The Asynchronous t-Step Approximation for Scheduling Batch Flow Systems

The Asynchronous t-Step Approximation for Scheduling Batch Flow Systems David R. Grimsman Department of Computer Science, BYU Master of Science Heap models in the max-plus algebra are interesting dynamical systems that can be used to model a variety of tetris-like systems, such as batch flow shops for manufacturing models. Each heap in the model can be identified with a single product to manufacture. The objective is to manufacture a group of products in such an order so as to minimize the total manufacturing time. Because this scheduling problem reduces to a variation of the Traveling Salesman Problem (known to be NP-complete), the optimal solution is computationally infeasible for many real-world systems. Thus, a feasible approximation method is needed. This work builds on and expands the existing heap model in order to more effectively solve the scheduling problems. Specifically, this work: 1. Further characterizes the admissible products to these systems. 2. Further characterizes sets of admissible products. 3. Presents a novel algorithm, the asynchronous t-step approximation, to approximate these systems. 4. Proves error bounds for the system approximation, and show why these error bounds are better than the existing approximation.