The authors first develop a model to determine the optimal repairable parts inventory for a maintenance center servicing machines containing a single m-out-of-n system. The model is then extended to handle a related problem, finding optimal maintenance center inventories for machines containing several m-out-of-n systems of different parts, minimising total expected costs subject to a constraint on total inventory investment. The authors assume that there is a fleet of machines, which experience identical workloads. There is a cycle time of T days between overhauls for an individual machine. A machine arrives at the maintenance center for an overhaul each day. At the overhaul, all failed parts are removed and sent to a repair shop, from which they eventually return to the maintenance center to be used again as spares. The total number of spares undergoing repair and on hand is constant. There are no backorders; if the number-on-hand spares is insufficient to meet demand at an overhaul, a shortage penalty is assessed which depends on the number and type of spares required. While computing holding costs is straightforward, computing expected shortage costs is more complex. Expected shortage costs are dependent upon several factors, including component failure rates, the values of m and n, part repair rates, and the initial number of spares on hand. The authors assume that the system of interest is well specified, so that the parameters of the model are known except for the number of initial spares of each type, which are decision variables. They model the on-hand inventory of each type as part as a Markov chain with the number of spares on hand at the end of each day as the states, under the assumptions that failure rates are constant and repair times follow independent exponential distributions. The authors then calculate the steady-state probabilities of stockout of various numbers of spares, as a function of the initial spares inventory. The expected shortage costs for a given type of spare may then be calculated by finding the product of the penalty cost for lacking p spares and the probability of lacking p spares and summing over all possible p values. Solutions to the problem of finding optimal initial inventory level for a machine containing a single m-out-of-n system may be found easily by enumeration. Solutions to the constrained problem where the machine contains several independent m-out-of-n systems, may be found by dynamic programming. Sensitivity analysis of costs to changes in the inventory investment constrain is clear, and computational effort is reasonable. A simple example is included to illustrate the solution method for both problems.
