Adaptive dynamic cost updating procedure for solving fixed charge network flow problems

Nahapetyan, Artyom G.; Pardalos, Pãnos M.

doi:10.1007/s10589-007-9060-x

Cited by 27 publications

(23 citation statements)

References 18 publications

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“…Using above described notations, we can state the following formulation for the fixed charge network flow problem [22]:…”

Section: Two Mathematical Formulations Of the Fixed Charge Network Flmentioning

confidence: 99%

“…Let us approximate the concave cost function f a in (1) by a piece-wise linear concave function with c a a = c a + s a a , [22]. Recognize that φ a a underestimates function f a for all a > 0, see Fig.…”

Section: Two Mathematical Formulations Of the Fixed Charge Network Flmentioning

confidence: 99%

“…In [22], authors proved that for a sufficiently small , CPLNF( ) correctly models the fixed charge network flow problem. Below we briefly restate the theorem and for the proof we refer to [22].…”

Section: Two Mathematical Formulations Of the Fixed Charge Network Flmentioning

confidence: 99%

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Bilinear modeling solution approach for fixed charge network flow problems

2009

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“…Using above described notations, we can state the following formulation for the fixed charge network flow problem [22]:…”

Section: Two Mathematical Formulations Of the Fixed Charge Network Flmentioning

confidence: 99%

Section: Two Mathematical Formulations Of the Fixed Charge Network Flmentioning

confidence: 99%

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Bilinear modeling solution approach for fixed charge network flow problems

2009

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“…Such arcs are called discrete arcs, and their cost structure makes the incurred cost a concave function of the flow amount f . We thus use the near-optimal concave min-cost flow algorithm of [10] in all our network flow computations.…”

Section: The Discretized Network Flow Techniquementioning

confidence: 99%

Selection of Multiple SNPs in Case-Control Association Study Using a Discretized Network Flow Approach

Dutt¹,

Dai²,

Ren³

et al. 2009

Bioinformatics and Computational Biology

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Abstract. Recent large scale genome-wide association studies have been considered to hold promise for unraveling the genetic etiology of complex diseases. It becomes possible now to use these data to assess the influence of interactions from multiple SNPs on a disease. In this paper we formulate the multiple SNP selection problem for determining genetic risk profiles of certain diseases by formulating novel 0/1 IP formulations for this problem, and solving them using a new near-optimal and efficient discrete optimization technique called discretized network flow that has recently been developed by us. One of the highlights of our approach to solving the multiple SNP selection problem is recognizing that there could be different genetic profiles of a disease among the patient population, and it is thus desirable to classify/cluster patients with similar genetic profiles of the disease while simultaneously selecting the right genetic marker sets of the disease for each cluster. This approach coupled with the DNF technique has yielded results for several diseases with some of the highest sensitivities seen so far and specificities that are higher or comparable to state-of-the art techniques, at a fraction of the runtime of these techniques.

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“…Recently we have proposed a bilinear reduction technique, which can be used to find an approximate solution of concave piecewise linear and fixed charge network flow problems (see [27] and [28]). However, because of a different structure of the objective function, these methods cannot be directly applied to the CMDP problems.…”

Section: Introductionmentioning

confidence: 99%

A bilinear reduction based algorithm for solving capacitated multi-item dynamic pricing problems

Nahapetyan

Pardalos

2008

Computers & Operations Research

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In a capacitated multi-item dynamic pricing problem one maximizes the profit by choosing a proper production level as well as pricing policy, where the latter depends on a satisfied demand. The objective function involves inventory, production and setup costs, and revenue functions. The products are required to satisfy joined production capacities. We consider a bilinear reduction of the linear mixed integer formulation of the problem and prove that the problem is equivalent to finding a global maximum of the bilinear problem. A heuristic algorithm is proposed, based on the reduction technique. Numerical experiments confirm the efficiency of the proposed technique.

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Adaptive dynamic cost updating procedure for solving fixed charge network flow problems

Cited by 27 publications

References 18 publications

Bilinear modeling solution approach for fixed charge network flow problems

Bilinear modeling solution approach for fixed charge network flow problems

Selection of Multiple SNPs in Case-Control Association Study Using a Discretized Network Flow Approach

A bilinear reduction based algorithm for solving capacitated multi-item dynamic pricing problems

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