Modeling of production and logistics systems with non-identical hardware setup
Authors: Medvedieva M.I.
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Purpose and subject of research
We consider the problems of function modeling production and logistics systems with unreliable equipment and non-identical readjustment before servicing the next batch of orders, based on queuing theory models. To solve this problem we present the flexible manufacturing system in the form of a single-channel queuing system, where the input Poisson flow intensity of orders per unit time.
The study used formal mathematical methods, the method of economic and mathematical modeling, queuing theory, analytical methods of research.
Order processing takes place in the order of their receipt, the order processing time has exponential distribution law with parameter . The device has a feature consisting in the fact that after the processing of all orders that are in the system, it goes into an idle state and to move it into working condition necessary readjustment, which begins after the date of the request to a free system. Duration changeover has an exponential distribution with parameter . In addition, it is assumed that the equipment in the process of its operation may fail and recover. In the event of equipment failure, it is repaired (recovery) work. Maintenance of equipment (recovery, prevention and readjustment) carries a team of workers.
We assume that the device can fail at any time, as during maintenance applications (running), the application is under maintenance at the time of failure of the device is lost. Orders that are in the system at the time of equipment failure (if any), are served after the repair. After the restoration is necessary to readjust the equipment, the duration of which is different from the duration, which began after the receipt of the request to a free system (from the initial changeover). For the described characteristics of the system are found, which are used to find the basic operating parameters of the system used to construct economical criteria.
Key words: queuing system, the stationary probability, reliability, prevention, rehabilitation and readjustment of equipment.