Le travail de ce mémoire apporte une brique fonctionnelle et théorique dans l'élaboration d'un outil informatique générique pour la planification automatisée et optimisée d'une équipe d'employés polyvalents avec une première application dans le domaine de la grande distribution. En pratique, il fournit la formalisation mathématique d'une problématique métier riche où les règles de planification (début, durée, fin, quantité, etc.) à respecter s’appliquent sur différentes granularité temporelle (quart d’heure, plage horaire, horaire journalier, semaine, mois, année). Différentes techniques issues de la Recherche Opérationnelle ont été adaptées et testées tout d’abord pour une version du problème restreint à une semaine, puis pour la version complète à l’année. Ces méthodes correspondent à des heuristiques basées sur la méthode de génération de colonnes où le problème de pricing est résolu par un algorithme dédié de programmation dynamique imbriquée. Les expérimentations ont été réalisées avec des instances issues de cas réels et des instances générées s’inspirant des cas réels comptant jusqu’à une soixantaine d’employés à planifier sur un horizon de planification allant d’une semaine à un an (divisé par périodes de 15 minutes). Les tests réalisés montrent que les méthodes implémentées permettent l’obtention de plannings d'équipe de grande qualité tout en préservant les caractéristiques individuelles de chaque employé (compétences, disponibilité, temps de travail, etc.), le tout utilisable avec un ordinateur de gamme moyenne (simple cœur, moins 4 GB de RAM) avec des temps de calcul raisonnables (quelques secondes à plusieurs heures selon l’instance et méthode). / The thesis provides a practical and theoretical brick for developing a generic software tool for producing automated and optimized schedules of a multi-skill employees team with a first application in retail. We provide a mathematical formulation of a rich staff scheduling problem in which planning rules (start, duration, end, amount, etc.) that must be respected are applied on different time granularity (15 minutes period, timeslot, day-shift, week, month, year). Two variants of the problem with different planning horizons have been considered: the first one with one week and the second one with one year planning horizon. Several methods from Operations Research have been adapted to solve the problem. We propose heuristics based on the column generation approach where the pricing problem is solved using a dedicated nested dynamic programming algorithm. The experiments were performed both on real-life instances and on random instances derived from real cases. Instances have up to sixty employees and a planning horizon from one week to one year (divided by 15 minutes periods). The tests show that the proposed methods are able to find high-quality team schedules while taking into account the individual characteristics of each employee (skills, availability, working time, etc.) and run with a standard PC (single core, less than 4 GB of RAM) with a reasonable computation time (from several seconds to one hour depending on the instance and the used method).

Universiẗat, Diss., 2005--Karlsruhe.

Pickup and delivery problems (PDPs) have been studied extensively in past decades. A wide variety of research exits on both exact algorithms and heuristics for generic variations of the problem as well as real-life applications, which continue to spark new challenges and open up new opportunities for researchers. In this dissertation, we study two variations of pickup and delivery problem that arise in industry and develop new computational methods that are shown to be effective with respect to existing algorithms and scheduling procedures found in practice. The first problem is the pickup and delivery problem with transshipment (PDPT). The work presented here was inspired by a daily route planning problem at a regional air carrier. In structuring the analysis, we describe a unique way to model the transshipment option on a directed graph. With the graph as the foundation, we implemented a branch and price algorithm. Preliminary results showed that it has difficulty in solving large instances. As an alternative, we developed a greedy randomized adaptive search procedure (GRASP) with several novel features. In the construction phase, shipment requests are inserted into routes until all demand is satisfied or no feasible insertion exists. In the improvement phase, an adaptive large neighborhood search algorithm is used to reconstruct portions of the feasible routes. Specialized removal and insertion heuristics were designed for this purpose. We also developed a procedure for generating problem instances in the absence of any in the literature. Testing was done on existing PDP data sets and generated PDPT data set. For the former, the performance and solution quality of the GRASP were comparable to the best known heuristics. For the latter, GRASP found the near optimal solution in most test cases. In the second part of the dissertation, we focus on a new version of the heterogeneous PDP in which the capacity of each vehicle can be modified by reconfiguring its interior to satisfy different types of customer demands. The work was motivated by a daily route planning problem arising at a senior activity center. A fleet of configurable vans is available each day to transport participants to and from the center as well as to secondary facilities for rehabilitative and medical treatment. To find solutions, we developed a two-phase heuristic that makes use of ideas from greedy randomized adaptive search procedures with multiple starts. In phase I, a set of good feasible solutions is constructed using a series of randomized procedures. A representative subset of those solutions is selected as candidates for improvement by solving a max diversity problem. In phase II, an adaptive large neighborhood search (ALNS) heuristic is used to find local optima by reconstructing portions of the feasible routes. Also, a specialized route feasibility check with vehicle type reassignment is introduced to take full advantage of the heterogeneous nature of vehicles. The effectiveness of the proposed methodology is demonstrated by comparing the solutions it provided for the equivalent of several weeks with those that were used in practice and derived manually. The analysis indicates that anywhere from 30% to 40% savings can be achieved with the multi-start ALNS heuristic. An exact method is introduced based on branch and price and cut for settings with more restricted time windows. In the procedure, the master problem at each node in the search tree is solved by column generation to find a lower bound. To improve the bound, subset-row inequalities are applied to the variables of the master problem. Columns are generated by solving the pricing subproblems with a labeling algorithm enhanced by new dominance conditions. Local search on the columns is used to quickly find promising alternatives. Implementation details and ways to improve the performance of the overall procedure are discussed. Testing was done on a set of real instances as well as a set of randomly generated instances with up to 50 customer requests. The results show that optimal solutions are obtained in majority of cases. / text

Zugl.: Diss.

This thesis describes a stochastic ship routing problem with inventory management. The problem involves finding a set of least costs routes for a fleet of ships transporting a single commodity when the demand for the commodity is uncertain. Storage at consumption and supply ports is limited and inventory levels are monitored in the model. Consumer demands are at a constant rate within each time period in the deterministic problem, and in the stochastic problem, the demand rate for a period is not known until the beginning of that period. The demand situation in each time period can be described by a scenario tree with corresponding probabilities. Several possible solution approaches for solving the problem are studied in the thesis. This problem can be formulated as a mixed integer programming (MIP) model. However solving the problem this way is very time consuming even for a deterministic problem with small problem size. In order to solve the stochastic problem, we develop a decomposition formulation and solve it using a Branch and Price framework. A master problem (set partitioning with extra inventory constraints) is built, and the subproblems, one for each ship, involve solving stochastic dynamic programming problems to generate columns for the master problem. Each column corresponds to one possible tree of schedules for one ship giving the schedule for the ship for all demand scenarios. In each branch-and-bound node, the node problem is solved by iterating between the master problem and the subproblems. Dual variables can be obtained solving the master problem and are used in the subproblems to generate the most promising columns for the master problem. Computational results are given showing that medium sized problems can be solved successfully. Several extensions to the original model are developed, including a variable speed model, a diverting model, and a model which allows ships to do extra tasks in return for a bonus. Possible solution approaches for solving the variable speed and the diverting model are presented and computational results are given.

The maximum weight-independent set problem (MWISP) is one of the most well-known and well-studied NP-hard problems in the field of combinatorial optimization. In the first part of the dissertation, I explore efficient branch-and-price (B&P) approaches to solve MWISP exactly. B&P is a useful integer-programming tool for solving NP-hard optimization problems. Specifically, I look at vertex- and edge-disjoint decompositions of the underlying graph. MWISP’s on the resulting subgraphs are less challenging, on average, to solve. I use the B&P framework to solve MWISP on the original graph G using these specially constructed subproblems to generate columns. I demonstrate that vertex-disjoint partitioning scheme gives an effective approach for relatively sparse graphs. I also show that the edge-disjoint approach is less effective than the vertex-disjoint scheme because the associated DWD reformulation of the latter entails a slow rate of convergence. In the second part of the dissertation, I address convergence properties associated with Dantzig-Wolfe Decomposition (DWD). I discuss prevalent methods for improving the rate of convergence of DWD. I also implement specific methods in application to the edge-disjoint B&P scheme and show that these methods improve the rate of convergence. In the third part of the dissertation, I focus on identifying new cut-generation methods within the B&P framework. Such methods have not been explored in the literature. I present two new methodologies for generating generic cutting planes within the B&P framework. These techniques are not limited to MWISP and can be used in general applications of B&P. The first methodology generates cuts by identifying faces (facets) of subproblem polytopes and lifting associated inequalities; the second methodology computes Lift-and-Project (L&P) cuts within B&P. I successfully demonstrate the feasibility of both approaches and present preliminary computational tests of each.

No description available.

Nas últimas décadas, diversas propostas de técnicas e de processos visando aumentar a sustentabilidade da agricultura ganharam evidência. Tais propostas geram novos modelos de planejamento em que devem ser considerados aspectos técnicos e ecológicos de produção, bem como o acesso de pequenos agricultores familiares ao mercado consumidor. Neste tipo de planejamento da produção, a rotação de culturas desempenha um papel fundamental, pois contribui para a manutenção dos recursos produtivos, para a minimização do uso de recursos não-renováveis e para o controle biológico da população de herbívoros, patógenos e plantas espontâneas. Nesta tese abordamos dois problemas de Programação de Rotação de Culturas (PRC) focados na produção de base sustentável de hortaliças: o problema de PRC com restrições de Adjacências (PRC-A) e o problema de PRC com atendimento da Demanda (PRC-D). O planejamento da produção de hortaliças é complexo pois envolve, em geral, um grande número de culturas com limitações específicas quanto à época de plantio e com períodos de cultivo e produtividades muito variáveis. A programação de rotação de culturas para as áreas de plantio é formulada como um modelo de otimização 01 e, para os dois problemas, em cada programação considera se tanto aspectos técnicos (época de plantio e colheita etc.) quanto ecológicos (adubação verde, pousio etc.). No problema PRC-A o objetivo é a maximização da ocupação das áreas produtivas em que as restrições de plantio são estendidas às áreas adjacentes. Como a formulação matemática para o problema tem, em geral, um número muito grande de restrições e variáveis, com matriz de restrições esparsa e bloco-diagonal, o modelo é reformulado com a Decomposição DantzigWolfe, o que permitiu sua resolução por procedimentos baseados em geração de colunas, heurísticos e exatos. No problema PRC-D desejase suprir a demanda de um conjunto de hortaliças tendo-se disponível um conjunto de áreas heterogêneas. As culturas passíveis de plantio, bem como as suas produtividades, dependem da área considerada. O problema foi formulado como um modelo de otimização linear em que cada variável está associada a uma programação de rotação de culturas. O modelo contém potencialmente um número grande de programações de rotação e é resolvido por geração de colunas. Experimentos computacionais usando instâncias baseadas em dados reais confirmam a eficácia dos modelos e das metodologias propostos para os problemas / Over the last decades, various proposals for techniques and processes to increase agricultural sustainability have been put forward. These proposals bring new planning models in which technical and ecological production aspects must be considered, as well as the access of small farmers to the consumer market. In this type of agricultural production planning, crop rotation plays a fundamental role as it contributes to maintaining productive resources, to reducing the use of non-renewable resources, and to biologically controlling the population of herbivores, pathogens and spontaneous plants. In this thesis, two problems concerning the Crop Rotation Schedule (CRS) focusing on sustainable production vegetables are addressed: the problem of the CRS having Adjacent constraints (CRS-A) and the problem of the CRS under Demand constraints (CRS-D). Production planning of vegetables is complex as it generally involves a large number of crop species having specific limitations regarding the planting season and very varied production times and productivity. The crop rotation schedule problem is formulated as an optimization model 0-1, and for both problems, in each schedule technical (planting and harvesting season etc.) and ecological (green manure, fallow etc.) aspects are considered. Concerning the CRS-A problem, the aim is to maximize the occupation of cropping areas in which planting constraints are extended to adjacent areas. As the mathematical formulation for the problem generally has a large number of restrictions and variables and the structure of the constraint matrix of the problem is sparse and block-diagonal, the model has been reformulated using the Dantzig-Wolfe Decomposition strategy, which has enabled the use of a heuristic and exact procedures based on the column generation approach for its resolution. In the CRS-D problem, the aim is to meet the market demands for vegetables having a set of heterogeneous cropping areas available. The potential planting crops, as well as their productivity, depend on the considered cropping area. The problem is formulated as an optimization linear model in which each variable is associated to a crop rotation schedule. The model may include a large number of rotation schedules and is solved by the column generation approach. Computational experiments using instances based on real-world data confirm the efficiency of models and methodologies proposed for the problems

This study considers a vehicle routing problem with time windows, accessibility restrictions on customers and a fleet that is heterogeneous with regard to capacity, average speed and cost. A vehicle can perform multiple routes per day, all starting and ending at a single depot, and it is assigned to a single driver, whose total work hours are limited. The available fleet is divided into an owned fleet, for which a variable cost is incurred, and a chartered fleet, for which only a fixed cost is incurred for each vehicle used. A column generation algorithm embedded in a branch-and-bound framework is proposed. The column generation pricing subproblem required a specific elementary shortest path problem with resource constraints algorithm to address the possibility for each vehicle performing multiple routes per day and to address the need to determine the workdays start time within the planning horizon. To make the algorithm efficient, a constructive heuristic and a learning metaheuristic algorithm based on tabu search were also developed. Both were used on branch-and-bound tree nodes to generate a good initial solution to the linear restricted master problem; particularly, to find a good initial primal bound to the branch-and-bound tree. / Este estudo aborda um problema de roteirização de veículos com janelas de tempo, restrições de acessibilidade nos clientes e uma frota que é heterogênea em relação à capacidade de carga, velocidade média de deslocamento e custo. Um veículo pode percorrer múltiplas rotas por dia, todas começando e terminando em um mesmo depósito, e está designado a um único motorista, cujo total de horas trabalhadas no dia está limitado a um valor máximo. A frota disponível é dividida em uma frota própria, para a qual um custo variável é incorrido, e uma frota de freteiros, para a qual apenas um custo fixo é incorrido para cada veículo utilizado. Um algoritmo baseado em geração de colunas, integrado a um procedimento de branch-and-bound, é proposto neste estudo. O subproblema de precificação da geração de colunas requereu um algoritmo específico para o problema do caminho mínimo elementar com restrições sobre recursos capaz de lidar com a possibilidade de cada veículo percorrer múltiplas rotas por dia e capaz de lidar com a necessidade de determinar o instante de início do dia de trabalho do motorista dentro do horizonte de planejamento. Para tornar o algoritmo eficiente, uma heurística construtiva e uma heurística de melhoria baseada em busca tabu também foram desenvolvidos. Ambos são utilizados nos nós da árvore de branch-and-bound para gerar boas soluções iniciais para o problema mestre restrito da geração de colunas; particularmente, para encontrar um bom limitante primal inicial para a árvore de branch-and-bound.

This study considers a vehicle routing problem with time windows, accessibility restrictions on customers and a fleet that is heterogeneous with regard to capacity, average speed and cost. A vehicle can perform multiple routes per day, all starting and ending at a single depot, and it is assigned to a single driver, whose total work hours are limited. The available fleet is divided into an owned fleet, for which a variable cost is incurred, and a chartered fleet, for which only a fixed cost is incurred for each vehicle used. A column generation algorithm embedded in a branch-and-bound framework is proposed. The column generation pricing subproblem required a specific elementary shortest path problem with resource constraints algorithm to address the possibility for each vehicle performing multiple routes per day and to address the need to determine the workdays start time within the planning horizon. To make the algorithm efficient, a constructive heuristic and a learning metaheuristic algorithm based on tabu search were also developed. Both were used on branch-and-bound tree nodes to generate a good initial solution to the linear restricted master problem; particularly, to find a good initial primal bound to the branch-and-bound tree. / Este estudo aborda um problema de roteirização de veículos com janelas de tempo, restrições de acessibilidade nos clientes e uma frota que é heterogênea em relação à capacidade de carga, velocidade média de deslocamento e custo. Um veículo pode percorrer múltiplas rotas por dia, todas começando e terminando em um mesmo depósito, e está designado a um único motorista, cujo total de horas trabalhadas no dia está limitado a um valor máximo. A frota disponível é dividida em uma frota própria, para a qual um custo variável é incorrido, e uma frota de freteiros, para a qual apenas um custo fixo é incorrido para cada veículo utilizado. Um algoritmo baseado em geração de colunas, integrado a um procedimento de branch-and-bound, é proposto neste estudo. O subproblema de precificação da geração de colunas requereu um algoritmo específico para o problema do caminho mínimo elementar com restrições sobre recursos capaz de lidar com a possibilidade de cada veículo percorrer múltiplas rotas por dia e capaz de lidar com a necessidade de determinar o instante de início do dia de trabalho do motorista dentro do horizonte de planejamento. Para tornar o algoritmo eficiente, uma heurística construtiva e uma heurística de melhoria baseada em busca tabu também foram desenvolvidos. Ambos são utilizados nos nós da árvore de branch-and-bound para gerar boas soluções iniciais para o problema mestre restrito da geração de colunas; particularmente, para encontrar um bom limitante primal inicial para a árvore de branch-and-bound.