Finding an optimal scrap size to reduce waste in the tire body ply cutting process

The problem that concerns with the cutting of a fixed-length stock material into shorter pieces of specific length while minimizing the waste is commonly known as the cutting-stock problem (CSP). The standard CSP is usually formulated as an integer linear program and there have been a number of off-the-shelf solvers and softwares dedicated to such a problem. In this talk, we shall discuss an optimization model describing a CSP of tyre cutting from a stock of specific characteristics that requires a machine with special sensor-based automation. In contrast to the standard assumption of a CSP where the cutting is fully programmable, we rely on the sensor reading from the automated machine. Such assumption induces conditional constraints which are highly nonlinear and requires a special reformulation. The novelty in our work lies within the formulation and reformulation of the machine's automation. We obtain the final model that is in the form of a cubic mixed-integer program. The model is then solved with SCIP solver under the hood of Julia's JuMP package.