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Analysis of a production-inventory system with machine breakdowns and shutdowns
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Optimal management of the machine repair problem with working vacation: Newton's method
Journal of Computational and Applied Mathematics
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Computers & Mathematics with Applications
WSEAS Transactions on Information Science and Applications
WSEAS Transactions on Mathematics
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Operations Research Letters
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Computers and Industrial Engineering
Computers and Industrial Engineering
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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 (mc). 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.