Model approximation for batch flow shop scheduling with fixed batch sizes

Abstract

Batch flow shops model systems that process a variety of job types using a fixed infrastructure. This model has applications in several areas including chemical manufacturing, building construction, and assembly lines. Since the throughput of such systems depends, often strongly, on the sequence in which they produce various products, scheduling these systems becomes a problem with very practical consequences. Nevertheless, optimally scheduling these systems is NP-complete. This paper demonstrates that batch flow shops can be represented as a particular kind of heap model in the max-plus algebra. These models are shown to belong to a special class of linear systems that are globally stable over finite input sequences, indicating that information about past states is forgotten in finite time. This fact motivates a new solution method to the scheduling problem by optimally solving scheduling problems on finite-memory approximations of the original system. Error in solutions for these "t-step" approximations is bounded and monotonically improving with increasing model complexity, eventually becoming zero when the complexity of the approximation reaches the complexity of the original system.

Petri Net Model Predictive Control Method for Batch Chemical Systems

“…Lai et al [11] model a pipeline network of a batch chemical plant as a Petri net and use integer programming to determine the shortest material transfer paths. With max-plus algebra, Weyerman et al [12] construct a scheduling optimization model of batch flow shops to find optimal processing sequences. Given a batch chemical system, Lin et al [13] design a Petri-net-based A* algorithm to obtain the optimal paths within a reachable graph and map the paths to valve operational instructions.…”

“…Batch chemical systems involve complex scheduling strategies and specific valve control commands translated from scheduling strategies [5][6][7][8][9][10][11][12][13][14]. Since scheduling and control commands require real-time computation and execution, responding quickly to unforeseen events, such as emergency orders and equipment failures, becomes challenging.…”