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 pape r. The realistic manufacturing based on multi-level bills of materials , flexible machines, controllable buffers and deterministic demand pro files is modeled in the canonical form of optimal control. Carrying bu ffer costs are minimized by controlling production rates of all machin es that can be set up instantly. The maximum principle for the model i s studied and properties of the optimal production regimes are reveale d. The solution method developed rests on the iterative approach gener alizing the method of projected gradient, but takes advantage of the a nalytical properties of the optimal solution to reduce significantly c omputational efforts. Computational experiments presented demonstrate effectiveness of the approach in comparison with pure iterative method .