Sensitivity and parametric bound analysis for a single pass machining problem

In this paper, the problem of optimizing the machining conditions for a single pass machining problem is analyzed. The problem is a Geometric Programming (GP) model, with two variables, the speed and the feed. A convex equivalent problem to the GP model is solved. Sensitivity analysis is conducted, supported by a verification of the assumptions of the sensitivity theorem for nonlinear programming. Finally bounds on the optimal value function when some of the problem parameters are perturbed are obtained. The results obtained show that the binding constraints are the maximum cutting temperature constraint and the bending constraint. A linear relation is found between the optimal value function and the cost parameters, as well as the time parameters, and a convex relation is found between the optimal value function and the cutting force, the maximum cutting temperature and other right-hand side parameters. The computer package used is SENSUMT which interface a classical penalty function algorithm with the sensitivity and bounds theory.