Mathematical modeling of flexible production lines with different part types on unreliable machines by a priority rule

In this paper, we offer an analysis and model of a manufacturing line that uses a priority mechanism to process various types of parts in faulty machinery. The manufacturing line comprises machines separated in a set order by storage rooms where components are fluxed. When it is possible, a machine works on the most important part first and only switches to less important parts if it is unable to produce the most important ones. Only one sort of function is required for each section. Because it is expected that the processing line machinery can handle a range of part types, switching from one kind of component to another will not result in any setup penalty. Only when unable to process higher priority parts owing to obstruction or hunger can the machines work on the lower priority parts. The machines function according to a fixed priority rule. The purpose of this study is to develop mathematical formulations and procedures for each kind of component in a flexible production line. In a variety of supply and demand scenarios, the multipart line's qualitative behavior is described.. To better understand the line, we devise decomposition equations and a solution technique to put them to use. With suitable line parameters, the method converges consistently. The findings of the decomposition were verified using simulations. The line's fascinating behavior may be seen in the system's study of many parameters.