Scheduling of the optimal tool replacement times in a flexible manufacturing system

In Flexible Manufacturing Systems (FMSs), a cutting tool is frequently used for different operations and on different part types to minimize tool change-overs and the number of tools required, and to increase part-routing flexibility. In such situations, the tools become shared resources and work in job-dependent, changeable and nonhomogeneous conditions. It is well known that the tool failure rate depends on both age and machining conditions and that tool reliability is a function of the duration, machining conditions, and the sequence of the operations in FMS. The objective of this paper is to obtain a schedule of the optimal preventive replacement times for the cutting tools over a finite time horizon in a flexible manufacturing system. We assume that the tool will be replaced either upon failure during an operation or preventively after the completion of each operation, incurring different replacement costs. A standard stochastic dynamic programming approach is taken to obtain the optimal tool replacement times. The optimal schedule is obtained by minimizing the total expected cost over a finite time horizon for a given sequence of operations. A computational algorithm is developed and a numerical example is given to demonstrate the procedure.