A subset sum approach to coil selection for slitting

Abstract

Optimizing coil slitting operation requires not only the generation of efficient slitting patterns but also the selection of coils to be slit by each pattern. When the coils to be slit are not identical, the optimal coil selection can be quite a cumbersome task. In this paper, we consider the problem of selecting coils to be slit by a given particular slitting pattern when the available coils are not identical. The objective of our problem is to maximize the customer order fulfillment while minimizing the slitting loss and overproduction. We adopt and modify a dynamic programming scheme for the subset sum problem to develop an optimal pseudo-polynomial time algorithm for the problem and demonstrate that the algorithm is fast enough for solving realistic problem instances.