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This study is about contract evaluation and selection in an environment where there exist two or more parties, namely a producer and one or more outsourcing companies offering different contract options. The producer faces dynamic deterministic demand, which is known at the beginning of the planning horizon, and has to decide on the quantities of production, outsourcing, inventory carrying, and backorder. Among these decisions, the producer has the opportunity of subcontracting from a set of options offered by the subcontractors with possibly distinct contract terms. The contract options are in terms of length of the contract, fixed and variable costs associated with order placed, delivery lead-time and capacity guaranteed for use. A mathematical model is used for the evaluation of available options and for the selection of the ones in order to minimize cost incurred by the producer. The model provides desired quantities of production, inventory carrying and backorder, and also determines how different contract options will beused through the planning horizon. Extensive experimentation is performed using different factors affecting the optimal solution of the model in specific instances. These results are used in order to come up with a framework where various contracting schemes for subcontracting can be obtained. This framework can assist the producer in the decision of alternative courses of actions to be taken by him as a function of contract terms.

In this paper we study sensitivity analysis of the uncapacitated single level economic lot-sizing problem, which was introduced by Wagner and Whitin about thirty years ago. In particular we are concerned with the computation of the maximal ranges in which the numerical problem parameters may vary individually, such that a solution already obtained remains optimal. Only recently it was discovered that faster algorithms than the Wagner-Whitin algorithm exist to solve the economic lot-sizing problem. Moreover, these algorithms reveal that the problem has more structure than was recognized so far. When performing the sensitivity analysis we exploit these newly obtained insights.

Inventory control problems constitute one of the most important research problems due to their connection with real life applications. Naturally, real life is full of uncertainty so are the most of the inventory problems. Unfortunately, it is a very challenging task to manage inventories effectively especially under uncertainty. This dissertation mainly deals with single-item, periodic review, and stochastic dynamic inventory control problems particularly on replenishment cycle control rule known as the (R, S) policy. Contribution of this thesis is multiold. In each chapter a particular research question is investigated. At the end of the day, we will be showing that non-stationary (R, S) policies are indispensable not only for its cost efficiency but its effectiveness and practicality. More specifically, the non-stationary (R, S) policy provides a convenient, efficient, effective, and modular solution for non-stationary stochastic inventory control problems.

Le principal objet de cet thèse réside dans la modélisation et l’optimisation de services de transport à la demande aussi différents soient-ils (ou seront-ils). Les techniques de supervision doivent alors pouvoir supporter différents objectifs et différentes contraintes pour s’adapter aux services actuels et futurs. Ainsi, ce rapport de thèse développe différentes variantes du DARP - ang. Dial-a-Ride Problem -, le problème de Recherche Opérationnelle modélisant et optimisant un service classique de transport à la demande. Le DARP standard a été étendu de façon à prendre en compte des hypothèses de fonctionnement prometteuses, comme le fait de séparer les composants d’une même requête pour les dispatcher sur des véhicules différents ou encore la présence de mécanismes d’intermodalité. Cette thèse permet également d’inscrire les véhicules autonomes tels que les VIPA dans de nouvelles problématiques de la Recherche Opérationnelle tout en restant dans le domaine du transport à la demande. La modélisation puis l’optimisation de ces systèmes permet de créer les plannings de ces nouveaux véhicules. A long terme, l’évolution technologique devrait permettre de ne plus se soucier du fait qu’ils sont automatiques. Ces travaux tentent de fournir un cadre suffisamment générique permettant à la fois de fournir une solution exploitable aujourd’hui et qui soit adaptable demain. / The main objective of the thesis is modeling and optimization of several on-demand transportation services. Supervision techniques must be able to handle numerous criteria and numerous constraints to adapt to the current and future services. Thus, this research develops several types of DARP - Dial-a-Ride Problem -, the operation research problem modeling and optimizing an on-demand transportation system. The standard DARP has been adapted to promising systems, such as those allowing to split the components of the same request and the possibility to dispatch them on different vehicles or the presence of intermodal mechanisms. This thesis also formulates new Operations Research problems in order to integrate autonomous vehicles such as the VIPA in an optimized on-demand transportation system. Modeling and optimizing these systems create schedules of these new vehicles. In the future, technological evolutions are expected and the automatic feature of the vehicles will not be taken into account anymore. These studies attempt to provide a generic framework in order to provide a usable tool for today and an adaptable tool for tomorrow.

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Segundo uma pesquisa recente realizada junto ao setor de fundições, uma importante preocupação do setor é melhorar seu planejamento de produção. Um plano de produção em uma fundição envolve duas etapas interdependentes: a determinação das ligas a serem fundidas e dos lotes que serão produzidos. Neste trabalho, estudamos o problema de dimensionamento de lotes para fundições de pequeno porte, cujo objetivo é determinar um plano de produção de mínimo custo. Como sugerido na literatura, a heurística proposta trata as etapas do problema de forma hierárquica: inicialmente são definidas as ligas e, posteriormente, os lotes que são produzidos a partir delas. Para a solução do problema, propomos um algoritmo genético que explora um conjunto de possibilidades para a determinação das ligas e utiliza uma heurística baseada em relaxação lagrangiana para determinação dos itens a serem produzidos. Além disso, uma abordagem para o mesmo problema é proposta utilizando o problema da mochila para determinar os itens a serem produzidos. Bons resultados foram obtidos pelos métodos propostos / According to a recent research made by the foundry sector, one of the most concern of the industry is to improve its production planning. A foundry production plan involves two independent stages: the determination of alloys to be merged and the lots that will be produced. In this work, we studied the lot-sizing problem for small foundries, whose purpose is to determine a plan of minimum production cost. As suggested in the literature, the heuristic proposed addresses the problem stages in a hierarchical way: rst we dene the alloys and, subsequently, the lots that are produced from them. We propose a genetic algorithm that explores some possible sets of alloys produced and uses a Lagrangian heuristic to determine the items to be produced. Also, we propose one approach to the same problem that uses the knapsack problem to determine the items to be produced. Good results were obtained by the methods proposed

A partial description of the convex hull of solutions to the economic lot-sizing problem with start-up costs (ELSS) has been derived recently. Here a larger class of valid inequalities is given and it is shown that these inequalities describe the convex hull of ELSS. This in turn proves that a plant location formulation as a linear program solves ELSS. Finally a separation algorithm is given.

Based on the recent successes in stochastic linear programming and mixed integer programming, in this thesis we combine these two important areas of mathematical programming; specifically we study stochastic integer programming. We first study a simple and important stochastic integer programming problem, called stochastic uncapacitated lot-sizing (SLS), which is motivated by production planning under uncertainty. We describe a multi-stage stochastic integer programming formulation of the problem and develop a family of valid inequalities, called the (Q, S) inequalities. We establish facet-defining conditions and show that these inequalities are sufficient to describe the convex hull of integral solutions for two-period instances. A separation heuristic for (Q, S) inequalities is developed and incorporated into a branch-and-cut algorithm. A computational study verifies the usefulness of the inequalities as cuts. Then, motivated by the polyhedral study of (Q, S) inequalities for SLS, we analyze the underlying integer programming scheme for general stochastic integer programming problems. We present a scheme for generating new valid inequalities for mixed integer programs by taking pair-wise combinations of existing valid inequalities. The scheme is in general sequence-dependent and therefore leads to an exponential number of inequalities. For some special cases, we identify combination sequences that lead to a manageable set of all non-dominated inequalities. For the general scenario tree case, we identify combination sequences that lead to non-dominated inequalities. We also analyze the conditions such that the inequalities generated by our approach are facet-defining and describe the convex hull of integral solutions. We illustrate the framework for some deterministic and stochastic integer programs and we present computational results which show the efficiency of adding the new generated inequalities as cuts.

This research is motivated by the need for considering lot sizing while accepting customer orders in a make-to-order (MTO) environment, in which each customer order must be delivered by its due date. Job shop is the typical operation model used in an MTO operation, where the production planner must make three concurrent decisions; they are order selection, lot size, and job schedule. These decisions are usually treated separately in the literature and are mostly led to heuristic solutions. The first phase of the study is focused on a formal definition of the problem. Mathematical programming techniques are applied to modeling this problem in terms of its objective, decision variables, and constraints. A commercial solver, CPLEX is applied to solve the resulting mixed-integer linear programming model with small instances to validate the mathematical formulation. The computational result shows it is not practical for solving problems of industrial size, using a commercial solver. The second phase of this study is focused on development of an effective solution approach to this problem of large scale. The proposed solution approach is an iterative process involving three sequential decision steps of order selection, lot sizing, and lot scheduling. A range of simple sequencing rules are identified for each of the three sub-problems. Using computer simulation as the tool, an experiment is designed to evaluate their performance against a set of system parameters. For order selection, the proposed weighted most profit rule performs the best. The shifting bottleneck and the earliest operation finish time both are the best scheduling rules. For lot sizing, the proposed minimum cost increase heuristic, based on the Dixon-Silver method performs the best, when the demand-to-capacity ratio at the bottleneck machine is high. The proposed minimum cost heuristic, based on the Wagner-Whitin algorithm is the best lot-sizing heuristic for shops of a low demand-to-capacity ratio. The proposed heuristic is applied to an industrial case to further evaluate its performance. The result shows it can improve an average of total profit by 16.62%. This research contributes to the production planning research community with a complete mathematical definition of the problem and an effective solution approach to solving the problem of industry scale.