(An) algorithm for a cutting route problem with precedence constraints

Abstract

In this paper, we consider the cutting sequencing problem arising in a steel cutting process within a shipbuilding company. Given a set of lines to be cut, precedence constraints are imposed on them and some cutting lines have constraints on their cutting directions because of the heat generated during the cutting operation. Under these constraints, we consider the problem of deciding the cutting directions and sequence, minimizing the total moving time of the cutting robot. This problem can be modeled as the precedence constrained traveling salesman problem (PCATSP), which has been well-studied among the precedence related problems. We present an integer programming (IP) model for our problem. Though the model has integer variables and exponentially many constraints, it can be solved efficiently by branch-and-cut (B&C) algorithm. B&C algorithm works by solving linear programming (LP) relaxations using cutting planes in the branch-and-bound tree. To solve LP relaxations, we use some valid inequalities known to be most efficient from the literature to get feasibility and improve integrality. We test our algorithm on randomly generated test problems. The computational results show that our problem can be solved to optimality in a very reasonable time by branch-and-cut algorithm.