The order selection and lot sizing problem in the make-to-order environment

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 subproblems. 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.

Formulações e algoritmos para o problema das p-medianas heterogêneo livre de penalidade

This work presents a new model for the Heterogeneous p-median Problem (HPM), proposed to recover the hidden category structures present in the data provided by a sorting task procedure, a popular approach to understand heterogeneous individual’s perception of products and brands. This new model is named as the Penalty-free Heterogeneous p-median Problem (PFHPM), a single-objective version of the original problem, the HPM. The main parameter in the HPM is also eliminated, the penalty factor. It is responsible for the weighting of the objective function terms. The adjusting of this parameter controls the way that the model recovers the hidden category structures present in data, and depends on a broad knowledge of the problem. Additionally, two complementary formulations for the PFHPM are shown, both mixed integer linear programming problems. From these additional formulations lower-bounds were obtained for the PFHPM. These values were used to validate a specialized Variable Neighborhood Search (VNS) algorithm, proposed to solve the PFHPM. This algorithm provided good quality solutions for the PFHPM, solving artificial generated instances from a Monte Carlo Simulation and real data instances, even with limited computational resources. Statistical analyses presented in this work suggest that the new algorithm and model, the PFHPM, can recover more accurately the original category structures related to heterogeneous individual’s perceptions than the original model and algorithm, the HPM. Finally, an illustrative application of the PFHPM is presented, as well as some insights about some new possibilities for it, extending the new model to fuzzy environments

Cooperative routing for collision minimization in wireless sensor networks

Cooperative communication has gained much interest due to its ability to exploit the broadcasting nature of the wireless medium to mitigate multipath fading. There has been considerable amount of research on how cooperative transmission can improve the performance of the network by focusing on the physical layer issues. During the past few years, the researchers have started to take into consideration cooperative transmission in routing and there has been a growing interest in designing and evaluating cooperative routing protocols. Most of the existing cooperative routing algorithms are designed to reduce the energy consumption; however, packet collision minimization using cooperative routing has not been addressed yet. This dissertation presents an optimization framework to minimize collision probability using cooperative routing in wireless sensor networks. More specifically, we develop a mathematical model and formulate the problem as a large-scale Mixed Integer Non-Linear Programming problem. We also propose a solution based on the branch and bound algorithm augmented with reducing the search space (branch and bound space reduction). The proposed strategy builds up the optimal routes from each source to the sink node by providing the best set of hops in each route, the best set of relays, and the optimal power allocation for the cooperative transmission links. To reduce the computational complexity, we propose two near optimal cooperative routing algorithms. In the first near optimal algorithm, we solve the problem by decoupling the optimal power allocation scheme from optimal route selection. Therefore, the problem is formulated by an Integer Non-Linear Programming, which is solved using a branch and bound space reduced method. In the second near optimal algorithm, the cooperative routing problem is solved by decoupling the transmission power and the relay node se- lection from the route selection. After solving the routing problems, the power allocation is applied in the selected route. Simulation results show the algorithms can significantly reduce the collision probability compared with existing cooperative routing schemes.

Optimal Capital Requirements in Financial Networks with Fire Sales

I explore and analyze a problem of finding the socially optimal capital requirements for financial institutions considering two distinct channels of contagion: direct exposures among the institutions, as represented by a network and fire sales externalities, which reflect the negative price impact of massive liquidation of assets.These two channels amplify shocks from individual financial institutions to the financial system as a whole and thus increase the risk of joint defaults amongst the interconnected financial institutions; this is often referred to as systemic risk. In the model, there is a trade-off between reducing systemic risk and raising the capital requirements of the financial institutions. The policymaker considers this trade-off and determines the optimal capital requirements for individual financial institutions. I provide a method for finding and analyzing the optimal capital requirements that can be applied to arbitrary network structures and arbitrary distributions of investment returns.

In particular, I first consider a network model consisting only of direct exposures and show that the optimal capital requirements can be found by solving a stochastic linear programming problem. I then extend the analysis to financial networks with default costs and show the optimal capital requirements can be found by solving a stochastic mixed integer programming problem. The computational complexity of this problem poses a challenge, and I develop an iterative algorithm that can be efficiently executed. I show that the iterative algorithm leads to solutions that are nearly optimal by comparing it with lower bounds based on a dual approach. I also show that the iterative algorithm converges to the optimal solution.

Finally, I incorporate fire sales externalities into the model. In particular, I am able to extend the analysis of systemic risk and the optimal capital requirements with a single illiquid asset to a model with multiple illiquid assets. The model with multiple illiquid assets incorporates liquidation rules used by the banks. I provide an optimization formulation whose solution provides the equilibrium payments for a given liquidation rule.

I further show that the socially optimal capital problem using the ``socially optimal liquidation" and prioritized liquidation rules can be formulated as a convex and convex mixed integer problem, respectively. Finally, I illustrate the results of the methodology on numerical examples and

discuss some implications for capital regulation policy and stress testing.

Shift Scheduling in Services When Employees Have Limited Availability: An L. P. Approach

This paper compares two linear programming (LP) models for shift scheduling in services where homogeneously-skilled employees are available at limited times. Although both models are based on set covering approaches, one explicitly matches employees to shifts, while the other imposes this matching implicitly. Each model is used in three forms—one with complete, another with very limited meal break placement flexibility, and a third without meal breaks—to provide initial schedules to a completion/improvement heuristic. The term completion/improvement heuristic is used to describe a construction/ improvement heuristic operating on a starting schedule. On 80 test problems varying widely in scheduling flexibility, employee staffing requirements, and employee availability characteristics, all six LP-based procedures generated lower cost schedules than a comparison from-scratch construction/improvement heuristic. This heuristic, which perpetually maintains an explicit matching of employees to shifts, consists of three phases which add, drop, and modify shifts. In terms of schedule cost, schedule generation time, and model size, the procedures based on the implicit model performed better, as a group, than those based on the explicit model. The LP model with complete break placement flexibility and implicitly matching employees to shifts generated schedules costing 6.7% less than those developed by the from-scratch heuristic.

Improving the Utilization of Front-Line Service Delivery System Personnel

There are two types of work typically performed in services which differ in the degree of control management has over when the work must be done. Serving customers, an activity that can occur only when customers are in the system is, by its nature, uncontrollable work. In contrast, the execution of controllable work does not require the presence of customers, and is work over which management has some degree of temporal control. This paper presents two integer programming models for optimally scheduling controllable work simultaneously with shifts. One model explicitly defines variables for the times at which controllable work may be started, while the other uses implicit modeling to reduce the number of variables. In an initial experiment of 864 test problems, the latter model yielded optimal solutions in approximately 81 percent of the time required by the former model. To evaluate the impact on customer service of having front-line employees perform controllable work, a second experiment was conducted simulating 5,832 service delivery systems. The results show that controllable work offers a useful means of improving labor utilization. Perhaps more important, it was found that having front-line employees perform controllable work did not degrade the desired level of customer service.

Schedulazione delle rotte marittime nel settore ortofrutticolo. Modelli e Metodi

Il trasporto marittimo è una delle modalità più utilizzate soprattutto per la movimentazione di grandi volumi di prodotti tra i continenti in quanto è a basso costo, sicuro e meno inquinante rispetto ad altri mezzi di movimentazione. Ai giorni nostri è responsabile di circa l’80% del commercio globale (in volume di carichi trasportati). Il settore del trasporto marittimo ha avuto una lunga tradizione di pianificazione manuale effettuata da progettisti esperti.
 L’obiettivo principale di questa trattazione è stato quello di implementare un modello matematico lineare (MILP, Mixed-Integer Linear Programming Model) per l’ottimizzazione delle rotte marittime nell’ambito del mercato orto-frutticolo che si sviluppa nel bacino del Mediterraneo (problema di Ship-Scheduling). Il modello fornito in questa trattazione è un valido strumento di supporto alle decisioni che può utilizzare uno spedizioniere nell’ambito della pianificazione delle rotte marittime della flotta di navi in suo possesso. Consente di determinare l’insieme delle rotte ottimali che devono essere svolte da un insieme di vettori al fine di massimizzare il profitto complessivo dello spedizioniere, generato nell’arco di tempo considerato. Inoltre, permette di ottenere, per ogni nave considerata, la ripartizione ottimale della merce (carico ottimale).

Discrete-time positive periodic systems with state and control constraints

The aim of this paper is to provide an efficient control design technique for discrete-time positive periodic systems. In particular, stability, positivity and periodic invariance of such systems are studied. Moreover, the concept of periodic invariance with respect to a collection of boxes is introduced and investigated with connection to stability. It is shown how such concept can be used for deriving a stabilizing state-feedback control that maintains the positivity of the closed-loop system and respects states and control signals constraints. In addition, all the proposed results can be efficiently solved in terms of linear programming.

Contribution à la planification tactique et opérationnelle du transport forestier

Cette thèse est une contribution à la modélisation, la planification et l’optimisation du transport pour l’approvisionnement en bois de forêt des industries de première transformation. Dans ce domaine, les aléas climatiques (mise au sol des bois par les tempêtes), sanitaires (attaques bactériologiques et fongiques des bois) et commerciaux (variabilité et exigence croissante des marchés) poussent les divers acteurs du secteur (entrepreneurs et exploitants forestiers, transporteurs) à revoir l’organisation de la filière logistique d’approvisionnement, afin d’améliorer la qualité de service (adéquation offre-demande) et de diminuer les coûts. L’objectif principal de cette thèse était de proposer un modèle de pilotage améliorant la performance du transport forestier, en respectant les contraintes et les pratiques du secteur. Les résultats établissent une démarche de planification hiérarchique des activités de transport à deux niveaux de décision, tactique et opérationnel. Au niveau tactique, une optimisation multi-périodes permet de répondre aux commandes en minimisant l’activité globale de transport, sous contrainte de capacité agrégée des moyens de transport accessibles. Ce niveau permet de mettre en œuvre des politiques de lissage de charge et d’organisation de sous-traitance ou de partenariats entre acteurs de transport. Au niveau opérationnel, les plans tactiques alloués à chaque transporteur sont désagrégés, pour permettre une optimisation des tournées des flottes, sous contrainte des capacités physiques de ces flottes. Les modèles d’optimisation de chaque niveau sont formalisés en programmation linéaire mixte avec variables binaires. L’applicabilité des modèles a été testée en utilisant un jeu de données industrielles en région Aquitaine et a montré des améliorations significatives d’exploitation des capacités de transport par rapport aux pratiques actuelles. Les modèles de décision ont été conçus pour s’adapter à tout contexte organisationnel, partenarial ou non : la production du plan tactique possède un caractère générique sans présomption de l’organisation, celle-ci étant prise en compte, dans un deuxième temps, au niveau de l’optimisation opérationnelle du plan de transport de chaque acteur.

Metodologia de otimização estocástica para coordenação eólico-fotovoltaica

Esta dissertação incide sobre o tema da coordenação entre sistemas eólicos e fotovoltaicos que participam no mercado de eletricidade. A incerteza da potência eólica e fotovoltaica é uma caraterística predominante nesta coordenação, devendo ser considerada no planeamento ótimo de sistemas eólico-fotovoltaicos. A fim de modelizar a incerteza é apresentada uma metodologia de otimização estocástica baseada em programação linear para maximizar o lucro esperado de uma empresa produtora de energia elétrica que participa no mercado diário. A coordenação entre sistemas eólicos e fotovoltaicos visa mitigar os desequilíbrios de energia, resultantes das ofertas horárias submetidas no mercado diário e, consequentemente, reduzir as penalizações financeiras. Os resultados da coordenação entre um sistema eólico e um sistema fotovoltaico são comparados com os resultados obtidos para a operação não coordenada. Estes resultados permitem concluir que a metodologia desenvolvida aplicada à coordenação apresenta um lucro esperado superior ao lucro obtido para a operação não coordenada; Abstract Stochastic Optimization Methodology for Wind-Photovoltaic Coordination This dissertation focuses on the issue of coordination between wind and photovoltaic systems participating in electricity markets. The uncertainty of wind and photovoltaic power is a main characteristic of these systems, which must be included in the optimal scheduling of the coordination of wind with photovoltaic systems. In order to model the uncertainty is presented a stochastic approach based on linear programming to maximize the profit of a wind photovoltaic power producer which participates in electricity markets. The coordination of wind with photovoltaic systems aims to mitigate the energy deviations, as a result of the participation in day-ahead market and therefore reducing economic penalties. The results obtained by the coordination are compared to results obtained by the separated operation of wind and photovoltaic systems. The results allow concluding that the proposed approach applied to the coordination presents an expected profit higher than the expected profit without coordination.

The suppliers selection problem: a case study

The effective supplier evaluation and purchasing processes are of vital importance to business organizations, making the suppliers selection problem a fundamental key issue to their success. We consider a complex supplier selection problem with multiple products where minimum package quantities, minimum order values related to delivery costs, and discounted pricing schemes are taken into account. Our main contribution is to present a mixed integer linear programming (MILP) model for this supplier selection problem. The model is used to solve several examples including three real case studies from an electronic equipment assembly company.

CLIMATE CHANGE ADAPTATION IN VULNERABLE CROP AND LIVESTOCK PRODUCTION SYSTEMS IN MGETA, TANZANIA

Increased occurrence of drought and dry spells during the growing season have resulted in increased interest in protection of tropical water catchment areas. In Mgeta, a water catchment area in the Uluguru Mountains in Tanzania, water used for vegetable and fruit production is provided through canals from the Uluguru South Forest Reserve. The clearing of forest land for cultivation in the steep slopes in the area is causing severe land degradation, which is threatening the water catchment area, livelihoods, and food security of the local communities, as well as the major population centers in the lowlands. In this paper, the economic performance of a traditional cropping-livestock system with East African (EA)-goats and pigs and extensive vegetable production is compared with a more sustainable and environmentally friendly crop-dairy goat production system. A linear programming (LP) crop-livestock model, maximizing farm income considering the environmental constraints in the area was applied for studying the economic performance of dairy goats in the production system. The model was worked out for the rainy and dry seasons and the analysis was conducted for a basic scenario representing the current situation, based on the variability in the 30 years period from 1982-2012, and in a scenario of both lower crop yields and increased crop variability due to climate change. Data obtained from a sample of 60 farmers that were interviewed using a questionnaire was used to develop and parameterize the model. The study found that in the steep slopes of the area, a crop-dairy goat system with extensive use of grass and multipurpose trees (MPTs) would do better than the traditional vegetable gardening with the EA goat production system. The crop-dairy goat system was superior both in the basic and in a climate change scenario since the yield variation of the grass and MPTs system was less affected compared to vegetable crops due to more tree cover and the use of perennial grasses. However, the goat milk production in the area was constrained by inadequate feeding and lack of an appropriate breeding program. Hence, farmers should enhance goat milk production by supplementing with more concentrate feed and by implementing goat-breeding principles. Moreover, policy measures to promote such a development are briefly discussed.

Utilização de inteligência competitiva, da gestão de riscos e da computação aplicada para ganhos de competitividade em instituição organizadora de concursos

Dissertação (mestrado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Ciência da Computação, 2015.