Cutting stock problem with leveling of the weight of lots

This paper deals with the cutting stock problem for manufacturing processes in the paper industry. An order consists of plural sizes of cut paper sheet with same basis weight. They are divided into several lots. A lot cutting machine uses the same size positions of its two blades. One of them is named the slitter and is used for separating of output paper from the paper machine in the output direction. The other is named as cutter and is used for separating in the perpendicular direction against the output paper. The planning of the set position of the cutter is treated as the cutting stock problem. In this case, the requirements for the solution of the problem are decreasing the loss paper, leveling of the weight of lots and decreasing of the number of lots. In this paper, the authors propose a successive decision process of the combination and members of sizes in the order. For each lot state, they use the proposed two-stage optimization. This uses the sum of two criterion functions. The former is one for the concerned lot, and the latter is the next stage criterion function by predicted values. By using this conventional algorithm, on can obtain a good rate of usefulness, leveling for the weight of lots and smaller numbers of lots. This algorithm has been installed in an actual paper manufacturing works, and has shown the same degree of effectiveness as that of expert paper mill personnel