Solution approaches for the cutting stock problem with setup cost

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.