A modified column generation algorithm for scheduling problem of reentrant hybrid flow shops with queue constraints

Abstract

This paper investigates a two-stage reentrant hybrid flow shops scheduling problem. In this problem, each product is processed layer by layer with different processing time. To be more practical, the queue time between the parallel machines and the batch processing machine is restricted. The objective is to minimise the total completion time. A column generation algorithm is proposed to solve the scheduling problem by decomposing this problem into main problem and workpiece level sub-problem. In the proposed method, dynamic programming with multiple decision-making is designed to solve each sub-problem and the adaptive accelerating strategy is provided creatively to effectively improve the convergence of the algorithm. In the branch-and-bound method to generate feasible solution, the innovative method of neighbourhood mutation is employed. Computational experiments demonstrate that the proposed method for the two-stage hybrid flow shops problem is quite stable and effective compared with other conventional formulation.