Procedures for solving a 1-dimensional cutting problem

The different varieties of a particular article for widespread consumption are characterized by the material used and its length. Each material is acquired in jumbos of a particular length. By cutting them, we must obtain for each production period at least as many items for each variety as are required to cover consumption for the following period; anything above this value will be used in later periods. In order to minimize the cost associated with this process (that of offcuts plus the inventory holding cost), procedures combining integer linear programming with heuristics based on dynamic programming have been designed; these heuristics have been applied to the daily resolution of the industrial problem.