Optimal repair policy for a machine service problem

✍ Scribed by Gustav Feichtinger

• Publisher: John Wiley and Sons
• Year: 2007
• Tongue: English
• Weight: 430 KB
• Volume: 3
• Category: Article
• ISSN: 0143-2087
• DOI: 10.1002/oca.4660030102

✦ Synopsis

Abstract

The paper considers a two‐state stochastic process with a non‐linear cost structure evaluating sojourn in states and transition between them. One transition rate serves as the control variable, and one state probability is selected as the state variable. A non‐linear autonomous optimal control problem is then defined and solved by saddle‐point analysis. Next, a variant of the machine interference problem is analysed (M machines, M repairmen, time‐dependent service intensity). Under reasonable assumptions, the repair intensity is shown to be decreasing for finite planning periods. Analogous results on the qualitative structure of optimal policies can be derived for some other related models, e.g. for an autonomous version of the Kamien‐Schwartz maintenance model and for a simple model of optimal dunning of credit repayment.