A single-product bounded production model with heterogeneous facilities

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Abstract
The production of a certain amount of a single product in the minimum time using n heterogeneous facilities is considered. The production quantities for particular facilities must lie within certain bounds at certain times. Thus, in general, the production at every facility is performed in periods, the numbers of which are a priori unknown. During these periods the numbers have to be found together with the production quantities. An effective algorithm is presented for solving the above problem optimally for time/production quantity, convex or concave functions. In the algorithm, some special properties of optimal solutions are used, and because of this it may be useful in practice.