ترکیب یک M / M / C / M صف مرکز نگهداری در مدل مقدار تولید اقتصادی با شکست و تعمیر تصادفی دستگاه

This article considers a production system in which “m” identical machines produce nonidentical products at production rates. Products made by each machine are on the other hand consumed at a specific demand rate. Machines may be affected by unwanted breakdowns. Machines break down according to a Poisson distribution with equal rates and the failed machines are sent to maintenance center for repair which is consisted of “c” servers or servicemen. However, Number of machines is greater than number of servicemen (m > c). Hence, if the number of failed machines is greater than that of servicemen, the machines have to be put in a queue. Machines are put in one queue with the order of queue being FCFS. The queue has a typical M/M/c/m system. If machines are broken down during production, shortage will occur. This problem has been considered to obtain a single production cycle for the machines and an optimum number of the servers such that costs are minimized. For this purpose, distribution of waiting time for machines in repair center is calculated and a cost function is formed. Steepest descent and direct search methods are applied in this work to obtain optimal production cycle and maintenance servers, respectively. The proposed methods are studied using a comprehensive example.

One of the most famous models being used in production–inventory area of industry which contributes to find the size of economic production lot is Economic Production Quantity (EPQ) model. This is a simple mathematical model to confront inventory management issues in production–inventory systems, where production economic quantity is determined in such a way that total production–inventory costs are minimized. By means of this model, economic production quantity is achieved in instances, where one product is produced by one machine and definitive demand is met within limited time horizon. EPQ model is generally proposed under simplified assumptions which are rather far from the reality.

In this article Economic Production Quantity (EPQ) Problem was investigated in the case, where more than one machine are being operated with machine stochastic breakdown. In all previous works, EPQ problem was considered just for one machine. On the other hand, maintenance time of machine is assumed to be a constant parameter or with a predefined probability distribution function and sometimes with a general distribution function in relevant literatures. Therefore, the aim of this paper was to deal with EPQ model for m operating machines which are operated at specific production rate and are exposed to unwanted breakdowns. Failed machines are referred to maintenance center and may be put in a queue. Waiting time distribution of machines in maintenance center was considered as their non-producing time distribution. According to this distribution, total cost function was calculated.