Flexible flowshop scheduling with multiprocessor tasks: Two Lagrangian relaxation algorithms

This paper considers the minimal earliness tardiness flexible flowshop problem with multiprocessor tasks in order to represent just in time production. The multiprocessor task property allows a job to be processed on more than one processor. This strongly NP-hard problem is formulated as an integer programming model and then solved respectively using subgradient-based and interleaved subgradient-based Lagrangian relaxation algorithms. The application steps and key problems of the designed algorithms are discussed detailedly, which include the resolution of Lagrangian subproblems, the development of subgradient optimization and interleaved subgradient optimization for updating multipliers and the construction of feasible schedules. Numerical calculation results with different sized problem instances are used to demonstrate that all of the test instances can be solved in a shorter running time with acceptable duality gaps.