Exact approaches for the cutting path determination problem

Abstract Cutting phases occur in many production processes when a larger object must be cut into multiple smaller pieces. Some examples of relevant industries being clothing, footwear, metalware and furniture. The cutting phase is composed of two stages. The first stage consists of finding a good layout for the set of small pieces that must be cut from the larger object and minimizing some objective such as raw-material waste (The Cutting and Packing Problem). Once this good layout has been established, it is provided as input for the second stage which consists of determining the path to cut the pieces which minimizes another objective, such as the total cutting time or distance (The Cutting Path Determination Problem). This second stage is crucial for efficient production planning. Only one linear mathematical model has previously been proposed for the Cutting Path Determination Problem. In this paper, this problem is addressed using two exact approaches based on the Rural Postman Problem (RPP) and the Traveling Salesman Problem (TSP). The RPP approach, in particular, is able to produce optimal solutions for instances containing more than 2000 edges in under 1 h.