An Ant-Bidding Algorithm for Generalized Flow Shop Scheduling Problem: Optimisation and Phase Transitions

In this paper we present the integration of an ant-based algorithm with a greedy algorithm for solving the scheduling of a multi-stage plant. A multi-stage manufacturing plant is comprised of different stages: mixing, storage, packing and finished goods storage, and is an extension of the classic Flow Shop Scheduling Problem (FSP). The algorithmic details for the Multi Stage Flow Shop Scheduling Problem (MSFSP) are introduced for finding optimized solutions. The scheduling must provide both optimal and flexible solutions to respond to fluctuations in the demand and operations of the plants while minimizing costs and times of operation. Optimization of each stage in the plant is an increasingly complex task when considering limited capacity and connectivity of the stages, and the constraints they mutually impose on each other. We discuss how our approach may be useful not just for dynamic scheduling optimization, but also for analyzing the design of the plant in order for it to optimally cope with changes in the demand from one cycle of production to the next. Phase transitions can be identified in a multidimensional space, where it is possible to vary the number of resources available. Lastly we discuss how one can use this approach to understand the global constrainedness of the problem, and the nature of phase transitions in the difficulty of finding viable solutions.