Heuristic for constrained T-shape cutting patterns of rectangular pieces

T-shape patterns are often used in dividing stock plates into rectangular pieces, because they make good balance between plate cost and cutting complexity. A dividing cut separates the plate into two segments, each of which contains parallel strips, and the strip orientations of the two segments are perpendicular to each other. This paper presents a heuristic algorithm for constrained T-shape patterns, where the optimization objective is to maximize the pattern value, and the frequency of each piece type does not exceed the demand. The algorithm considers many dividing-cut positions, determines the pattern value associated to each position using a layout-generation procedure, and selects the one with the maximum pattern value as the solution. Pseudo upper bounds are used to skip some non-promising positions. The computational results show that the algorithm is fast and able to get solutions better than those of the optimal two-staged patterns in terms of material utilization.