215 research outputs found
Multistage Benders' Decomposition applied to Multiperiod, Multicommodity Production, Distribution and Inventory System
It has become more and more important for some industries to have an efficient program for their long range activities. Such a program usually means a production, distribution, and inventory plan of multicommodity over a multiperiod range. The network flow model is a standard way to represent the problem. Recent advances in the computational aspect of the generalized network (Glover et al. 1978:24, 1209-1220) gives us an indication of broader areas of application. However, the real world imposes complicated constraints upon us which can not be represented in the network models, not even in generalized network models.
In a previous paper (Tone 1977a:20, 77-93), the author tried a decomposition of network type constraints and nonnetwork type constraints (called pattern constraints) by using Benders' partitioning procedure (Benders 1962:4, 238-252). The computational experiments show that the decomposition technique works well.
In this paper, the author develops a method to handle the multiperiod problem, where the problems in each period are coupled with the succeeding one by the existence of the inventory activities. Our system is doubly decomposable; by the existence of the pattern constraints and by inventory activities. The algorithm consists of two parts, one for solving the network flow problem in each period and the other for solving the pattern and coupling constraints which may be called a master problem. Finite convergence is guaranteed
On the Transformation Mechanism for Formulating a Multiproduct Two-Layer Supply Chain Network Design Problem as a Network Flow Model
The multiproduct two-layer supply chain is very common in various industries. In this paper, we introduce a possible modeling and algorithms to solve a multiproduct two-layer supply chain network design problem. The decisions involved are the DCs location and capacity design decision and the initial distribution planning decision. First we describe the problem and give a mixed integer programming (MIP) model; such problem is NP-hard and it is not easy to reduce the complexity. Inspired by it, we develop a transformation mechanism of relaxing the fixed cost and adding some virtual nodes and arcs to the original network. Thus, a network flow problem (NFP) corresponding to the original problem has been formulated. Given that we could solve the NFP as a minimal cost flow problem. The solution procedures and network simplex algorithm (INS) are discussed. To verify the effectiveness and efficiency of the model and algorithms, the performance measure experimental has been conducted. The experiments and result showed that comparing with MIP model solved by genetic algorithm (GA) and Benders, decomposition algorithm (BD) the NFP model and INS are also effective and even more efficient for both small-scale and large-scale problems
Satellite Network, Design, Optimization, and Management
We introduce several network design and planning problems that arise in the context of commercial satellite networks. At the heart of most of these problems we deal with a traffic routing problem over an extended planning horizon. In satellite networks route changes are associated with significant monetary penalties that are usually in the form of discounts (up to 40%) offered by the satellite provider to the customer that is affected. The notion of these rerouting penalties requires the network planners to consider management problems over multiple time periods and introduces novel challenges that have not been considered previously in the literature.
Specifically, we introduce a multiperiod traffic routing problem and a multiperiod network design problem that incorporate rerouting penalties. For both of these problems we present novel path-based reformulations and develop branch-and-price-and-cut approaches to solve them. The pricing problems in both cases present new challenges and we develop special purpose approaches that can deal with them. We also show how these results can be extended to deal with traffic routing and network design decisions in other settings with much more general rerouting penalties. Our computational work demonstrates the benefits of using the branch-and-price-and-cut procedure developed that can deal with the multiperiod nature of the problem as opposed to straightforward, myopic period-by-period optimization approaches.
In order to deal with cases in which future demand is not known with certainty we present the stochastic version of the multiperiod traffic routing problem and formulate it as a stochastic multistage recourse problem with integer variables at all stages. We demonstrate how an appropriate path-based reformulation and an associated branch-and-price-and-cut approach can solve this problem and other more general multistage stochastic integer multicommodity flow problems.
Finally, we motivate the notion of reload costs that refer to variable (i.e., per unit of flow) costs for the usage of pairs of edges, as opposed to single edges. We highlight the practical and theoretical significance of these cost structures and present two extended graphs that allow us to easily capture these costs and generate strong formulations
Learning-Based Matheuristic Solution Methods for Stochastic Network Design
Cette dissertation consiste en trois Ă©tudes, chacune constituant un article de recherche.
Dans tous les trois articles, nous considérons le problème de conception de réseaux
multiproduits, avec coût fixe, capacité et des demandes stochastiques en tant que programmes
stochastiques en deux étapes. Dans un tel contexte, les décisions de conception
sont prises dans la première étape avant que la demande réelle ne soit réalisée, tandis
que les décisions de flux de la deuxième étape ajustent la solution de la première étape
à la réalisation de la demande observée. Nous considérons l’incertitude de la demande
comme un nombre fini de scénarios discrets, ce qui est une approche courante dans la
littérature. En utilisant l’ensemble de scénarios, le problème mixte en nombre entier
(MIP) résultant, appelé formulation étendue (FE), est extrêmement difficile à résoudre,
sauf dans des cas triviaux. Cette thèse vise à faire progresser le corpus de connaissances
en développant des algorithmes efficaces intégrant des mécanismes d’apprentissage en
matheuristique, capables de traiter efficacement des problèmes stochastiques de conception
pour des réseaux de grande taille.
Le premier article, s’intitulé "A Learning-Based Matheuristc for Stochastic Multicommodity
Network Design". Nous introduisons et décrivons formellement un nouveau
mécanisme d’apprentissage basé sur l’optimisation pour extraire des informations
concernant la structure de la solution du problème stochastique à partir de solutions
obtenues avec des combinaisons particulières de scénarios. Nous proposons ensuite
une matheuristique "Learn&Optimize", qui utilise les méthodes d’apprentissage pour
déduire un ensemble de variables de conception prometteuses, en conjonction avec un
solveur MIP de pointe pour résoudre un problème réduit.
Le deuxième article, s’intitulé "A Reduced-Cost-Based Restriction and Refinement
Matheuristic for Stochastic Network Design". Nous Ă©tudions comment concevoir efficacement
des mécanismes d’apprentissage basés sur l’information duale afin de guider la
détermination des variables dans le contexte de la conception de réseaux stochastiques.
Ce travail examine les coûts réduits associés aux variables hors base dans les solutions
déterministes pour guider la sélection des variables dans la formulation stochastique.
Nous proposons plusieurs stratégies pour extraire des informations sur les coûts réduits
afin de fixer un ensemble approprié de variables dans le modèle restreint. Nous proposons
ensuite une approche matheuristique utilisant des techniques itératives de réduction
des problèmes.
Le troisième article, s’intitulé "An Integrated Learning and Progressive Hedging
Method to Solve Stochastic Network Design". Ici, notre objectif principal est de concevoir
une méthode de résolution capable de gérer un grand nombre de scénarios. Nous
nous appuyons sur l’algorithme Progressive Hedging (PHA), ou les scénarios sont regroupés
en sous-problèmes. Nous intégrons des methodes d’apprentissage au sein de
PHA pour traiter une grand nombre de scénarios. Dans notre approche, les mécanismes
d’apprentissage developpés dans le premier article de cette thèse sont adaptés pour résoudre
les sous-problèmes multi-scénarios. Nous introduisons une nouvelle solution
de référence à chaque étape d’agrégation de notre ILPH en exploitant les informations
collectĂ©es Ă partir des sous problèmes et nous utilisons ces informations pour mettre Ă
jour les pénalités dans PHA. Par conséquent, PHA est guidé par les informations locales
fournies par la procédure d’apprentissage, résultant en une approche intégrée capable de
traiter des instances complexes et de grande taille.
Dans les trois articles, nous montrons, au moyen de campagnes expérimentales approfondies,
l’intérêt des approches proposées en termes de temps de calcul et de qualité
des solutions produites, en particulier pour traiter des cas très difficiles avec un grand
nombre de scénarios.This dissertation consists of three studies, each of which constitutes a self-contained
research article. In all of the three articles, we consider the multi-commodity capacitated
fixed-charge network design problem with uncertain demands as a two-stage stochastic
program. In such setting, design decisions are made in the first stage before the actual
demand is realized, while second-stage flow-routing decisions adjust the first-stage solution
to the observed demand realization. We consider the demand uncertainty as a finite
number of discrete scenarios, which is a common approach in the literature.
By using the scenario set, the resulting large-scale mixed integer program (MIP)
problem, referred to as the extensive form (EF), is extremely hard to solve exactly in
all but trivial cases. This dissertation is aimed at advancing the body of knowledge
by developing efficient algorithms incorporating learning mechanisms in matheuristics,
which are able to handle large scale instances of stochastic network design problems
efficiently.
In the first article, we propose a novel Learning-Based Matheuristic for Stochastic
Network Design Problems. We introduce and formally describe a new optimizationbased
learning mechanism to extract information regarding the solution structure of a
stochastic problem out of the solutions of particular combinations of scenarios. We subsequently
propose the Learn&Optimize matheuristic, which makes use of the learning
methods in inferring a set of promising design variables, in conjunction with a state-ofthe-
art MIP solver to address a reduced problem.
In the second article, we introduce a Reduced-Cost-Based Restriction and Refinement
Matheuristic. We study on how to efficiently design learning mechanisms based on dual
information as a means of guiding variable fixing in the context of stochastic network
design. The present work investigates how the reduced cost associated with non-basic
variables in deterministic solutions can be leveraged to guide variable selection within
stochastic formulations. We specifically propose several strategies to extract reduced
cost information so as to effectively identify an appropriate set of fixed variables within
a restricted model. We then propose a matheuristic approach using problem reduction techniques iteratively (i.e., defining and exploring restricted region of global solutions,
as guided by applicable dual information).
Finally, in the third article, our main goal is to design a solution method that is able
to manage a large number of scenarios. We rely on the progressive hedging algorithm
(PHA) where the scenarios are grouped in subproblems. We propose a two phase integrated
learning and progressive hedging (ILPH) approach to deal with a large number of
scenarios. Within our proposed approach, the learning mechanisms from the first study
of this dissertation have been adapted as an efficient heuristic method to address the
multi-scenario subproblems within each iteration of PHA.We introduce a new reference
point within each aggregation step of our proposed ILPH by exploiting the information
garnered from subproblems, and using this information to update the penalties. Consequently,
the ILPH is governed and guided by the local information provided by the
learning procedure, resulting in an integrated approach capable of handling very large
and complex instances.
In all of the three mentioned articles, we show, by means of extensive experimental
campaigns, the interest of the proposed approaches in terms of computation time and
solution quality, especially in dealing with very difficult instances with a large number
of scenarios
Approximating fluid schedules in packet-switched networks
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 145-151).We consider a problem motivated by the desire to provide exible, rate-based, quality of service guarantees for packets sent over switches and switch networks. Our focus is solving a type of on-line, traffic scheduling problem, whose input at each time step is a set of desired traffic rates through the switch network. These traffic rates in general cannot be exactly achieved since they treat the incoming data as fluid, that is, they assume arbitrarily small fractions of packets can be transmitted at each time step. The goal of the traffic scheduling problem is to closely approximate the given sequence of traffic rates by a sequence of switch uses throughout the network in which only whole packets are sent. We prove worst-case bounds on the additional delay and buffer use that result from using such an approximation. These bounds depend on the network topology, the resources available to the scheduler, and the types of fluid policy allowed.by Michael Aaron Rosenblum.Ph.D
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