A continuous-time integrated model for discrete control of production flows in a multi-level bills of material environment

An integrated dynamic model for discrete production scheduling and continuous capacity expansion is presented in this paper. The modeled manufacturing system, based on multi-level bills of materials, is characterized by flexible machines with negligible setups and production rates fixed for the current capacity. Make-to-stock formulation of the problem is studied and optimal behavior of the system is determined with the help of the maximum principle. A fast time-decomposition algorithm is suggested to locate the optimal solution.