Theoretical and computational advances in finite-size facility placement and assignment problems

The goal of this research is to develop fundamental theory and exact solution methods for the optimal placement of multiple, finite-size, rectangular facilities in presence of existing rectangular facilities, in a plane. Applications of this research can be found in facility layout (re)design in manufacturing, distribution systems, services (retail outlets, hospital floors, etc.), and printed circuit board design; where designing an efficient layout can save millions of dollars in operational costs. Main difficulty of this optimization problem lies in its continuous non-convex/non-concave feasible space, which makes it tough to escape local optimality. Through this research, novel approaches will be proposed which can be used to distill this continuous space into a finite set of candidate solutions, making it amenable to search for the global optimum. The first two parts of this research deal with establishing a unified theory for the finite-size facility placement problem and establishing the theory of dominance for pruning the sub-optimal solutions. Traditionally, the facility location/layout problems are modeled as the Quadratic Assignment Problem (QAP), which is strongly NP-hard. Also, for getting strong lower bounds in the dominance procedure, we may need to solve an instance of the NP-hard Quadratic Semi-Assignment Problem (QSAP). To this end, the third part of this research deals with investigating parallel and High Performance Computing (HPC) methods for solving the Linear Assignment Problem (LAP), which is an important sub-problem of the QAP. The final part of this research deals with investigating parallel and HPC methods for obtaining strong lower bounds and possibly solving large QAPs. Since QAP is known to be a computationally intensive problem, it should be noted that large in this context means problem instances with up to 30 facilities and locations

COLUMN GENERATION MODELS FOR OPTIMAL PACKAGE TOUR COMPOSITION

Our work aims to introduce a combinatorial optimization problem orbiting in Revenue Management, called Package Tour Composition (PTC) and to discuss its resolution with a mathematical programming method called column generation method. The classic Network Revenue Management problem considers a set of resources of finite capacity to be allocated to a set of products characterized by a given price and a given demand. The models of Network Revenue Management are applied by airline companies in order to decide how many seats to allocate on each flight leg (resource) to each fare (product) that is characterized by origin, destination and fare class. The model we propose aims to deal with a similar problem in which the demand is not expressed towards a set of products but towards a set of resources. This problem arises, for instance, in the composition of package tours where customer preferences towards events that compose a package tour are more relevant, and easier to be traced, than customer preferences for the whole package. In the PTC problem customers buy products that are bundles of resources in combinations under various terms and conditions. However demand is linked to resources not to products. The resource composition of each product is a decision variable. As a consequence product price is not known but is the sum of reservation prices of each resource in the bundle. The resource set is partitioned into several subsets corresponding to different resource types. A parameter states how many resources of each type characterize each product type. We refer to resources as 'events' and to products as 'package tours' or simply 'packages'. The resulting Package Tour Composition problem is a non-linear problem with integer variables that represent the number of tourists assigned to each package tour and binary variables that represent which events are assigned to each package tour. Each event is characterized by a reservation price, a demand and a capacity. Each package tour belongs to a package tour type that is characterized by its event type composition parameter. The number of tourists assigned to each event cannot exceed its actual capacity, which is defined as the minimuml value between the event capacity and the event demand. We also impose that the binary variables respect the composition constraint for every package tour according to its type. The objective function to be maximized is the total revenue, that is the number of packages to be sold times their price. We propose a column generation model to solve the linear relaxation of the Package Tour Composition problem. The Column Generation technique splits the problem in two sub-problems: the pricing problem and the master problem. The pricing problem dynamically generates, for every package type, several columns containing an event combination according to the package type composition parameter. The master problem chooses which event combinations to use and in which quantity, imposing that event actual capacity is respected, in order to maximize revenue. Chapter 1 concerns the motivation of our research. At first we analyze the previous literature on the theory of Revenue Management focusing our attention on the most important mathematical models that tackle two main Revenue Management problems: Single Resource Capacity Control and Network Capacity Control. We analyze the assumptions of these models to find improvement directions. After that, we present the state-of-the-art of mathematical models applied to tourist operators industry, in particular in the composition of tour itineraries. We propose a taxonomy to classify several possible Package Tour Composition problem formulations. In Chapter 2 the Package Tour Composition Model is formally defined and we propose the application of Column Generation method and a Column generation heuristics method to determine an optimal solution to the linear relaxation problem and a rounded solution to the integer problem. Two formulations are compared: the integer master formulation and the binary master formulation. Thereafter we present the dataset description and we display the results of integer and binary master formulations. In Chapter 3 we illustrate several extensions of the basic models. The extensions take into account market segmentation, inconvenience costs, tourist groups and stochastic demand. For each extension we present computational results obtained with the state-of-the-art mathematical programming solver CPLEX. Finally Chapter 4 presents some conclusions and possible future research directions

A Polyhedral Study of Mixed 0-1 Set

We consider a variant of the well-known single node fixed charge network flow set with constant capacities. This set arises from the relaxation of more general mixed integer sets such as lot-sizing problems with multiple suppliers. We provide a complete polyhedral characterization of the convex hull of the given set

Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization

International audienceThe Cologne-Twente Workshop (CTW) on Graphs and Combinatorial Optimization started off as a series of workshops organized bi-annually by either Köln University or Twente University. As its importance grew over time, it re-centered its geographical focus by including northern Italy (CTW04 in Menaggio, on the lake Como and CTW08 in Gargnano, on the Garda lake). This year, CTW (in its eighth edition) will be staged in France for the first time: more precisely in the heart of Paris, at the Conservatoire National d’Arts et Métiers (CNAM), between 2nd and 4th June 2009, by a mixed organizing committee with members from LIX, Ecole Polytechnique and CEDRIC, CNAM

Metaheuristics for the unit commitment problem : The Constraint Oriented Neighbourhoods search strategy

Tese de mestrado. Faculdade de Engenharia. Universidade do Porto. 199

A hybrid genetic approach to solve real make-to-order job shop scheduling problems

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro TecnologicoProcedimentos de busca local (ex. busca tabu) e algoritmos genéticos têm apresentado excelentes resultados em problemas clássicos de programação da produção em ambientes job shop. No entanto, estas abordagens apresentam pobres habilidades de modelamento e poucas aplicações com restrições de ambientes reais de produção têm sido publicadas. Além disto, os espaços de busca considerados nestas aplicações são nomlalmente incompletos e as restrições reais são poucas e dependentes do problema em questão. Este trabalho apresenta uma abordagem genética híbrida para resolver problemas de programação em ambientes job shop com grande número de restrições reais, tais como produtos com vários níveis de submontagem, planos de processamento altemativos para componentes e recursos alternativos para operações, exigência de vários recursos para executar uma operação (ex., máquina, ferramentas, operadores), calendários para todos os recursos, sobreposição de operações, restrições de disponibilidade de matéria-prima e componentes comprados de terceiros, e tempo de setup dependente da sequência de operações. A abordagem também considera funções de avaliação multiobjetivas. O sistema usa algoritmos modificados de geração de programação, que incorporam várias heurísticas de apoio à decisão, para obter um conjunto de soluções iniciais. Cada solução inicial é melhorada por um algoritmo de subida de encosta. Então, um algoritmo genético híbrido com procedimentos de busca local é aplicado ao conjunto inicial de soluções localmente ótimas. Ao utilizar técnicas de programação de alta perfomlance (heurísticas construtivas, procedimentos de busca local e algoritmos genéticos) em problemas reais de programação da produção, este trabalho reduziu o abismo existente entre a teoria e a prática da programação da produção

Mixed integer programming on transputers

Mixed Integer Programming (MIP) problems occur in many industries and their practical solution can be challenging in terms of both time and effort. Although faster computer hardware has allowed the solution of more MIP problems in reasonable times, there will come a point when the hardware cannot be speeded up any more. One way of improving the solution times of MIP problems without further speeding up the hardware is to improve the effectiveness of the solution algorithm used. The advent of accessible parallel processing technology and techniques provides the opportunity to exploit any parallelism within MIP solving algorithms in order to accelerate the solution of MIP problems. Many of the MIP problem solving algorithms in the literature contain a degree of exploitable parallelism. Several algorithms were considered as candidates for parallelisation within the constraints imposed by the currently available parallel hardware and techniques. A parallel Branch and Bound algorithm was designed for and implemented on an array of transputers hosted by a PC. The parallel algorithm was designed to operate as a process farm, with a master passing work to various slave processors. A message-passing harness was developed to allow full control of the slaves and the work sent to them. The effects of using various node selection techniques were studied and a default node selection strategy decided upon for the parallel algorithm. The parallel algorithm was also designed to take full advantage of the structure of MIP problems formulated using global entities such as general integers and special ordered sets. The presence of parallel processors makes practicable the idea of performing more than two branches on an unsatisfied global entity. Experiments were carried out using multiway branching strategies and a default branching strategy decided upon for appropriate types of MIP problem