Linear programming with interval coefficients

Chinneck, John W.; Ramadan, Khaled

doi:10.1057/palgrave.jors.2600891

Cited by 252 publications

(116 citation statements)

References 6 publications

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“…In Wang et al (2011) a RO approach is considered where the uncertainty set on the load is a simple interval, so that methods from interval LP (e.g., Chinneck and Ramadan 2000) can be employed together with Benders' decomposition to solve the model. The main focus of the work is on network security.…”

Section: Robust Optimization Approachesmentioning

confidence: 99%

Large-scale Unit Commitment under uncertainty

Ackooij²,

et al. 2015

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The Unit Commitment problem in energy management aims at finding the optimal productions schedule of a set of generation units while meeting various system-wide constraints. It has always been a large-scale, non-convex difficult problem, especially in view of the fact that operational requirements imply that it has to be solved in an unreasonably small time for its size. Recently, the ever increasing capacity for renewable generation has strongly increased the level of uncertainty in the system, making the (ideal) Unit Commitment model a large-scale, non-convex, uncertain (stochastic, robust, chance-constrained) program. We provide a survey of the literature on methods for the Uncertain Unit Commitment problem, in all its variants. We start with a review of the main contributions on solution methods for the deterministic versions of the problem, focusing on those based on mathematical programming techniques that are more relevant for the uncertain versions of the problem. We then present and categorize the approaches to the latter, also providing entry points to the relevant literature on optimization under uncertainty

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Section: Robust Optimization Approachesmentioning

confidence: 99%

Large-scale Unit Commitment under uncertainty

Ackooij²,

et al. 2015

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“…in Chanas and Kuchta (1996); Chinneck and Ramadan (2000); Fiedler et al (2006); Inuiguchi et al (2003); Jansson and Rump (1991); Machost (1970), and Mráz (1998). Let us denote by…”

Section: Introductionmentioning

confidence: 97%

“…This nonlinear program can be replaced by computing exponentially many linear programs, each of which is applied on the corresponding orthant of R m [cf. Chinneck and Ramadan (2000)]. In this way we have…”

Section: Introductionmentioning

confidence: 99%

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Optimal value range in interval linear programming

Hladík

2009

Fuzzy Optim Decis Making

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We deal with the linear programming problem in which input data can vary in some given real compact intervals. The aim is to compute the exact range of the optimal value function. We present a general approach to the situation the feasible set is described by an arbitrary linear interval system. Moreover, certain dependencies between the constraint matrix coefficients can be involved. As long as we are able to characterize the primal and dual solution set (the set of all possible primal and dual feasible solutions, respectively), the bounds of the objective function result from two nonlinear programming problems. We demonstrate our approach on various cases of the interval linear programming problem (with and without dependencies).

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“…Because there is no existing method for solving an IFBLP model directly; an IFBLP is pre-converted into two There is no method that could directly crisp an interval-coefficient BLP. However, the approach developed by Chinneck and Ramadan (2000), originally designed to crisp an interval-coefficient LP, it is modified in this Paper. It is worth mentioning that the proposed approach in this Paper is not simply defuzzifying and crisping the IFBLP problems; it uses an innovative manner to deal with the problem of the infinite optimal alpha results that are caused by the integration process of the defuzzification and crisping.…”

Section: Introductionmentioning

confidence: 99%

A Fuzzy-stochastic Approach for Binary Linear Programming under Uncertainties

Peng¹,

Mayorga²

2017

JMR

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This paper presents an innovative Fuzzy-Stochastic Approach (FSA) to solve Binary Linear Programming (BLP) problems under uncertainties. An Interval-coefficient Fuzzy Binary Linear Programming (IFBLP) model is applied here to reflect two different types of uncertainty in a BLP problem. In the proposed IFBLP model the interval coefficient is used to reflect parameter uncertainty, and the fuzzy goal & fuzzy constraints are used to represent model structure uncertainty. The proposed FSA would de-fuzzify the fuzzy constraints in an IFBLP model by considering its fuzzy goal; and then derive two linear BLPs with extreme crisp-coefficients from the IFBLP model, which here are called as a best optimum BLP and a worst optimum BLP. The results of the two-extreme linear BLPs are used to bound the outcome distribution of the IFBLP model. The proposed FSA is applied into a long-term traffic noise control planning to present its applicability.

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Linear programming with interval coefficients

Cited by 252 publications

References 6 publications

Large-scale Unit Commitment under uncertainty

Large-scale Unit Commitment under uncertainty

Optimal value range in interval linear programming

A Fuzzy-stochastic Approach for Binary Linear Programming under Uncertainties

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