The mathematical problem of synchronization of material flows in small-scale production is a statement of objectives, criteria and optimization demonstration. It is proposed to use the best practices of Lean and QRM approach as applied to small-scale production, taking into account the specifics. There is an approach to the optimization of production by creating a module synchronization of material flows in accordance with the mathematical formulation of production problems of synchronization.

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... he criterion of maximizing the priorities of current orders and criteria for prioritization of work with minimal planned start time is used. The authors considered a test case that illustrates the principle of synchronized production management systems in ever-changing production conditions. The authors demonstrated the selected virtual production system, consisting of five production sites. Using the synchronized production management system allowed one to profit from the execution of orders by 30% higher than without it. When assessing the level of work in progress, and the time and the amount of frozen assets, it becomes obvious that the use of a synchronized control system allows you to reduce the time and other direct and indirect costs, which exerts more positive impact on the net profit of the enterprise. Synchronization module production is seen as an additional ERP module built into the existing ERP.