This paper deals with the problem of optimizing the number of passes required together with the cutting speed, the feed, and the depth of cut at each pass for a given total depth of cut to be removed from a workpiece, considering both the probabilistic nature of the objective function and the constraints in the machining processes. Applying the concept of dynamic programming and stochastic programming, the problem is formulated in an analytically tractable form and a new algorithm is developed for determining the optimum value of the cutting speed, feed, depth of cut, and number of passes, simultaneously. For illustration, a typical example is solved to obtain the cost-minimizing cutting conditions in a turning operation, and the effect on the optimum cutting conditions of the various factors such as total depth of cut, uncertainty of the tool life, and constraints are discussed.

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