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Strong Decision and Forecast Horizons in a Convex Production Planning Problem

We consider a production-inventory planning problem with time-varying demands, convex production costs and a warehouse capacity constraint. It is solved by use of the Lagrangian form of the maximum principle. The possible existence of strong decision and forecast horizons is demonstrated. When they exist, they permit the breaking up of the whole problem into a set of smaller problems which can be solved independently because optimal decisions up to a strong decision horizon are completely independent of demand data beyond the next forecast horizon. A forward branch and bound algorithm is developed to determine such horizons and to solve the whole problem.