Mathematical model for footwear upper material consumption estimation

Abstract

Appropriate material consumption estimation since the design phase for footwear fabrication is a vital issue as material costs account for a sizeable portion of the overall production cost of a pair of shoes. This paper presents a mathematical model to predict the calculation of footwear upper material consumption to improve the utilization ratio of materials through a suitable nesting map onto leather. The proposed model concentrates on the two-dimensional geometry of footwear components and the application of rich mathematical concepts. The model reflects the outlines of individual footwear components while determining the area using definite integral calculus. Five distinct rotational kinds are applied for component arrangements that correlate to the physiognomy of leather because nesting onto the leather is intractable. The simple concept of a minimal-area polygonal enclosure is applied to maximize material utilization with minimum waste. Finally, the model was verified for four consecutive Oxford footwear sizes by comparing actual upper material consumption with predicted upper material consumption. The noble contribution of this analysis is to use ImageJ software to compute upper material consumption in real case analysis through image processing techniques and separate estimation of wastes, especially the fourth waste. The results of the comparison study show that the proposed model can reduce average material requirements by 2.06 %. This minimization of waste could be beneficial in terms of economic and environmental sustainability. Therefore, this study can be applied to estimate more accurately the amount of upper material required for footwear fabrication and support better utilization of material in the footwear industry.