The recycling of worn train-wheels and related problems

When train wheels wear they can be ground down to a smaller size and reused. This can be done several times. Small wheels are not however compatible with large wheels on the same train. So one has a fleet of trains in which any one train has wheels of similar size but the size differs from train to train. A stock of spare wheels is kept, and the problem is to manage the stock so that the long term cost ¦) is minimized. Usually the objective function ¦) is not known in closed form and can be computed only by long computer simulations of the management process. This leads to optimization problems that are computationally heavy at best, impracticable at worst. The authors introduce some management processes for which they can find stationary probability distributions for the state of the stock. Using ergodic theorems, the authors can find ¦) explicitly. Then they can solve the optimization problems by conventional methods.