The Chain-Reentrant Hybrid Flow Shop with Two Competing Agents

We address a two-stage chain-reentrant hybrid flow shop problem with deteriorating jobs and two competing agents. Every job must initially be scheduled on a primary machine (first stage) which is then scheduled on one of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$m$</tex> unrelated parallel machines of the second stage and returns back to the primary machine to complete its last operation. The jobs are constrained to a deterioration function linearly depending on their starting times. The objective is to minimize the makespan of the first agent and the total energy consumption of the second one, where each agent has its own set of jobs. We elaborate three meta-heuristics: a nondominated sorting genetic algorithm (NSGA2), an archived multi-objective simulated annealing method (AMOSA), and a particle swarm optimization method (PSO), for the resolution of this problem. An intensive experimental study is conducted to evaluate the performances of the proposed algorithms.