Scheduling flexible flow shops of no setup cost by a Lagrangian relaxation and network flow approach

The authors present further developments of a production scheduling algorithm introduced by S.C. Chang et al. (1990) for the class of discrete-part, make-to-order flexible flow shops where set-up costs and times are negligible. The scheduling problem is first formulated as a large-scale integer programming problems and a solution approach based on Lagrangian relaxation and minimum-cost linear network flow is then developed. Compared to the work of Chang et al., the present work modifies the objective of scheduling to meeting due dates just in time, considers finite buffers, completes the algorithm for finding a feasible schedule, and evaluates the algorithm through numerical experimentations. Numerical results indicate that the scheduling algorithm is near-optimal and has a reasonable computational efficiency for short-term scheduling. Algorithmic features and future research issues are also addressed