Profit-based FMS dynamic part type selection over time for mid-term production planning

The dynamic part type selection problem for mid-term scheduling to maximize profit over time in a general flexible manufacturing system is considered. Some mathematical programming models are developed to address this problem and their method of solution is based on a column generation technique. In the solutions to these models, the production plan is represented as a sequence of steady-state, periodical, cyclic schedulers. Each cyclic schedule allows a subset of parts of different types to be released periodically in appropriate production ratios. Parts can be produced according to these ratios and cycles until the production requirements for some part type are completed. Then new part types can enter production and new ratios and cycles can easily be found. A two-level procedure is developed. At the upper level, a large-scale linear programming Master Problem is solved, the columns of which are generated by solving a nonlinear, mixed-integer, profit-based part type selection subproblem that selects part types for simultaneous production over a period. Numerical experiments demonstrate that this model is computationally tractable to solve problems of practical size and over several periods of time.