6 research outputs found
A tighter continuous time formulation for the cyclic scheduling of a mixed plant
Get PDFAbstract In this paper, based on the cyclic scheduling formulation of Schilling and Pantelides [22], we propose a continuous time mixed integer linear programming (MILP) formulation for the cyclic scheduling of a mixed plant, i.e. a plant composed of batch and continuous tasks. The cycle duration is a variable of the model and the objective is to maximize productivity. By using strengthening techniques and the analysis of small polytopes related to the problem formulation, we strengthen the initial formulation by tightening some initial constraints and by adding valid inequalities. We show that this strengthened formulation is able to solve moderate size problems quicker than the initial one. However, for real size cases, it remains difficult to obtain the optimal solution of the scheduling problem quickly. Therefore, we introduce MILP-based heuristic methods in order to solve these larger instances, and show that they can provide quite good feasible solutions quickly
Applications of Mathematical Programming in Personnel Scheduling
Get PDFIn the few decades of its existence, mathematical programming has evolved into an important branch of operations research and management science. This thesis consists of four papers in which we apply mathematical programming to real-life personnel scheduling and project management problems. We develop exact mathematical programming formulations. Furthermore, we propose effective heuristic strategies to decompose the original problems into subproblems that can be solved effciently with tailored mathematical programming formulations. We opt for solution methods that are based on mathematical programming, because their advantages in practice are a) the exibility to easily accommodate changes in the problem setting, b) the possibility to evaluate the quality of the solutions obtained, and c) the possibility to use general-purpose solvers, which are often the only software available in practice
Modelos e métodos de optimização para problemas de planeamento e gestão integrada de operações
Get PDFTese de Doutoramento em Engenharia Industrial e de SistemasA resolução de problemas de optimização de processos no domínio da gestão de
cadeias de abastecimento tende cada vez mais a ser feita numa perspectiva integrada.
O objectivo é obter uma solução global que seja melhor do que aquela que é obtida
quando os problemas são resolvidos de forma independente. Atendendo a este facto,
esta tese tem como objectivo analisar e propor modelos de programação inteira
para a resolução de três problemas práticos de optimização integrada em cadeias
de abastecimento: o problema combinado de corte e escalonamento, o problema
integrado de planeamento e escalonamento e o problema de encaminhamento de
veículos com múltiplas rotas e gestão integrada de inventários.
Para o problema combinado de corte e escalonamento, foi proposto um modelo
de afectação que foi reforçado através de desigualdades obtidas utilizando funções
duais válidas. Um novo modelo pseudo-polinomial exacto de fluxos em rede foi
também proposto. Este modelo foi posteriormente revisto recorrendo-se à agregação
de intervalos de tempo, e resolvido através de heurísticas. Os testes computacionais
demonstraram a qualidade das abordagens tanto em termos das soluções obtidas
como dos tempos de resolução.
Para o problema integrado de planeamento e escalonamento, foi proposto um
novo modelo pseudo-polinomial de fluxos em rede. Foram exploradas estratégias de
redução para diminuir o número de restrições do modelo, cujos resultados supera-
ram os obtidos com outros modelos existentes. Nas instâncias com intervalos de
optimalidade elevados, foram testadas duas heurísticas utilizando diferentes tipos
de critérios de parâmetros e ordenação. As heurísticas consistiram na fixação de
variáveis segundo critérios alternativos, tendo como objectivo reduzira dimensão do
modelo, tornando-o mais fácil de resolver.
Por último, para o problema de encaminhamento de veículos com múltiplas rotas
e gestão integrada de inventários, foi proposto outro modelo pseudo-polinomial de
fluxos em rede, que implica a enumeração de todas as rotas válidas. Para analisar
a qualidade deste modelo, foram testados diferentes parâmetros com o objectivo
de se determinar a influência dos mesmo na construção das rotas e na solução fi-
nal. Os testes computacionais realizados mostraram que é possível resolver até à
optimalidade instâncias com até 50 clientes.Este trabalho foi financiado por Fundos FEDER através do Programa Operacional Factores de Competitividade COMPETE e por Fundos Nacionais através da FCT Fundação para a Ciência e a Tecnologia no âmbito do projecto PTDC/EGE-GES/116676/2010 (Ref. COMPETE: FCOMP-01-0124-FEDER-020430).The resolution of optimization problems in the field of supply chain management
in an integrated perspective has been increasingly used. The goal is to get a global
solution that is better than the one that is obtained when the problems are solved
independently. With this in mind, integer programming models are proposed and
analyzed in this thesis to solve three practical problems in an integrated optimization
of supply chains: the combined cutting stock and scheduling problem, the integrated
planning and scheduling problem and the integrated inventory routing problem with
multiple routes.
For the combined cutting stock and scheduling problem, an assignment model
is proposed and strengthened by using cutting planes obtained from dual-feasible
functions. A new exact pseudo-polynomial network flow model is also proposed.
This model is later revised using the aggregation of time intervals, and solved by
heuristics. The quality of the tested approaches is confirmed by the computational
results.
For the integrated planning and scheduling problem, a new pseudo-polynomial
network flow model is also developed. In order to reduce the number of constraints
in the model, reduction strategies were applied. This model was able to obtain
better results than other existing ones from the literature. In instances with high
optimality gaps two heuristics using different parameters and sorting criteria are
tested. The heuristics consist in fixing variables with alternative criteria, aiming to
reduce the model size and therefore making it easier to be solved.
Finally, for the integrated inventory routing problem with multiple routes, another
pseudo-polynomial network flow model is proposed. This model is based on the enu-
meration of all feasible routes. To analyze the quality of this model, tests were per-
formed on some parameters that were changed in order to determine their influence
in the construction of these routes and in the final solution. The computational tests
show that it is possible to solve to optimality instances with up to 50 customers
