Lagrangian relaxation algorithms for hybrid flow-shop with earliness/tardiness scheduling problems

This paper considers the characteristics of a hybrid flow shop with JIT technical constraints. Lagrangian relaxation is presented to solve the Earliness/Tardiness problem in the hybrid flow-shop. By introducing precedence constraints into the objective function, the original problem is decomposed into a series of parallel machine sub-problems and a dynamic programming algorithm is designed to solve these sub-problems. Heuristic approach is further applied to convert the infeasible solution into a feasible solution. Testing results demonstrated that the proposed method can generate near optimal schedules in an acceptable computational time.