Sustainable manufacturing is connected with the effectiveness of production processes. There are several solutions to improve manufacturing sustainability. This paper deals with the possibilities of the utilization of mathematical methods to solve optimization problems in the production process of furniture. The aim of the paper is to create a mathematical model of the key processes in order to maximize productivity and cost reduction by identifying key processes and parameters influencing manufacturing effectiveness. After identification of the parameters describing the key process (milling), an abstract model of the manufacturing process was created. Identified input parameters were the cutting velocity, feed rate, and a total volume of removed material. The output parameters were surface roughness, process duration, and process cost. The experimentally measured and calculated values of the output parameters were analyzed by a multiple regression tool. The method of an artificial neural network was used as a numeric method for optimization. The results showed that the maximal effectiveness of the sub-process can be achieved if the CNC machine is set at the cutting velocity of 4398.23 m·min−1
and feed rate of 11.00 m·min−1
. Maximal values of the created neural network showed optimal values of input and output parameters.
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