In the context of Industry 4.0, data management is a key point for decision aid approaches. Large amounts of manufacturing digital data are collected on the shop floor. Their analysis can then require a large amount of computing power. The Big Data issue can be solved by aggregation, generating smart and meaningful data. This paper presents a new knowledge-based multi-level aggregation strategy to support decision making. Manufacturing knowledge is used at each level to design the monitoring criteria or aggregation operators. The proposed approach has been implemented as a demonstrator and successfully applied to a real machining database from the aeronautic industry. Decision Making; Machining; Knowledge based system

This chapter presents the "group of permutable jobs" structure to represent set of solutions to disjunctive scheduling problems. Traditionally, solutions to disjunctive scheduling problems are represented by assigning sequence of jobs to each machine. The group of permutable jobs structure assigns an ordered partition of jobs to each machine, i.e. a group sequence. The permutation of jobs inside a group must be all feasible with respect to the problem constraints. Such a structure provides more flexibility to the end user and, in particular, allows a better reaction to unexpected events. The chapter considers the robust scheduling framework where uncertainty is modeled via a discrete set of scenarios, each scenario specifying the problem parameters values. The chapter reviews the models and algorithms that have been proposed in the literature for evaluating a group sequence with respect to scheduling objectives for a fixed scenario as well as the recoverable robust optimization methods that have been proposed for generating robust group sequence5) M 2 (4) 7 0 2 4 Fig. 9.9: Gantt representation of a group sequence for the single machine problem Example 2: Job Shop EnvironmentIn Fig. 9.10, two groups of permutable operations are proposed. The first one is composed by the operations of J 1 and J 3 performed on the first machine. The second is composed of the operations of the same jobs on the third machine. One can see that whatever the order of the operations inside each group, the sequence remains feasible. Of course, this flexibility has a price since the makespan is now equal to 32.

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Groups of permutable operations is a well-known robust scheduling method that represents a particular set of schedules to be used in a real-time human-machine decision system where the aim is to absorbe uncertainties. This method guarantees a minimal quality corresponding to the worst-case. The best-case quality is also of interest; associated with the worst-case, it will provide a range of all possible qualities of the final schedule. The best-case quality is an NP-hard problem that can be solved optimally using an exact method. The performance of this exact method relies on the accuracy of its lower bounds. In this paper, we propose new improved lower bounds for the best-case quality of the groups of permutable operations. These lower bounds can either be used in an exact method to seek for the optimal best solution or can be used in a real-time human-machine decision system. The experiments made on very well-known job shop instances, using the makespan objective, exhibit very good performances.