Capacitated lot sizing problems with inventory bounds

Ayse Akbalik (), Bernard Penz () and Christophe Rapine ()

Annals of Operations Research, 2015, vol. 229, issue 1, 18 pages

Abstract: 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 $$O(T^4)$$ O ( T 4 ) by adapting a well-known algorithm in the literature. Restricting to non-speculative costs, we propose an $$O(T^3)$$ O ( T 3 ) time dynamic programming algorithm. For the multi-item CLSP-IB, we consider the lot-sizing problem with item dedicated machines and a common capacitated storage space shared by all the items. We show that this problem is $$\text{ NP }$$ NP -hard in the strong sense even if all the cost parameters and capacities of the instance are stationary and identical for each item. Copyright Springer Science+Business Media New York 2015

Keywords: Lot sizing problem; Multi-item; Single-item; Inventory bounds; Dynamic programming; Complexity (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (8)

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DOI: 10.1007/s10479-015-1816-6

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