Abstract
The production line of an enterprise with a flow method of organizing production is considered as a dynamic distributed system. The technological route for manufacturing products for many modern enterprises contains several hundreds of technological operations, in the inter-operating reserve of each of which there are thousands of products awaiting processing. Technological routes of different parts of the same type of products intersect. This leads to the fact that the distribution of objects of labor along the technological route has a significant impact on the throughput capacity of the production line. To describe such systems, a new class of production line models (PDE-model) has been introduced. Models of this class use partial differential equations to describe the behaviour of production line flow parameters. In this article, a PDE-model of the production line is built, the flow parameters of which depend on the load factor of the process equipment for each operation. For the description of a distributed dynamic system, the PDE model of the production line was used. At the same time, the single-shift mode of operation of a production enterprise is considered as a basic mode of operation.
Highlights
The production line is required to process a batch of products on the enterprise [1]
We introduce a function W t, S that characterizes the work of additional equipment
Functional (5) defines the criterion for the quality of control of flow parameters during the production cycle Td, reflects the excess costs for all technological operations associated with the use of additional equipment
Summary
The production line is required to process a batch of products on the enterprise [1]. Let us introduce the distribution density of the value of the excess costs of technological resources required to use additional equipment within an hour for a technological route in the interval 0; Sd : Sm z t, S dS = zс t, Sm , Sd. M z t, S dS = z t, S dS = zс t,Sm. We introduce a function W t, S that characterizes the work of additional equipment (main equipment in the second or third shift, shift factor KSm 1 ). The excess costs Сcb (Td ) required to ensure the operation of additional equipment located on the segment Sm Sm 1, Sm and used to perform the m -th operation for the duration of the production cycle Td , and the integral is defined: Td Sd. Relevance and practical significance The scientific novelty consists in the development of a method for designing control systems for the parameters of the production line in enterprises with a continuous method of organizing production based on the PDE model of the object control. The discontinuity of the function 0 t, S corresponding to the value 1q Sm W tq, Sm , is determined by the work of the additional equipment with the capacity 1q Sm included between tq and tq 1 the shift for processing the subject of labor for a time W tq , Sm
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