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22
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
Efficient Algorithms for Separated Continuous Linear Programs: The Multicommodity Flow Problem with Holding Costs and Extensions
, 2005
"... We give an approximation scheme for separated continuous linear programming problems. Such problems arise as fluid relaxations of multiclass queueing networks and are used to find approximate solutions to complex job shop scheduling problems. In a network with linear flow costs and linear, perunit ..."
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We give an approximation scheme for separated continuous linear programming problems. Such problems arise as fluid relaxations of multiclass queueing networks and are used to find approximate solutions to complex job shop scheduling problems. In a network with linear flow costs and linear, perunittime holding costs, our algorithm finds a drainage of the network that, for given constants �>0 and �>0, has total cost �1 + ��OPT + �, where OPT is the cost of the minimum cost drainage. The complexity of our algorithm is polynomial in the size of the input network, 1/�, and log�1/��. The fluid relaxation is a continuous problem. While the problem is known to have a piecewise constant solution, it is not known to have a polynomially sized solution. We introduce a natural discretization of polynomial size and prove that this discretization produces a solution with low cost. This is the first polynomial time algorithm with a provable approximation guarantee for fluid relaxations.
The continuous assignment problem and its application to Preemptive And NonPreemptive scheduling with irregular cost functions
, 2002
"... It is with the aim of solving scheduling problems with irregular cost functions that this paper focuses on the continuous assignment problem. It consists in partitioning a region of R into subregions of prescribed volumes so that the total cost is minimized. ..."
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Cited by 5 (2 self)
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It is with the aim of solving scheduling problems with irregular cost functions that this paper focuses on the continuous assignment problem. It consists in partitioning a region of R into subregions of prescribed volumes so that the total cost is minimized.
A Heuristic Method for Scheduling and Dispatching of Factory Production Using Multiclass Fluid Networks
 University of Texas at Austin
, 2003
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Optimal Routing and Scheduling in Flexible Manufacturing Systems using Integer Programming
"... Abstract — Here we consider the problem of maximum throughput routing and scheduling for flexible manufacturing systems/cells (FMS/FMC) and processing networks. Such a system consists of a set of machines which process materials and a transport network for moving materials among the machines. The go ..."
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Abstract — Here we consider the problem of maximum throughput routing and scheduling for flexible manufacturing systems/cells (FMS/FMC) and processing networks. Such a system consists of a set of machines which process materials and a transport network for moving materials among the machines. The goal in this problem is to find a policy for introducing jobs into the network and routing jobs through the network that maximizes the average number of jobs entering the system per unit time. We present an 01 linear program formulation of the maximum throughput routing and scheduling problem. This formulation is based on an extension of the linear programming formulation of the multistage network flow problem. For small problem instances, existing 01 solvers can be used to find an optimal schedule. For larger problem instances, we discuss the use of linear programming relaxations to find performance guarantees and rounding techniques for extracting feasible 01 solutions from the linear program solution. Finally, we demonstrate the general techniques described in the paper on a largescale example. For this example, solving the linear programming relaxation and extracting a feasible schedule produces an optimal solution. I.
Optimal Node Visitation in Acyclic Stochastic Digraphs with Multithreaded Traversals and Internal Visitation Requirements
, 2008
"... The original definition of the problem of optimal node visitation (ONV) in acyclic stochastic digraphs concerns the identification of a routing policy that will enable the visitation of each leaf node a requested number of times, while minimizing the expected number of the graph traversals. The orig ..."
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The original definition of the problem of optimal node visitation (ONV) in acyclic stochastic digraphs concerns the identification of a routing policy that will enable the visitation of each leaf node a requested number of times, while minimizing the expected number of the graph traversals. The original work of [1] formulated this problem as a Stochastic Shortest Path (SSP) problem, and since the state space of this SSP formulation is exponentially sized with respect to the number of the target nodes, it also proposed a suboptimal policy that is computationally tractable and asymptotically optimal. This paper extends the results of [1] to the cases where (i) the tokens traversing the graph can “split ” during certain transitions to a number of (sub)tokens, allowing, thus, the satisfaction of many visitation requirements during a single graph traversal, and (ii) there are additional visitation requirements attached to the internal graph nodes, which, however, can be served only when the visitation requirements of their successors have been fully met. In addition, the presented set of results establishes stronger convergence properties for the proposed suboptimal policies, and it provides a formal complexity analysis of the considered ONV formulations. From a practical standpoint, the extension of the original results performed in this paper enables their effective usage in the application domains that motivated the ONV problem, in the first place.
Optimal Node Visitation in Stochastic Digraphs
 Preprint. School of Industrial & Systems Engineering. Georgia Institute of Technology
, 2007
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Network Flow Modeling for Flexible Manufacturing Systems with Reentrant Lines
"... Abstract — A relaxed version of the process planning problem for flexible manufacturing systems/cells (FMS/FMC) and processing networks, such as flexible flow shops and general job shops, is formulated using a simple extension of multicommodity network flow problems. Our multistage multicommodity ne ..."
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Abstract — A relaxed version of the process planning problem for flexible manufacturing systems/cells (FMS/FMC) and processing networks, such as flexible flow shops and general job shops, is formulated using a simple extension of multicommodity network flow problems. Our multistage multicommodity network formulation allows for simultaneous routing and resource allocation and also captures the case of reentrant lines (recirculation). It can be used to perform rapid, albeit crude, explorations of the combinatorial space of possible configurations and failure scenarios. The technique can also provide bounds on the limits of system performance (eg: throughput, link usage, bottlenecks, etc). This can be used to guide the design of robust FMS architectures with high degree of redundancy in machines and routes, as demonstrated in numerical examples. Being a relaxation to the full discrete problem, our method could potentially be used as an admissible heuristic for pruning AIbased planning methods. We demonstrate our approach on a realistic industrial problem. I.
Exponential penalty function control with queues
 Annals of Applied Probability
, 2002
"... We introduce penaltyfunctionbased admission control policies to approximately maximize the expected reward rate in a loss network. These control policies are easy to implement and perform well both in the transient period as well as in steady state. A major advantage of the penalty approach is tha ..."
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We introduce penaltyfunctionbased admission control policies to approximately maximize the expected reward rate in a loss network. These control policies are easy to implement and perform well both in the transient period as well as in steady state. A major advantage of the penalty approach is that it avoids solving the associated dynamic program. However, a disadvantage of this approach is that it requires the capacity requested by individual requests to be sufficiently small compared to total available capacity. We first solve a related deterministic linear program (LP) and then translate an optimal solution of the LP into an admission control policy for the loss network via an exponential penalty function. We show that the penalty policy is a targettracking policy—it performs well because the optimal solution of the LP is a good target. We demonstrate that the penalty approach can be extended to track arbitrarily defined target sets. Results from preliminary simulation studies are included. 1. Introduction. We