Operation sequencing and machining economics

Solution techniques for the combined machining economics-operations sequencing problem are proposed. The paper examines the problem of determining the sequence and the cutting speeds for a number of operations performed using the same tool, where the independently calculated optimal cutting speeds differ among operations. The essence of the proposed solution method is that it may be beneficial to perform some operations at non-optimal speeds in order to reduce the cost associated with speed changes. The problem is initially formulated as a continuous nonlinear optimization problem combined with a discrete combinatorial scheduling problem. After the problem is descretized, an efficient heuristic technique (the overlapping speed ranges (OSR) heuristics) is proposed for finding good solutions to the problem quickly. The heuristic determines the cutting speeds and the sequencing of operations utilizing the indifference speed ranges which are based on the sensitivity of the operations’ unit machining costs to the speed change cost. A branch and bound algorithm is also proposed for finding optimal solutions to the problem. The branch and bound algorithm performs extremely well because it utilizes as a strong upper bound the complete solution provided by the OSR heuristic, and because tight lower bounds are computed for all nodes throughout the branching procedure. Finally, for large problems a heuristic variant of the branch and bound procedure is suggested (the filtered beam search method which does not backtrack).