1Management of demand-driven production systems

Abstract — Control-synthesis techniques are developed for demand-driven production systems. The resulting policies are time-optimal for a deterministic model, and approximately time-optimal for a stochastic model. Moreover, they are easily adapted to take into account a range of issues that arise in a realistic, dynamic environment. In particular, control synthesis techniques are developed for models in which resources are temporarily unavailable. This may be due to failure, maintenance, or an unanticipated change in demand. These conclusions are based upon the following development: (i) Workload models are investigated for demand-driven sys-tems, and an associated workload-relaxation is introduced as an approach to model-reduction. (ii) The impact of hard constraints on performance, and on optimal control solutions is addressed via Lagrange multiplier techniques. These include deadlines and buffer constraints. (iii) Rules for choosing appropriate safety-stocks as well as hedging-points are described to ensure robustness of control solutions with respect to persistent disturbances, such as variability in demand and yield. Index Terms — Scheduling, routing, queueing networks, inven-tory models, optimal control