The spares provisioning problem with parts inventory

In this research, we consider the spares provisioning problem, where a finite population of homogeneous machines are being deployed to meet a constant demand. While a machine is operating, it could become inoperable due to the failure of a critical built-in part in the machine. Before repairs on the machine can be initiated, however, a replacement part must be obtained. If a replacement part is available from stock, the machine is immediately transferred to the repair subsystem, in which one or more repair stations operate in parallel. If the replacement part is not in stock, then the machine waits in the ordering subsystem for the arrival of a new part. Once a machine is repaired, it is immediately deployed to meet demand if needed, else it joins a queue of standby machines. The spare machines have zero probability of failure and, if available, a spare replaces a deployed machine immediately upon the latter's failure. The machine operating time, repair time, and ordering time of the parts are assumed to be exponentially distributed. The ordering subsystem for the parts brings a new aspect to the spares provisioning problem, and dramatically increases its difficulty. This is because the queuing network model which describes the system is a non-product-form network in the case of finite nonzero stocking policy, and specification of closed-form solutions is highly unlikely for such networks.

In this dissertation, we present efficient algorithms through which the optimal number of machines, repair stations and stocking level of the parts that minimize total operations costs subject to a service-level constraint can be obtained. The algorithms, which based on Little's result from queuing theory and some approximate models used for bounding, have proven to be extremely efficient in terms of computer storage and execution time, even for large problems.