An adaptive discretization algorithm for a class of continuous network programs

Philpott, Andy; Craddock, Mark

doi:10.1002/net.3230260102

Cited by 25 publications

(32 citation statements)

References 5 publications

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“…More interestingly, it also belongs to the class of the separated continuous linear programs that can be used to model a variety of optimal control problems but also some scheduling problems [6,7] and that was extensively studied. In particular, Pullan [18] presented a duality theory for these problems and practical algorithms exist to solve them [14,17].…”

Section: Problem Description 21 the Primal Problemmentioning

confidence: 99%

The Continuous Assignment Problem and Its Application to Preemptive and Non-Preemptive Scheduling with Irregular Cost Functions

Sourd

2004

INFORMS Journal on Computing

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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 d into subregions of prescribed volumes so that the total cost is minimized. The dual problem of the continuous assignment problem is an unconstrained maximisation of a non-smooth concave function. The preemptive variant of the scheduling problem with irregular cost functions corresponds to the one-dimensional continuous assignment problem and a lower bound for the non-preemptive variant can be derived. It is computationally tested in a branch-and-bound algorithm.

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Section: Problem Description 21 the Primal Problemmentioning

confidence: 99%

The Continuous Assignment Problem and Its Application to Preemptive and Non-Preemptive Scheduling with Irregular Cost Functions

Sourd

2004

INFORMS Journal on Computing

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“…The series of papers on SCLP by Pullan [41,42,43] deals with solution structure, duality theory, and numerical algorithms and to the best of our knowledge represents the state of the art of this area. Philpott and Craddock [39] later specialized Pullan's work to a network version of SCLP and presented encouraging numerical results.…”

Section: F Y(t) ≤ H(t) (4) U(t) ≥ 0 T∈ [0 T] Where B(t) C(t) G(mentioning

confidence: 99%

A New Algorithm for State-Constrained Separated Continuous Linear Programs

Luo¹,

Bertsimas

1998

SIAM J. Control Optim.

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Abstract. During the last few decades, significant progress has been made in solving largescale finite-dimensional and semi-infinite linear programming problems. In contrast, little progress has been made in solving linear programs in infinite-dimensional spaces despite their importance as models in manufacturing and communication systems. Inspired by the research on separated continuous linear programs, we propose a new class of continuous linear programming problems that has a variety of important applications in communications, manufacturing, and urban traffic control. This class of continuous linear programs contains the separated continuous linear programs as a subclass. Using ideas from quadratic programming, we propose an efficient algorithm for solving large-scale problems in this new class under mild assumptions on the form of the problem data. We prove algorithmically the absence of a duality gap for this class of problems without any boundedness assumptions on the solution set. We show this class of problems admits piecewise constant optimal control when the optimal solution exists. We give conditions for the existence of an optimal solution. We also report computational results which illustrate that the new algorithm is effective in solving large-scale realistic problems (with several hundred continuous variables) arising in manufacturing systems.

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“…A similar algorithm is suggested in Philpott and Craddock [37]. Luo and Bertsimas [33] have used quadratic programming techniques in conjunction with discretization, and implemented these to a more general problem, namely state constrained SCLP's.…”

Section: St G π(T) + H R(t) ≥ C(t) R(t) ≥ 0 π(0) = 0 π(T) Non-dementioning

confidence: 99%