Scheduling non-permutation flowshop with finite buffers and two competitive agents

Abstract

Flowshop scheduling is a popular and valuable optimisation model in academia. Application of the scheduling model for industrial problems has to consider real-world scenarios, such as non-permutation scheduling, finite buffers and individual competition from different customers. These non-negligibly factors can lead to a huge solution space, leaving it barely able to be effectively solved. Therefore, this study investigates a non-permutation bi-agent flowshop scheduling problem with limited buffers, where tasks are released over time and minimisation of a linear criterion (i.e. weighted combination of makespans) improves customer satisfaction. Mixed integer programming model is established for this strong NP-hardness problem that the optimum cannot be found in polynomial time. For small-scale instances, a branch and bound (B&B) algorithm is provided to achieve exact solutions, where effective non-delay pruning rules, well-designed lower and upper bounds are utilised to eliminate invalid nodes during searching. For medium-scale instances, a hybrid particle swarm optimisation (HPSO) algorithm is proposed to seek high-quality solutions, where a two-stage collaborative evolution promotes deep exploration, an efficient sequence-based rule amends infeasible solutions and several validated mechanisms enhances convergence. Evaluation of extensive computational experiments, including components evaluation and nonparametric test, demonstrate the effectiveness of the presented algorithms.