Abstract
The article deals with a formal approach to solving manufacturing problem with defects removal and presents the application of this approach to flow-shop system with defects. The defects are detected during quality control and thus they are unexpected events. Moreover, a job processing time is not predetermined, and it may contain the unknown time needed to repair. Therefore, stochastic uncertainties are considered, but in addition, we model the process of decision making. The algebraic-logical meta-model methodology constitutes the basis for our approach. A hybrid algorithm for constructing a solution based on the process simulation using special local optimizing task and algebraic-logical models switching when defect detection occurs is presented. In particular, the following elements of the presented approach are shown: disturbances type analyzing, definition of switching states set, definition of subproblems, algebraic-logical meta-models creating for all subproblems, switching types determining, determination of the switching rules, the switching function, and components of special local criterion definition. The article shows results of computer experiments.
Highlights
The article presents formal approach to solving manufacturing problem with defects removal, especially flow-shop problem
In the presence of quality defect, it contains the unknown time needed to repair because it depends on the size of defect, and in each case it may be different for the same job
We present in detail a complete example of solving the problem using hybrid algorithm, we provide the details of the problem analysis, the precise elements of the models, and the detailed stages resulting from the combination of two methods
Summary
The article presents formal approach to solving manufacturing problem with defects removal, especially flow-shop problem. The papers[1,2] present a general form of switching method, ALM models and definition of the switching functions, and the switching algorithm for the flow-shop system with defects and one additional repairing machine. In section ‘‘Flow-shop system with defects problem,’’ we describe the flow-shop manufacturing system with time limits, in which there are the quality control for the defects detection, removal of the manufacturing quality defects on an additional repairing machine, and job re-treatment in part or all technological routes. The elements of presented approach, i.e., types of disturbances analyzing, determining the set of switching states, definition of subproblems, ALM models creating for all subproblems, switching types specifying, determination of the switching rules, the switching function definition, and special local criterion determining for considered problem are given in section ‘‘Algorithm for flow-shop system with defects.’’ Section ‘‘Experiments and results’’ contains the results of computational experiments.
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