A Linear Approximation for Chance-Constrained Programming

Olson, David L.; Swenseth, Scott R.

doi:10.2307/2581946

Cited by 9 publications

(10 citation statements)

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“…In [19] [22] and [23], several uniformly tighter approximations have been developed to replace the non-linear constraint by a set of linear inequalities. However, these methods are only suited to problems with a small number of random coefficients.…”

Section: B Linear Approximation Of Optimization Problemmentioning

confidence: 99%

Secondary spectrum access in TV-bands with combined co-channel and adjacent channel interference constraints

Shi

Sung

Zander

2012

2012 IEEE International Symposium on Dynamic Spectrum Access Networks

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Abstract-The potential of VHF/UHF band as a candidate for secondary spectrum access, so called "TV white spaces", has been intensively investigated in recent years. However, the impact of the accumulated interference from multiple secondary users on different adjacent channels has not been well studied thus far, let alone the effect of combined interference from both co-channel and adjacent channels. This paper presents a framework for assessing secondary spectrum reuse opportunities for portable and mobile devices that comply with geo-location database concepts. The opportunity is evaluated in terms of the maximal number of secondary users that can access the "TV white space" simultaneously. Particular emphasis is given to the protection of TV receiver from harmful aggregate interference originated from not only the secondary users outside the TV coverage on the same channel but also those close to the TV receivers operating on different adjacent TV channels. An optimization problem is solved to maximize the number of secondary users admitted to the available TV channels at different locations. Through in-depth analysis of the interference characteristics of the optimal solution, it is identified that the cumulative effect of adjacent channel interferences has the dominant impact on TV reception, particularly for the case of secondary devices with limited transmit power. This suggests the possibility to achieve near-optimal exploitation of TV-bands for secondary reuse without explicit coordination of co-channel interference from the secondary users deployed over a wide geographical area.

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Section: B Linear Approximation Of Optimization Problemmentioning

confidence: 99%

Secondary spectrum access in TV-bands with combined co-channel and adjacent channel interference constraints

Shi

Sung

Zander

2012

2012 IEEE International Symposium on Dynamic Spectrum Access Networks

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“…Assuming resources of the projects are limited and renewable, the aim was maximization of the present value of profits of projects as the objective function. Olson et al [3] presented a linear approximation for chance constrained programming in their article which can be used in either the single or multiple objective cases. The approximation presented will place a bound on the chance constraint at least as tight as the true nonlinear form, thus it overachieves the chance constraint at the expense of other constraints or objectives.…”

Section: Literature Of Past Workmentioning

confidence: 99%

A New Model for Probabilistic Multi-Period Multi-Objective Project Selection Problem

Khalili‐Damghani¹,

Poortarigh²,

Pakgohar³

2018

dtetr

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The project selection problem is considered as one of the most imperative decisions for investor organizations. Due to non-deterministic nature of some criteria in the real world projects in this paper, a new model for project selection problem is proposed in which some parameters are assumed probabilistic. This model is formulated as a non-linear, multi-objective, multi-period, zero-one programming model. Then the epsilon constraint method and an algorithm are applied to check the Pareto front and to find optimal solutions. A case study is conducted to illustrate the applicability and effectiveness of the approach, with the results presented and analysed. Since the proposed model is more compatible with real world problems, the results are more tangible and trustable compared with deterministic cases. Implications of the proposed approach are discussed and suggestions for further work are outlined.Keywords: Project selection, multi objective programming, chance constraint, epsilon constraint method. INTRODUCTIONDecision making about selection or rejection of a project is considerable from both theoretical and practical aspects and it depends on satisfaction of financial and nonfinancial constraints of the problem. In the real world project selection problems there are normally more than one objective function. This makes the solution algorithm more complicated and time consuming. The purpose of this paper is decision making about selection of N projects in T periods of time such that the profit gets maximum and total cost of equipment, human resources and used raw materials become minimum. In real world problems many of parameters are unlikely to be deterministic and ignoring the stochastic model can lead to unreliable results. In this paper a new framework is proposed for modeling a project selection problem relying on the concept of risk and by applying a linear approximation on probabilistic constraints. The mentioned model is called "Mean-Risk" model which the main idea of it is maximizing the expected profit of selecting a project such that risk curve of this selection always be below of the confidence curve. Here without loss of generality and just for simplification, the confidence is assumed a linear function. Since some parameters are probabilistic, the constraints include these parameters are also probabilistic constraints. Chance constrained programming was developed as a means of describing constraints in the form of probability levels of attainment. Consideration of chance constraints allows the decision maker to consider objectives in terms of their attainment probability. This approach changes constraints with stochastic parameters to constraints with a confidence level as the threshold of decision maker, using variance-covariance matrix. If α is a predetermined confidence level desired by the decision maker, the implication is that a constraint will have a probability of satisfaction of α. After transforming the problem from probabilistic mode to deterministic mode, the resulting model i...

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“…Hence, the constraint confidence levels of the linearized chance-constrained model should be recalculated by substituting the solutions of them into the non-linear chance-constrained model. This recalculated confidence levels are called "true probability" (Olson and Swenseth 1987). In this way, it is seen that the true probability values (K p ) are bigger than the confidence levels determined at the beginning of the solution process (K p ) in linearized model.…”

Section: Analyze Of the Constraints Confidence Levelmentioning

confidence: 99%

“…The model of Olson and Swenseth (1987) includes only one chance-constraint and it is a binding constraint. Equation (22) is a valid formulization for binding constraints.…”

Section: Analyze Of the Constraints Confidence Levelmentioning

confidence: 99%

Stochastic optimization for blending problem in brass casting industry

2011

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A critical process in brass casting is blending of the raw materials in a furnace so that the specified metal ratios are satisfied. The uncertainties in raw material compositions may cause violations of the specification limits and extra cost. In this study, we proposed a chance-constrained stochastic programming approach for blending problem in brass casting industry to handle the statistical variations in raw material compositions. The proposed approach is a non-linear mathematical model that is solved global optimally by using GAMS/BARON solver. An application has been performed in MKEK brass factory in Kırıkkale, Turkey and the solution of the application has been compared with alternative solution approaches based on cost and specification violation risk conditions. This comparison demonstrates that the proposed model is the most effective solution approach for managing stochastic uncertainties in blending problems and successfully can be used other industries such as alloy steel or secondary aluminum production.

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A Linear Approximation for Chance-Constrained Programming

Cited by 9 publications

References 0 publications

Secondary spectrum access in TV-bands with combined co-channel and adjacent channel interference constraints

Secondary spectrum access in TV-bands with combined co-channel and adjacent channel interference constraints

A New Model for Probabilistic Multi-Period Multi-Objective Project Selection Problem

Stochastic optimization for blending problem in brass casting industry

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