Optimal Control of a Multistage Machining Operation on a Computer Numerically Controlled Machine

A multistage machining operation (

MMO) model is proposed for a computer numerically controlled (CNC) machine to minimise the production cost of a deterministic order quantity under deadline constraint. Using the Lagrange method, the optimal machining time for each cutting tool is then achieved and the cost-related property of the Lagrange multiplier is also verified. In addition, a computer simulation of a numerical case using the MATLAB program is fully discussed, and the cost function of the machine for machining such operations with respect to the production deadline, is then obtained. Through this study, the project scheduling, production cost estimating, and even the contract negotiating of a deterministic quantity scheduled on the CNC machine can be further accomplished. This paper not only contributes an applicable operational strategy for a machine, but also provides a valuable approach for minimising the production cost for manufacturing engineers.