Mathematical models and a hunting search algorithm for the no-wait flowshop scheduling with parallel machines

Majority of researches in no-wait flowshop scheduling assume that there is only one machine at each stage. But, factories commonly duplicate machines in parallel for each operation. In this case, they balance the speed of the stages, increase the throughput of the shop floor and reduce the impact of bottleneck stages. Despite their importance, there is no paper to study the general no-wait flowshop with parallel machines. This paper studies this problem where the objective is to minimise makespan. Since there is no mathematical model for the problem, we first mathematically formulate it in form of two mixed integer linear programming models. By the models, the small instances are optimally solved. We then propose a novel hunting search metaheuristic algorithm (HSA) to solve large instances of the problem. HSA is derived based on a model of group hunting of animals when searching for food. A set of experimental instances are carried out to evaluate the algorithm. The algorithm is carefully evaluated for its performance against an available algorithm by means of statistical tools. The related results show that the proposed HSA provides sound performance comparing with other algorithms.