The popularity of “personalized customization” has put forward higher requirements for industrial production, and how to achieve mass customization production has become one of the main problems plaguing manufacturing enterprises. This paper focuses on the layout optimization problem of square parts, and adopts a three-stage 2D rectangular cutting method, i.e., following the cutting idea of “sheet-strip-stack-item”. To solve this problem, we develop a mixed-integer linear programming model with the optimization objective of using as few square sheets as possible while satisfying the order demand and related constraints. Afterwards, we adopt the CPLEX solver to invoke the branch-and-bound algorithm package to solve the model. The experimental results show that the method can accomplish the scheduling of all the orders in the given four datasets and obtain a satisfactory solution within 30 min. The utilization rate of sheets in all datasets reaches more than 85%, proving that the method can utilize raw materials more efficiently, and achieve good economic benefits.