Development of a Linear Integer Programming Model for Solving Cutting Stock Problem in the Manufacturing Industry

Abstract

Cutting stock problem is a problem generally encountered in many manufacturing industries such as the furniture, clothing, glass production, leather, paper, textile, metals industries amongst others most especially during mass production. The problem usually arises during roll slitting whereby a large role is to be cut into smaller pieces. The challenge may be further compounded due to constraints and different variants that arises from product customization, process and machinery as well as customer requirements and quality issues. To address this problem, this study develops a linear integer programming technique and provides a practical guided approach. First mathematical formulation (having objective function and constraints) comprising of a list of q orders, that requires p j pieces was formulated and a list of all possible cuts combination of configuration and patterns were derived. The linear integer program was solved in the MATLAB 2022 environment. The results indicated that the large rolls can be cut into the desired length, number, patterns and configuration in a time effective manner using the developed linear integer programming technique. The results further show that for the total wastes generated was 24 for the optimal solutions. This number of wastes can be considered to be minimal considering the volume of demand and patterns generated from the stock material. Furthermore, 6 out of the 7 pattern optimal solutions generated zero waste. This study provides theoretical and empirical findings that can assist the manufacturing industries in minimizing time and cost variables while addressing stock cutting problems.