Mathematical Theory of Production Planning.

The book proposes a unified mathematical treatment of production planning and production smoothing problems, in the framework of optimal control theory. General concave and convex cost models which relate most closely to real life applications are considered. Planning horizon results are always central to the discussion and developments. This allows the treatment of finite horizon problems only, and guarantees that the production plan implemented over the first periods is optimal with regard to any demand pattern beyond the planning horizon. Algorithms are proposed to compute the optimal production policy, together with the corresponding software designed to be implemented on any microcomputer. The book is organized in seven chapters and a mathematical appendix, which provides the reader with all the necessary background to render the volume self-contained.