Minimization of the wood wastes for an industry of furnishing: a two dimensional cutting stock problem

This paper presents the modeling and the resolution of a two dimensional cutting stock problem for a wooden industry. It is about a real problem of minimization of the wood wastes for an industry of furnishing. The raw material to be cut is a set of beams of various sizes. The purpose of the cut is to supply a list of orders characterized by a set of articles of various sizes. The problem is converted into an integer linear program where the decision variables are the numbers of beams to cut according to a set of feasible “patterns”. The designed solution is a heuristic in two stages: – Generation of the feasible patterns by various classic heuristics of the Bin-packing Problem. – Resolution of the integer linear program with the generated patterns as input variables. Moreover, based on this approach, the “Application Cutting Optimization” is developed to allow the immediate resolution of the problem and widening the stock management horizon. To end, a real case is studied to confirm the effectiveness of this approach.