications of rescheduling manufacturing systems and describes a framework for understanding rescheduling strategies, policies, and methods. This framework is based on a wide varietyof experimental and practical approaches that have been described in the rescheduling literature. The paper also discusses studies that show how rescheduling affects the performance of a manufacturing system, and it concludes with a discussion of how understanding rescheduling can bring closer some aspects of scheduling theory and practice. KEY WORDS: rescheduling; predictivereactive scheduling; dynamic scheduling 1.
Multiproduct systems with both setup times and costs: Fluid bounds and schedules
 Operations Research
, 2004
"... This paper considers a multiproduct, singleserver production system where both setup times and costs are incurred whenever the server changes product. The system is maketoorder with a per unit backlogging cost. The objective is to minimize the longrun average cost per unit time. Using a fluid m ..."
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Cited by 18 (0 self)
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This paper considers a multiproduct, singleserver production system where both setup times and costs are incurred whenever the server changes product. The system is maketoorder with a per unit backlogging cost. The objective is to minimize the longrun average cost per unit time. Using a fluid model, we provide a closedform lower bound on system performance. This bound is also shown to provide a lower bound for stochastic systems when scheduling is static, but is only an approximation when scheduling is dynamic. Heavytraffic analysis yields a refined bound that includes secondmoment terms. The fluid bound suggests both dynamic and static scheduling In this paper we consider a production environment where a number of different products are produced on a single machine and setup activities are necessary when switches of product type are made. These setup activities require both time and cost that depend on the specific product type. Throughout the paper we assume that the setups do not depend on the previous product produced
EarliestDeadlineFirst Service in HeavyTraffic Acyclic Networks
 Annals of Applied Probability
, 2002
"... This paper presents a heavy traffic analysis of the behavior of multiclass acyclic queueing networks in which the customers have deadlines. We assume the queueing system consists of J stations, and there are K different customer classes. Customers from each class arrive to the network according to ..."
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Cited by 16 (4 self)
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This paper presents a heavy traffic analysis of the behavior of multiclass acyclic queueing networks in which the customers have deadlines. We assume the queueing system consists of J stations, and there are K different customer classes. Customers from each class arrive to the network according to independent renewal processes. The customers from each class are assigned a random deadline drawn from a deadline distribution associated with that class and they move from station to station according to a fixed acyclic route. The customers at a given node are processed according to the earliestdeadlinefirst (EDF) queue discipline. At any time, the customers of each type at each node have a lead time, the time until their deadline lapses. We model these lead times as a random counting measure on the real line. Under heavy traffic conditions and suitable scaling, it is proved that the measurevalued leadtime process converges to a deterministic function of the workload process. A twostation example is worked out in details, and simulation results are presented to illustrate the predictive value of the theory. This work is a generalization of Doytchinov, Lehoczky and Shreve [5], which developed these results for the single queue case.
Duedate scheduling: asymptotic optimality of generalized longest queue and generalized largest delay rules
 Operations Research
, 2003
"... Consider the following duedate scheduling problem in a multiclass, acyclic, singlestation service system: Any class k job arriving at time t must be served by its due date t +Dk. Equivalently, its delay �k must not exceed a given delay or leadtime Dk. In a stochastic system, the constraint �k � D ..."
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Cited by 6 (0 self)
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Consider the following duedate scheduling problem in a multiclass, acyclic, singlestation service system: Any class k job arriving at time t must be served by its due date t +Dk. Equivalently, its delay �k must not exceed a given delay or leadtime Dk. In a stochastic system, the constraint �k � Dk must be interpreted in a probabilistic sense. Regardless of the precise probabilistic formulation, however, the associated optimal control problem is intractable with exact analysis. This article proposes a new formulation which incorporates the constraint through a sequence of convexincreasing delay cost functions. This formulation reduces the intractable optimal scheduling problem into one for which the Generalized c � (Gc�) scheduling rule is known to be asymptotically optimal. The Gc � rule simplifies here to a generalized longest queue (GLQ) or generalized largest delay (GLD) rule, which are defined as follows. Let Nk be the number of class k jobs in system, �k their arrival rate, and ak the age of their oldest job in the system. GLQ and GLD are dynamic priority rules, parameterized by �: GLQ(�) serves FIFO within class and prioritizes the class with highest index �kNk, whereas GLD(�) uses index �k�kak. The argument is presented first intuitively, but is followed by a limit analysis that expresses the cost objective in terms of the maximal duedate violation probability. This proves that GLQ(�∗) and GLD(�∗), where �∗�k = 1/�kDk, asymptotically minimize the probability �k�ns � of maximal duedate violation in heavy traffic. Specifically, they minimize lim inf n→ � Pr�maxk sups∈�0�t � n1/2 � x � for all positive t and Dk x, where �k�s � is the delay of the most recent class k job that arrived before time s. GLQ with appropriate parameter � � also reduces “total variability ” because it asymptotically minimizes a weighted sum of �th delay moments. Properties of GLQ and GLD, including an expression for their asymptotic delay distributions, are presented.
Dynamic Scheduling to Minimize Lost Sales Subject to Setup Costs
, 1998
"... We consider scheduling a shared server in a twoclass, maketostock, closed queueing network. We include server switching costs and lost sales costs (equivalently, server starvation penalties) for lost jobs. If the switching costs are zero, the optimal policy has a monotonic threshold type of sw ..."
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Cited by 5 (2 self)
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We consider scheduling a shared server in a twoclass, maketostock, closed queueing network. We include server switching costs and lost sales costs (equivalently, server starvation penalties) for lost jobs. If the switching costs are zero, the optimal policy has a monotonic threshold type of switching curve provided that the service times are identical. For completely symmetric systems without setups, it is optimal to serve the longer queue. Using simple analytical models as approximations, we derive a heuristic scheduling policy. Numerical results demonstrate the effectiveness of our heuristic, which is typically within 10% of optimal. We also develop and test a heuristic policy for a model in which the shared resource is part of a series network under a CONWIP release policy.
General Dynamic Programming Algorithms Applied To Polling Systems
 COMMUNICATIONS IN STATISTICS: STOCHASTIC MODELS
, 1998
"... We formulate the problem of scheduling a single server in a multiclass queueing system as a Markov decision process under the discounted cost and the average cost criteria. We develop a new implementation of the modified policy iteration (MPI) dynamic programming algorithm to efficiently solve prob ..."
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Cited by 4 (3 self)
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We formulate the problem of scheduling a single server in a multiclass queueing system as a Markov decision process under the discounted cost and the average cost criteria. We develop a new implementation of the modified policy iteration (MPI) dynamic programming algorithm to efficiently solve problems with large state spaces and small action spaces. This implementation has an enhanced policy evaluation (PE) step and an adaptive termination test. To numerically evaluate various solution approaches, we implemented value iteration and forms of modified policy iteration, and we further developed and implemented aggregationdisaggregation based (replacement process decomposition and groupscaling) algorithms appropriate to controlled queueing system models. Tests provide evidence that MPI outperforms the other algorithms for both the discounted cost and the average cost optimal polling problems. In light of the complexity of implementation for the aggregationdisaggregation based algorithm...
Mean value analysis for polling systems in heavy traffic
 In Proceedings of ValueTools, Pisa Article
, 2006
"... In this paper we present a new approach to derive heavytraffic asymptotics for polling models. We consider the classical cyclic polling model with exhaustive service at each queue, and with general servicetime and switchover time distributions, and study its behavior when the load tends to one. F ..."
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Cited by 4 (2 self)
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In this paper we present a new approach to derive heavytraffic asymptotics for polling models. We consider the classical cyclic polling model with exhaustive service at each queue, and with general servicetime and switchover time distributions, and study its behavior when the load tends to one. For this model, we explore the recently proposed mean value analysis (MVA), which takes a new view on the dynamics of the system, and use this view to provide an alternative way to derive closedfrom expressions for the expected asymptotic delay; the expressions were derived earlier in [32], but in a different way. Moreover, the MVAbased approach enables us to derive closedform expressions for the heavytraffic limits of the covariances between the successive visit periods, which are key performance metrics in many application areas. These results, which have not been obtained before, reveal a number of insensitivity properties of the covariances with respect to the system parameters under heavytraffic assumptions, and moreover, lead to simple approximations for the covariances between the successive visit times for stable systems. Numerical examples demonstrate that the approximations are accurate when the load is close enough to one.
Improving Manufacturing System Performance through Rescheduling
, 2001
"... Many production facilities generate and update production schedules. Rescheduling is necessary because the manufacturing system is dynamic and unexpected events occur. This paper discusses rescheduling policies and how they affect the performance of manufacturing systems. The benefits of proper resc ..."
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Many production facilities generate and update production schedules. Rescheduling is necessary because the manufacturing system is dynamic and unexpected events occur. This paper discusses rescheduling policies and how they affect the performance of manufacturing systems. The benefits of proper rescheduling include improved manufacturing system performance with reduced cost due to computational effort (human or computer) and disruptions to existing plans (nervousness). The paper summarizes previous work in this area and also discusses how rescheduling requires methods to solve production scheduling problems. The goal is to help production planners, engineers, and researchers understand the importance of rescheduling and the proper role of production scheduling in dynamic manufacturing systems.
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.
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"... Towards a unifying theory on branchingtype polling systems in heavy traffic R.D. van der Mei ..."
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Towards a unifying theory on branchingtype polling systems in heavy traffic R.D. van der Mei