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Mathematical theory of production planning. (English) Zbl 0564.90010

Advanced Series in Management, Vol. 3. Amsterdam-New York-Oxford: North- Holland. XIV, 506 p. $ 76.50; Dfl. 180.00 (1983).
This book proposes a unified mathematical approach to production planning and production smoothing problems in the framework of optimal control theory. It considers general concave and convex cost models which include most of the cost structures discussed in the previous literature as special cases. Planning horizon results are always central to the discussion. They allow to consider only finite horizon problems and guarantee that a production plan implemented optimally over the first periods is also optimal with regard to any demand pattern beyond the planning horizon.
The book consists of seven chapters and one mathematical appendix. Demand is deterministic in the first three chapters and stochastic in chapter 4. The formulation is in discrete time except in chapter 3 where time is continuous. Chapter 1 considers production planning models for concave costs, chapter 2 production planning and production smoothing models for convex costs, chapter 3 production planning models for deterministic demands, chapter 4 production planning and production smoothing models with stochastic demand and the remaining three chapters are devoted to software for the production planning models discussed in the previous chapters.
Reviewer: H.Kise

MSC:

90B30 Production models
90C39 Dynamic programming
90-02 Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming