A maximum principle based combined method for scheduling in a flexible manufacturing system

A continuous time dynamic model of discrete scheduling problems for a large class of manufacturing systems is considered in the present paper. The realistic manufacturing based on multi-level bills of materials, flexible machines, controllable buffers and deterministic demand profiles is modeled in the canonical form of optimal control. Carrying buffer costs are minimized by controlling production rates of all machines that can be set up instantly. The maximum principle for the model is studied and properties of the optimal production regimes are revealed. The solution method developed rests on the iterative approach generalizing the method of projected gradient, but takes advantage of the analytical properties of the optimal solution to reduce significantly computational efforts. Computational experiments presented demonstrate effectiveness of the approach in comparison with pure iterative method.