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Centralized VERSUS decentralized production planning

Georgios K. Saharidis, Yves Dallery, Fikri Karaesmen (2006)

RAIRO - Operations Research

In the course of globalization, many enterprises change their strategies and are coupled in partnerships with suppliers, subcontractors and customers. This coupling forms supply chains comprising several geographically distributed production facilities. Production planning in a supply chain is a complicated and difficult task, as it has to be optimal both for the local manufacturing units and for the whole supply chain network. In this paper two analytical models are used to solve the production planning...

Chance constrained bottleneck transportation problem with preference of routes

Yue Ge, Minghao Chen, Hiroaki Ishii (2012)

Kybernetika

This paper considers a variant of the bottleneck transportation problem. For each supply-demand point pair, the transportation time is an independent random variable. Preference of each route is attached. Our model has two criteria, namely: minimize the transportation time target subject to a chance constraint and maximize the minimal preference among the used routes. Since usually a transportation pattern optimizing two objectives simultaneously does not exist, we define non-domination in this...

Chance constrained optimal beam design: Convex reformulation and probabilistic robust design

Jakub Kůdela, Pavel Popela (2018)

Kybernetika

In this paper, we are concerned with a civil engineering application of optimization, namely the optimal design of a loaded beam. The developed optimization model includes ODE-type constraints and chance constraints. We use the finite element method (FEM) for the approximation of the ODE constraints. We derive a convex reformulation that transforms the problem into a linear one and find its analytic solution. Afterwards, we impose chance constraints on the stress and the deflection of the beam....

Chance constrained problems: penalty reformulation and performance of sample approximation technique

Martin Branda (2012)

Kybernetika

We explore reformulation of nonlinear stochastic programs with several joint chance constraints by stochastic programs with suitably chosen penalty-type objectives. We show that the two problems are asymptotically equivalent. Simpler cases with one chance constraint and particular penalty functions were studied in [6,11]. The obtained problems with penalties and with a fixed set of feasible solutions are simpler to solve and analyze then the chance constrained programs. We discuss solving both problems...

Characterizations of error bounds for lower semicontinuous functions on metric spaces

Dominique Azé, Jean-Noël Corvellec (2004)

ESAIM: Control, Optimisation and Calculus of Variations

Refining the variational method introduced in Azé et al. [Nonlinear Anal. 49 (2002) 643-670], we give characterizations of the existence of so-called global and local error bounds, for lower semicontinuous functions defined on complete metric spaces. We thus provide a systematic and synthetic approach to the subject, emphasizing the special case of convex functions defined on arbitrary Banach spaces (refining the abstract part of Azé and Corvellec [SIAM J. Optim. 12 (2002) 913-927], and the characterization...

Characterizations of error bounds for lower semicontinuous functions on metric spaces

Dominique Azé, Jean-Noël Corvellec (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Refining the variational method introduced in Azé et al. [Nonlinear Anal. 49 (2002) 643-670], we give characterizations of the existence of so-called global and local error bounds, for lower semicontinuous functions defined on complete metric spaces. We thus provide a systematic and synthetic approach to the subject, emphasizing the special case of convex functions defined on arbitrary Banach spaces (refining the abstract part of Azé and Corvellec [SIAM J. Optim. 12 (2002) 913-927], and the characterization...

Characterizations of the Solution Sets of Generalized Convex Minimization Problems

Ivanov, Vsevolod (2003)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 90C26, 90C20, 49J52, 47H05, 47J20.In this paper we obtain some simple characterizations of the solution sets of a pseudoconvex program and a variational inequality. Similar characterizations of the solution set of a quasiconvex quadratic program are derived. Applications of these characterizations are given.

Characterizations of ɛ-duality gap statements for constrained optimization problems

Horaţiu-Vasile Boncea, Sorin-Mihai Grad (2013)

Open Mathematics

In this paper we present different regularity conditions that equivalently characterize various ɛ-duality gap statements (with ɛ ≥ 0) for constrained optimization problems and their Lagrange and Fenchel-Lagrange duals in separated locally convex spaces, respectively. These regularity conditions are formulated by using epigraphs and ɛ-subdifferentials. When ɛ = 0 we rediscover recent results on stable strong and total duality and zero duality gap from the literature.

Clasificación en programación multiobjetivo.

Carlos González Martín (1986)

Trabajos de Investigación Operativa

En el presente trabajo, después de justificar lo importante que resulta para el decisor, en muchos casos, el poder obtener clasificaciones en el conjunto de objetivos de un problema de Porgramación Multiobjetivo, se hace un estudio algorítmico que permite agruparlos en función de ciertos niveles de conformidad.

Clique partitioning of interval graphs with submodular costs on the cliques

Dion Gijswijt, Vincent Jost, Maurice Queyranne (2007)

RAIRO - Operations Research

Given a graph G = (V,E) and a “cost function” f : 2 V → ℝ (provided by an oracle), the problem [PCliqW] consists in finding a partition into cliques of V(G) of minimum cost. Here, the cost of a partition is the sum of the costs of the cliques in the partition. We provide a polynomial time dynamic program for the case where G is an interval graph and f belongs to a subclass of submodular set functions, which we call “value-polymatroidal”. This provides a common solution for various generalizations of the...

Clique-connecting forest and stable set polytopes

Denis Cornaz (2010)

RAIRO - Operations Research

Let G = (V,E) be a simple undirected graph. A forest F ⊆ E of G is said to be clique-connecting if each tree of F spans a clique of G. This paper adresses the clique-connecting forest polytope. First we give a formulation and a polynomial time separation algorithm. Then we show that the nontrivial nondegenerate facets of the stable set polytope are facets of the clique-connecting polytope. Finally we introduce a family of rank inequalities which are facets, and which generalize the clique inequalities. ...

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