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

To deal with a class of problems in which dimensions of objects to be cut are unknown beforehand, a cutting optimization technique is proposed. This solution has been applied to the wood industry. It is based on a two-level hierarchical structure consisting of a placement algorithm assigned to a given plank to optimize the cutting and a process control procedure permitting production of a requested list of pieces that is the best 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 samples systems is proposed, and under the given hypothesis, an optimal control policy is established