PRODUCTION PLANNING IN A DETERMINISTIC ENVIRONMENT: CONCAVE AND CONVEX COSTS - PLANNING HORIZON.

The purpose of this paper is to present an original approach of the dynamic inventory planning problem in discrete time with concave costs, under the general assumption of non stationarity and with any non-negative initial inventory. We then use the property of the cost function in order to set up a new definition of the planning horizon and to obtain some results. The last paragraph describes an algorithm to solve the same problem, but in the case of piecewise, linear and convex costs. Because we lack place, we do not give the whole demonstration of the results. Instead, we complete the explanations with many figures and applications.