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Método primal dual para modelos de planificación con costes cóncavos y limitaciones de capacidad.

Luis Onieva, S. Lozano, Juan Carlos Larrañeta Astola, Rafael Ruiz Usano (1987)

Qüestiió

Este trabajo estudia el problema de planificación de la producción representado por un modelo de costes cóncavos sujeto a limitaciones de capacidad. La relajación lineal del modelo es analizada usando un enfoque primal-dual. Las soluciones del dual se obtienen resolviendo para cada producto modelos sin restricciones de capacidad asignando un precio a las mismas. El primal reducido supone un test de admisibilidad de dichas soluciones. El dual reducido permite calcular los nuevos precios recomendados...

Métodos duales y algoritmos híbridos para problemas de "set partitioning".

Jaime Barceló Bugeda, Elena Fernández Areizaga (1990)

Trabajos de Investigación Operativa

En este artículo estudiamos la utilización de métodos duales en el diseño de algoritmos híbridos para la resolución de problemas de "Set Partitioning" (SP). Las técnicas duales resultan de gran interés para resolver problemas con estructura combinatoria no sólo porque generan cotas inferiores sino porque, además, su utilización junto con heurísticas y procedimientos de generación de desigualdades en el diseño de algoritmos híbridos permite evaluar la calidad de las cotas superiores obtenidas. Los...

Metric subregularity for nonclosed convex multifunctions in normed spaces

Xi Yin Zheng, Kung Fu Ng (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In terms of the normal cone and the coderivative, we provide some necessary and/or sufficient conditions of metric subregularity for (not necessarily closed) convex multifunctions in normed spaces. As applications, we present some error bound results for (not necessarily lower semicontinuous) convex functions on normed spaces. These results improve and extend some existing error bound results.

Minimization of a convex quadratic function subject to separable conical constraints in granular dynamics

Pospíšil, Lukáš, Dostál, Zdeněk (2015)

Programs and Algorithms of Numerical Mathematics

The numerical solution of granular dynamics problems with Coulomb friction leads to the problem of minimizing a convex quadratic function with semidefinite Hessian subject to a separable conical constraints. In this paper, we are interested in the numerical solution of this problem. We suggest a modification of an active-set optimal quadratic programming algorithm. The number of projection steps is decreased by using a projected Barzilai-Borwein method. In the numerical experiment, we compare our...

Minimizing and maximizing a linear objective function under a fuzzy max - * relational equation and an inequality constraint

Zofia Matusiewicz (2022)

Kybernetika

This paper provides an extension of results connected with the problem of the optimization of a linear objective function subject to max - * fuzzy relational equations and an inequality constraint, where * is an operation. This research is important because the knowledge and the algorithms presented in the paper can be used in various optimization processes. Previous articles describe an important problem of minimizing a linear objective function under a fuzzy max - * relational equation and an inequality constraint,...

Minimizing risk probability for infinite discounted piecewise deterministic Markov decision processes

Haifeng Huo, Jinhua Cui, Xian Wen (2024)

Kybernetika

The purpose of this paper is to study the risk probability problem for infinite horizon piecewise deterministic Markov decision processes (PDMDPs) with varying discount factors and unbounded transition rates. Different from the usual expected total rewards, we aim to minimize the risk probability that the total rewards do not exceed a given target value. Under the condition of the controlled state process being non-explosive is slightly weaker than the corresponding ones in the previous literature,...

Minimizing the earliness and tardiness cost of a sequence of tasks on a single machine

Philippe Chrétienne (2001)

RAIRO - Operations Research - Recherche Opérationnelle

Assume that n tasks must be processed by one machine in a fixed sequence. The processing time, the preferred starting time and the earliness and tardiness costs per time unit are known for each task. The problem is to allocate each task a starting time such that the total cost incurred by the early and tardy tasks is minimum. Garey et al. have proposed a nice O ( n log n ) algorithm for the special case of symmetric and task-independent costs. In this paper we first extend that algorithm to the case of asymmetric...

Minimizing the Earliness and Tardiness Cost of a Sequence of Tasks on a Single Machine

Philippe Chrétienne (2010)

RAIRO - Operations Research

Assume that n tasks must be processed by one machine in a fixed sequence. The processing time, the preferred starting time and the earliness and tardiness costs per time unit are known for each task. The problem is to allocate each task a starting time such that the total cost incurred by the early and tardy tasks is minimum. Garey et al. have proposed a nice O(nlogn) algorithm for the special case of symmetric and task-independent costs. In this paper we first extend that algorithm to the...

Minimizing the fuel consumption of a vehicle from the Shell Eco-marathon: a numerical study

Sophie Jan (2013)

ESAIM: Control, Optimisation and Calculus of Variations

We apply four different methods to study an intrinsically bang-bang optimal control problem. We study first a relaxed problem that we solve with a naive nonlinear programming approach. Since these preliminary results reveal singular arcs, we then use Pontryagin’s Minimum Principle and apply multiple indirect shooting methods combined with homotopy approach to obtain an accurate solution of the relaxed problem. Finally, in order to recover a purely bang-bang solution for the original problem, we...

Minimizing the number of tardy jobs for the single machine scheduling problem: MIP-based lower and upper bounds

Cyril Briand, Samia Ourari (2013)

RAIRO - Operations Research - Recherche Opérationnelle

This paper considers the problem of scheduling n jobs on a single machine. A fixed processing time and an execution interval are associated with each job. Preemption is not allowed. The objective is to find a feasible job sequence that minimizes the number of tardy jobs. On the basis of an original mathematical integer programming formulation, this paper shows how good-quality lower and upper bounds can be computed. Numerical experiments are provided for assessing the proposed approach.

Minimum convex-cost tension problems on series-parallel graphs

Bruno Bachelet, Philippe Mahey (2003)

RAIRO - Operations Research - Recherche Opérationnelle

We present briefly some results we obtained with known methods to solve minimum cost tension problems, comparing their performance on non-specific graphs and on series-parallel graphs. These graphs are shown to be of interest to approximate many tension problems, like synchronization in hypermedia documents. We propose a new aggregation method to solve the minimum convex piecewise linear cost tension problem on series-parallel graphs in O ( m 3 ) operations.

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