Earliness tardiness production planning and scheduling in flexible flowshop systems under finite planning horizon

This paper studies a general flexible flowshop scheduling problem to minimize the earliness and tardiness penalties. We consider a finite planning horizon including some equal periods. There is a known demand for each product in each period. The objective in the all periods, except the last period is minimizing the total penalties of E/T which are originated from the less or excess quantity produced as compared with the cumulative undelivered demands. It is assumed that total demands of each product should be delivered at the end of the planning horizon, so the objective of last period is changed to minimizing the total penalties of E/T which are originated from the difference between completion time and final due date. Because of dividing the problem to some subproblems, we can use optimal algorithms (e.g., B&B) to solve the problem and find suboptimal solution in real-size problems. In the solution procedure, using the unused capacities of the past periods for producing the demand of each period, the solution is improved.