Bounds for Row-Aggregation in Linear Programming

Zipkin, Paul

doi:10.1287/opre.28.4.903

Cited by 74 publications

(24 citation statements)

References 4 publications

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“…Finally, we note that there might be connections, which could be investigated, between the procedure used in this paper and "aggregation" in linear programming, see Zipkin (1980).…”

Section: Discussionmentioning

confidence: 99%

An Improved IP Formulation for the Uncapacitated Facility Location Problem: Capitalizing on Objective Function Structure

Berman

Krass

2005

Ann Oper Res

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In this paper we examine the Uncapacitated Facility Location Problem (UFLP) with a special structure of the objective function coefficients. For each customer the set of potential locations can be partitioned into subsets such that the objective function coefficients in each are identical. This structure exists in many applications, including the Maximum Cover Location Problem. For the problems possessing this structure, we develop a new integer programming formulation that has all the desirable properties of the standard formulation, but with substantially smaller dimensionality, leading to significant improvement in computational times. While our formulation applies to any instance of the UFLP, the reduction in dimensionality depends on the degree to which this special structure is present.

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“…Finally, we note that there might be connections, which could be investigated, between the procedure used in this paper and "aggregation" in linear programming, see Zipkin (1980).…”

Section: Discussionmentioning

confidence: 99%

An Improved IP Formulation for the Uncapacitated Facility Location Problem: Capitalizing on Objective Function Structure

Berman

Krass

2005

Ann Oper Res

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“…In our case, the stochastic LP has a finite number of discrete scenarios and is therefore an ordinary LP. So we can think of aggregating scenarios also in terms of first aggregating columns (Zipkin 1980a) and then either aggregating rows (Zipkin 1980b) or aggregating columns in the dual.…”

Section: Aggregating Scenarios As Sub-filtrationsmentioning

confidence: 99%

LP Modeling for Asset-Liability Management: A Survey of Choices and Simplifications

Sodhi

2005

Operations Research

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Dynamic linear programming (LP) models for asset-liability management (ALM) are quite powerful and flexible but face two challenges: (1) many modeling choices, not all consistent with one another or with finance theory, and (2) solution difficulties due to the large number of scenarios obtained from standard interest-rate models. We first survey these modeling choices with a view to help researchers make self-consistent choices. Next, we review how the dynamic LP model for ALM and the representation of uncertainty therein have been simplified in the past to motivate new or hybrid models emphasizing tractability. To this end, we review existing static LP models as extreme modeling simplifications and aggregation as a simplification of uncertainty.

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“…Outside-the-solver strategies perform clustering on the scenario data (right-hand sides, matrices, and gradients) prior to the solution of the problem [5,8,13,16]. This approach can provide lower bounds and error bounds for linear programs (LPs) and this feature can be exploited in branch-and-bound procedures [1,5,22,28].…”

Section: Related Work and Contributionsmentioning

confidence: 99%

Clustering-based preconditioning for stochastic programs

2015

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We present a clustering-based preconditioning strategy for KKT systems arising in stochastic programming within an interior-point framework. The key idea is to perform adaptive clustering of scenarios (inside-the-solver) based on their influence on the problem at hand. This approach thus contrasts with existing (outside-the-solver) approaches that cluster scenarios based on problem data alone. We derive spectral and error properties for the preconditioner and demonstrate that scenario compression rates of up to 94 % can be obtained, leading to dramatic computational savings. In addition, we demonstrate that the proposed preconditioner can avoid scalability issues of Schur decomposition in problems with large first-stage dimensionality.

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Bounds for Row-Aggregation in Linear Programming

Cited by 74 publications

References 4 publications

An Improved IP Formulation for the Uncapacitated Facility Location Problem: Capitalizing on Objective Function Structure

An Improved IP Formulation for the Uncapacitated Facility Location Problem: Capitalizing on Objective Function Structure

LP Modeling for Asset-Liability Management: A Survey of Choices and Simplifications

Clustering-based preconditioning for stochastic programs

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