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17
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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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
The stochastic economic lot scheduling problem: heavy traffic analysis of dynamic cyclic policies
, 2000
"... We consider two queueing control problems that are stochastic versions of the economic lot scheduling problem: A single server processes N customer classes, and completed units enter a finished goods inventory that services exogenous customer demand. Unsatisfied demand is backordered, and each class ..."
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Cited by 13 (2 self)
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We consider two queueing control problems that are stochastic versions of the economic lot scheduling problem: A single server processes N customer classes, and completed units enter a finished goods inventory that services exogenous customer demand. Unsatisfied demand is backordered, and each class has its own general service time distribution, renewal demand process, and holding and backordering cost rates. In the first problem, a setup cost is incurred when the server switches class, and the setup cost is replaced by a setup time in the second problem. In both problems we employ a longrun average cost criterion and restrict ourselves to a class of dynamic cyclic policies, where idle periods and lot sizes are statedependent, but the N classes must be served in a fixed sequence. Motivated by existing heavy traffic limit theorems, we make a time scale decomposition assumption that allows us to approximate these scheduling problems by diffusion control problems. Our analysis of the approximating setup cost problem yields a closedform dynamic lotsizing policy and a computational procedure for an idling threshold. We derive structural results and an algorithmic procedure for the setup time problem. A computational study compares the proposed policy and several alternative policies to the numerically computed optimal policy.
Iterative approximation of klimited polling systems
, 2006
"... The present paper deals with the problem of calculating queue length distributions in a polling model with (exhaustive) klimited service under the assumption of general arrival, service and setup distributions. The interest for this model is fueled by an application in the field of logistics. Knowl ..."
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Cited by 9 (0 self)
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The present paper deals with the problem of calculating queue length distributions in a polling model with (exhaustive) klimited service under the assumption of general arrival, service and setup distributions. The interest for this model is fueled by an application in the field of logistics. Knowledge of the queue length distributions is needed to operate the system properly. The multiqueue polling system is decomposed into singlequeue vacation systems with klimited service and statedependent vacations, for which the vacation distributions are computed in an iterative approximate manner. These vacation models are analyzed via matrixanalytic techniques. The accuracy of the approximation scheme is verified by means of an extensive simulation study. The developed approximation turns out be accurate, robust and computationally efficient.
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.
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.
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.
the Dutch Ministry of Economic Affairs.
"... Abstract The present paper deals with the problem of calculating queue length distributions in a polling model with (exhaustive) klimited service under the assumption of general arrival, service and setup distributions. The interest for this model is fueled by an application in the field of logis ..."
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Abstract The present paper deals with the problem of calculating queue length distributions in a polling model with (exhaustive) klimited service under the assumption of general arrival, service and setup distributions. The interest for this model is fueled by an application in the field of logistics. Knowledge of the queue length distributions is needed to operate the system properly. The multiqueue polling system is decomposed into singlequeue vacation systems with klimited service and statedependent vacations, for which the vacation distributions are computed in an iterative approximate manner. These vacation models are analyzed via matrixanalytic techniques. The accuracy of the approximation scheme is verified by means of an extensive simulation study. The developed approximation turns out to be accurate, robust and computationally efficient.
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.
2Department of Technology Management
, 2006
"... The present paper considers the class of polling systems that allow a multitype branching process interpretation. This class contains the classical exhaustive and gated policies as special cases. We present an exact asymptotic analysis of the delay distribution in such systems, when the setup times ..."
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The present paper considers the class of polling systems that allow a multitype branching process interpretation. This class contains the classical exhaustive and gated policies as special cases. We present an exact asymptotic analysis of the delay distribution in such systems, when the setup times tend to infinity. The motivation to study these setup time asymptotics in polling systems is based on the specific application area of basestock policies in inventory control. Our analysis provides new and more general insights into the behavior of polling systems with large setup times.
Heavy traffic analysis of polling models by Mean Value Analysis
, 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 or gated service at each queue, and with general servicetime and switchover time distributions, and study its behavior when the load tends ..."
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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 or gated 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 [31], 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.