In this paper, we study the Cutting Stock Problem with Setup Cost (CSP‐S) which is a more general case of the well‐known Cutting Stock Problem (CSP). In the classical CSP, one wants to minimize the number of stock items used while satisfying the demand for smaller‐sized items. However, the number of patterns/setups to be performed on the cutting machine is ignored. In most cases, one has to find the trade‐off between the material usage and the number of setups in order to come up with better production plans. In CSP‐S, we have different cost factors for the material and the number of setups, and the objective is to minimize total production cost including both material and setup costs. We develop a mixed integer linear program and analyze a special case of the problem. Motivated by this special case, we propose two local search algorithms and a column generation based heuristic algorithm. We demonstrate the effectiveness of the proposed algorithms on the instances from the literature.
