The simplex SON algorithm for LP/embedded network problems

Glover, Fred; Klingman, Darwin

doi:10.1007/bfb0120942

Cited by 77 publications

(29 citation statements)

References 30 publications

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“…The dual model contains T (T −1) variables u t,t but the number of constraints (excluding the SUB structure) is proportional to T . Moreover, the constraints (48) take the form of typical network flow thus allowing for a special algorithmic treatment within the simplex method [6].…”

Section: T ; T = Tmentioning

confidence: 99%

On Extending the LP Computable Risk Measures to Account Downside Risk

Krzemienowski

Ogryczak

2005

Comput Optim Applic

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Abstract.A mathematical model of portfolio optimization is usually quantified with mean-risk models offering a lucid form of two criteria with possible trade-off analysis. In the classical Markowitz model the risk is measured by a variance, thus resulting in a quadratic programming model. Following Sharpe's work on linear approximation to the mean-variance model, many attempts have been made to linearize the portfolio optimization problem. There were introduced several alternative risk measures which are computationally attractive as (for discrete random variables) they result in solving linear programming (LP) problems. Typical LP computable risk measures, like the mean absolute deviation (MAD) or the Gini's mean absolute difference (GMD) are symmetric with respect to the below-mean and over-mean performances. The paper shows how the measures can be further combined to extend their modeling capabilities with respect to enhancement of the below-mean downside risk aversion. The relations of the below-mean downside stochastic dominance are formally introduced and the corresponding techniques to enhance risk measures are derived. The resulting mean-risk models generate efficient solutions with respect to second degree stochastic dominance, while at the same time preserving simplicity and LP computability of the original models. The models are tested on real-life historical data.

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Section: T ; T = Tmentioning

confidence: 99%

On Extending the LP Computable Risk Measures to Account Downside Risk

Krzemienowski

Ogryczak

2005

Comput Optim Applic

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“…Taking advantages of the constraints structure specificity may remarkably extend the solution capabilities. In particular, the simplex SON algorithm [2] may be used for exploiting the LP embedded network structure in the dual form of the model.…”

Section: Discussionmentioning

confidence: 99%

“…Since the average complexity of the simplex method depends on the number of constraints, the dual model (19) can be directly solved for quite large values of m and n. Moreover, the columns corresponding to mn variables z ik form the transportation/assignment matrix thus allowing one to employ special techniques of the simplex SON algorithm [2] for implicit handling of these variables. Such techniques increase dramatically efficiency of the simplex method but they require a special tailored implementation.…”

Section: The Lp Model For Wowa Optimizationmentioning

confidence: 99%

On Decision Support Under Risk by the WOWA Optimization

Ogryczak

Śliwiński

2007

Lecture Notes in Computer Science

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Abstract. The problem of averaging outcomes under several scenarios to form overall objective functions is of considerable importance in decision support under uncertainty. The fuzzy operator defined as the so-called Weighted OWA (WOWA) aggregation offers a well-suited approach to this problem. The WOWA aggregation, similar to the classical ordered weighted averaging (OWA), uses the preferential weights assigned to the ordered values (i.e. to the worst value, the second worst and so on) rather than to the specific criteria. This allows one to model various preferences with respect to the risk. Simultaneously, importance weighting of scenarios can be introduced. In this paper we analyze solution procedures for optimization problems with the WOWA objective function. A linear programming formulation is introduced for optimization of the WOWA objective with monotonic preferential weights. Its computational efficiency is analyzed.

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“…The development of efficient solution methods and new modeling techniques for expressing problems in a pictorial network formulation [1,2,6,7,8,9,10] has led to the increased use of network-based models in government and business. These models range from rather straightforward network applications such as production planning and distribution to less obvious applications involving the refueling of nuclear reactors and optimal lot sizing and machine loading for multiple products.…”

Section: 4mentioning

confidence: 99%

Netgen-II: A System for Generating Structured Network-Based Mathematical Programming Test Problems

Elam

Klingman

1982

Evaluating Mathematical Programming Techniques

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The increased importance of designing and implementing algorithms to solve particular management problems has created the need for more robust test proble i generators that can match the overall structure and parameter values of these problems.Of particular interest are management problems that can be modeled using a network structure. This paper discusses the design of a system for generating network-based mathematical programming test problems that conform to user-supplied structural and parameter characteristics.

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The simplex SON algorithm for LP/embedded network problems

Cited by 77 publications

References 30 publications

On Extending the LP Computable Risk Measures to Account Downside Risk

On Extending the LP Computable Risk Measures to Account Downside Risk

On Decision Support Under Risk by the WOWA Optimization

Netgen-II: A System for Generating Structured Network-Based Mathematical Programming Test Problems

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