A standard model of the placement problem aimed at resolving a cutting stock problem

The authors propose a wood cutting optimization technique to deal with a class of problems, in which dimensions of objects to be cut are unknown beforehand. The technique is based on a two-level hierarchical structure: a placement algorithm charged on a given plank to optimize the cutting and a process control procedure permitting production of a requested list of pieces in the best way on a limited horizon. The placement algorithm is modeled in order to formalize the control strategy. In particular, a method for connecting a system of discrete events to the more classical theory of continuous sampled systems is proposed. With this model, and under the given hypothesis, an optimal control policy is established.<>