A Two-Phase Pattern Generation and Production Planning Procedure for the Stochastic Skiving Process

Figure 4

(a) The initial solution is free of item availability restrictions and serves as an initial reference point. (b) The step size augments the search space. (c) The available items cannot produce the upper bound or the optimal point (greyed-out point). The item availability constraints are binding and lead to another solution (shown in black). (d) The DA finds new patterns and augments the pattern set to produce the upper bound. The available items can produce the upper bounds. This augmented pattern set is proper. (e) The SAA finds a new optimal solution with item availabilities. (f) The new upper bound is calculated and a different upper bound than the previous iteration. The solution may improve when new patterns are added. We check if this new upper bound triggers new pattern generation. (g) The existing pattern set cannot produce the most recent upper bound. Hence, the DA is rerun until it can. (h) The SAA is rerun with all patterns found. The solution is the same as the previous iteration. The addition of new patterns did not affect the solution. Hence, the production amounts have converged. (i) Since convergence is caught, we accept this solution as the optimal solution.