Eficiencia Energética y Robustez en Problemas de Scheduling

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[EN] Many industrial problems can be modelled as a scheduling problem where some resources are assigned to tasks so as to minimize the completion time, to reduce the use of resources, idle time, etc. There are several scheduling problems which try to represent different kind of situations that can appear in real world problems. Job Shop Scheduling Problem (JSP) is the most used problem. In JSP there are different jobs, every job has different tasks and these tasks have to be executed by different machines. JSP can be extended to other problems in order to simulate more real problems. In this work we have used the problem job shop with operators JSO(n,p) where each task must also be assisted by one operator from a limited set of them. Additionally, we have extended the classical JSP to a job-shop scheduling problem where machines can consume different amounts of energy to process tasks at different rates (JSMS). In JSMS operation has to be executed by a machine that has the possibility to work at different speeds. Scheduling problems consider optimization indicators such as processing time, quality and cost. However, governments and companies are also interested in energy-consumption due to the rising demand and price of fuel, the reduction in energy commodity reserves and growing concern about global warming. In this thesis, we have developed new metaheuristic search techniques to model and solve the JSMS problem. Robustness is a common feature in real life problems. A system persists if it remains running and maintains his main features despite continuous perturbations, changes or incidences. We have developed a technique to solve the $JSO(n,p)$ problem with the aim of obtaining optimized and robust solutions. We have developed a dual model to relate optimality criteria with energy consumption and robustness/stability in the JSMS problem. This model is committed to protect dynamic tasks against further incidences in order to obtain robust and energy-aware solutions. The proposed dual model has been evaluated with a memetic algorithm to compare the behaviour against the original model. In the JSMS problem there are a relationship between Energy-efficiency, Robustness and Makespan. Therefore, the relationship between these three objectives is studied. Analytical formulas are proposed to analyse the relationship between these objectives. The results show the trade-off between makespan and robustness, and the direct relationship between robustness and energy-efficiency. To reduce the makespan and to process the tasks faster, energy consumption has to be increased. When the energy consumption is low it is because the machines are not working at highest speed. So, if an incidence appears, the speed of these machines can be increased in order to recover the time lost by the incidence. Hence robustness is directly related with energy consumption. Additionally, robustness is also directly related with makespan because, when makespan increases, there are more gaps in the solution, these incidences can be absorbed by these…