A note on 'Dynamic optimization of multipass milling operations via geometric programming'

An article published in this journal by Sonmez et al. [A.I. Sönmez, A. Baykasoğlu, I.H. Filiz, Dynamic optimization of multipass milling operations via geometric programming, International Journal of Machine Tools & Manufacture, 39(1999) 297-320] developed a mathematical model using 'geometric programming' for determination of the cutting parameters in multipass milling operations, such as plain milling and face milling. The developed strategy is based on the maximum production rate criterion subject to several practical technological constraints. Their published results for the production rates for the two passes show that it appears Sonmez et al. added the value of invariant time of 1.7 (for n=1) to each solution of the passes, thereby having incorrect solutions for the production rates for the rough and finish passes. This note works through the solutions to show how Sonmez et al. [1] incorrectly handled the addition of the invariant time to their solution. Moreover, the note raises the question of how correct their 'dynamic programming' model for production rate is, since it was used to find a range of values, which were then used for the optimization process.