Competitive bi-agent flowshop scheduling to minimise the weighted combination of makespans

Customer satisfaction is a prevalent issue amongst manufacturing enterprises. Multi-agent scheduling models aim to optimise the given criteria for improving customer satisfaction by fulfilling the customisation requirements. An investigation is executed on a bi-agent flowshop scheduling model, where a mass of tasks maintained by two competitive agents share a group of successive processors over time. The objective is to determine a feasible schedule that minimises the weighted combination of makespans belonging to two different agents. Asymptotic and worst-case analyses are conducted on a class of dominant-agent-based heuristics proposed to find approximate solutions for large-scale instances. An effective branch and bound algorithm is presented to achieve optimal solutions for small-scale instances, where the release-date-based branching rules and the preemption-based lower bounds significantly speed up the convergence of the proposed algorithm. A discrete artificial bee colony algorithm is introduced to find high-quality solutions for medium-scale instances. Extensive computational experiments are conducted to reveal the effectiveness of the proposed algorithms.