The scarcity of non-renewable energy sources, geopolitical problems in its supply, increasing prices, and the impact of climate change, force the global economy to develop more energy-efficient solutions for their operations. The Manufacturing sector is not excluded from this challenge as one of the largest consumers of energy. Energy-efficient scheduling is a method that attracts manufacturing companies to reduce their consumption as it can be quickly deployed and can show impact immediately. In this study, the hybrid flow shop scheduling problem with blocking constraint (BHFS) is investigated in which we seek to minimize the latest completion time (i.e. makespan) and overall energy consumption, a typical manufacturing setting across many industries from automotive to pharmaceutical. Energy consumption and the latest completion time of customer orders are usually conflicting objectives. Therefore, we first formulate the problem as a novel multi-objective mixed integer programming (MIP) model and propose an augmented epsilon-constraint method for finding the Pareto-optimal solutions. Also, an effective multi-objective metaheuristic algorithm. Refined Iterated Pareto Greedy (RIPG), is developed to solve large instances in reasonable time. Our proposed methods are benchmarked using small, medium, and large-size instances to evaluate their efficiency. Two well-known algorithms are adopted for comparing our novel approaches. The computational results show the effectiveness of our method.

In the flowshop problem, one has to schedule jobs, where each job has to follow the same route of machines. The goal is to find a job order that minimizes some criteria. The permutation flowshop, also called PFSP, is a common (and fundamental) variant that imposes the machines to process jobs in the same order (thus, a permutation of jobs is enough to describe a solution). The permutation flowshop has been one of the most studied problems in the literature [35, 30] and has been considered on various industrial applications [16, 42]. We may also note that the permutation flowshop is at the origin of multiple other variants, for instance, the blocking permutation flowshop [45], the multiobjective permutation flowshop [20], the distributed permutation flowshop [11], the no-idle permutation flowshop [31], the permutation flowshop with buffers [28] and many others. Regarding the criteria to minimize, we study in this paper, two of the most studied objectives: the makespan (minimizing the completion time of the last job on the last machine) and the flowtime (minimizing the sum of completion times of each job on the last machine).

A distinctive characteristic of combinatorial problems is their massive search space. This huge domain is due to the number of possible solutions that although finit e, grows exponentially with the amount of data. Some typical combinatorial problems are the search fo r the cheapest or shortest paths, internet data packets routing, protein structure prediction, and planni ng and scheduling of resources. In theory it is possible to find the optimal solution for each c ombinatorial problem by conducting an exhaustive search. However, in practice finding an optimal s olution is often an intractable problem, even for problems of modest size. In this paper, Answer Set Programming (ASP) is used to explor e how to solve the scheduling problem for an Automated Wet-etch Station (A WS) of a Semiconduct or Manufacturing System where the optimization objective is the makespan. If a robot is not use d to transfer jobs between baths, the problem can be approximated as a special case of the most general n o-wait scheduling flowshop problem. A flowshop is a multistage production process where all jobs m ust pass through the same stages. There is a set J of jobs with J N jobs in total.

The no-wait flowshop scheduling problem is a variant of the classical permutation flowshop problem, with the additional constraint that jobs have to be processed by the successive machines without waiting time. To efficiently address this NP-hard combinatorial optimization problem we conduct an analysis of the structure of good quality solutions. This analysis shows that the No-Wait specificity gives them a common structure: they share identical sub-sequences of jobs, we call super-jobs. After a discussion on the way to identify these super-jobs, we propose IG-SJ, an algorithm that exploits super-jobs within the state-of-the-art algorithm for the classical permutation flowshop, the well-known Iterated Greedy (IG) algorithm. An iterative approach of IG-SJ is also proposed. Experiments are conducted on Taillard's instances. The experimental results show that exploiting super-jobs is successful since IG-SJ is able to find 64 new best solutions.