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In this paper, we study the single-item and the multi-item capacitated lot sizing problem in presence of inventory bounds (CLSP-IB). That is, in any period, both the quantity produced and the stock on hand are limited. For the single-item CLSP-IB with a stationary production capacity, time-dependent inventory bounds and concave costs, we show that the problem can be solved in time $$O(T^4)$$ ...
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