Currently, any production process is viewed as the primary means of profit and competitiveness, in other words, becomes the dominant process approach. In this approach, the final product production appears network of interconnected processing steps during which the conversion of inputs into outputs, with a stable, accurate executable, high process most efficiently and cost-effectively provides a planned quality. An example is the organization of bread production. For the modern period is characterized by the classical recovery technology that allows to improve the palatability of bread, enhance its flavor, longer-lasting freshness. Baking is a process to be controlled in order to obtain the required quality parameters of the final product. One of the new and promising methods of quality management processes is a probabilistic method to determine the increase in the probability of release of quality products within the resources allocated for measures to improve the quality level. The paper was applied a quality management concept is based on a probabilistic approach for the multi-step process, which consists in the fact that as one of the main criteria adopted by the probability of release of high-quality products. However, it is obvious that the implementation of certain measures for its improvement requires the connection of certain resources that, first of all, is inevitably associated with certain cash costs. Thus, we arrive at an optimal control problem, which has at least two criteria - probability qualitative completion of the process, which should be maximized and the total costs of the corrective measures that need to be minimized. The authors of the idealized model of optimal control has been developed for the case when a single event affects only a single step. a special case of vector Uorshall-Floyd algorithm was used to optimize the structure of a multi-step process. The use of vector optimization on graphs allowed the authors to get a detailed picture of consequences of different management options at each stage of the process, which then can be used for technological preparation of production or to control the operation of the operational process

multicriteriality, process, graph theory, probability method

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