A simplex based algorithm to solve separated continuous linear programs

Weiss, Gideon

doi:10.1007/s10107-008-0217-x

Cited by 101 publications

(76 citation statements)

References 38 publications

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“…Anderson (1981), Anderson and Nash (1987), Bellman (1953) and Pullan (1993). A simplex based algorithm that solves a wide class of SCLP problems optimally in a finite number of steps has been recently found, see Weiss (2001). This has been an open problem for half a century.…”

Section: The Multi-class Fluid Network Optimization Problemmentioning

confidence: 99%

“…The analysis in Weiss (2001) reveals important features of the solution, essential to our control method. The MCFN problem is always feasible and bounded, and the SCLP simplex algorithm will always produce a fluid solution that consists of a partition of the time horizon 0 = t 0 < t 1 < · · · < t M = T , where M is bounded, and in each of the time intervals the server allocations u k (t) are constant, and as a result the fluid buffer levels q k (t) are continuous piecewise linear.…”

Section: The Multi-class Fluid Network Optimization Problemmentioning

confidence: 99%

“…As suggested in Weiss (1999), the method we use is to solve a deterministic fluid optimization problem which approximates the system, and then use decentralized local on-line controls to track the fluid solution. To carry this out we integrate three recent ideas which have been developed independently: (1) Solution of separated continuous linear programs (SCLP) by means of an exact simplex type algorithm, see Weiss (2001). (2) Modeling of queueing systems with unlimited supply of work by means of infinite virtual queues, as used in Weiss (2005, 2006), Weiss (2002, 2007) and Weiss (2005).…”

Section: Introductionmentioning

confidence: 99%

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Near optimal control of queueing networks over a finite time horizon

Nazarathy

Weiss

2008

Ann Oper Res

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We propose a method for the control of multi-class queueing networks over a finite time horizon. We approximate the multi-class queueing network by a fluid network and formulate a fluid optimization problem which we solve as a separated continuous linear program. The optimal fluid solution partitions the time horizon to intervals in which constant fluid flow rates are maintained. We then use a policy by which the queueing network tracks the fluid solution. To that end we model the deviations between the queuing and the fluid network in each of the intervals by a multi-class queueing network with some infinite virtual queues. We then keep these deviations stable by an adaptation of a maximum pressure policy. We show that this method is asymptotically optimal when the number of items that is processed and the processing speed increase. We illustrate these results through a simple example of a three stage re-entrant line.

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Section: The Multi-class Fluid Network Optimization Problemmentioning

confidence: 99%

Section: The Multi-class Fluid Network Optimization Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Near optimal control of queueing networks over a finite time horizon

Nazarathy

Weiss

2008

Ann Oper Res

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“…A value convergent approximation scheme for linear programs in function spaces was proposed in [31]. Weiss worked on separated continuous linear programs [52] and developed an implementable algorithm for their solution in MATLAB. Earlier, Pulan also worked on similar problems [39,40].…”

Section: Introductionmentioning

confidence: 99%

A Shadow Simplex Method for Infinite Linear Programs

Ghate

Sharma

Smith

2010

Operations Research

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We present a Simplex-type algorithm, that is, an algorithm that moves from one extreme point of the infinite-dimensional feasible region to another not necessarily adjacent extreme point, for solving a class of linear programs with countably infinite variables and constraints. Each iteration of this method can be implemented in finite time, while the solution values converge to the optimal value as the number of iterations increases. This Simplex-type algorithm moves to an adjacent extreme point and hence reduces to a true infinite-dimensional Simplex method for the important special cases of non-stationary infinite-horizon deterministic and stochastic dynamic programs.

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“…The latter problem is much more difficult in general and falls into the class of separated continuous linear programs (see, e.g., [1]). These problems have received attention in a number of studies, a short list of which includes [4,7,10,28,29,34,35].…”

Section: Introductionmentioning

confidence: 99%

Minimizing Makespan in a Multiclass Fluid Network With Parameter Uncertainty

Büke

Hasenbein

Morton

2009

Prob. Eng. Inf. Sci.

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We introduce and investigate a new type of decision problem related to multiclass fluid networks. Optimization problems arising from fluid networks with known parameters have been studied extensively in the queueing, scheduling, and optimization literature. In this article, we explore the makespan problem in fluid networks, with the assumption that the parameters are known only through a probability distribution. Thus, the decision maker does not have complete knowledge of the parameters in advance. This problem can be formulated as a stochastic nonlinear program. We provide necessary and sufficient feasibility conditions for this class of problems. We also derive a number of other structural results that can be used in developing effective computational procedures for solving stochastic fluid makespan problems.

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A simplex based algorithm to solve separated continuous linear programs

Abstract: We consider the separated continuous linear programming problem with linear data. We characterize the form of its optimal solution, and present an algorithm which solves it in a finite number of steps, using simplex pivot iterations.

Cited by 101 publications

References 38 publications

Near optimal control of queueing networks over a finite time horizon

Near optimal control of queueing networks over a finite time horizon

A Shadow Simplex Method for Infinite Linear Programs

Minimizing Makespan in a Multiclass Fluid Network With Parameter Uncertainty

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