# Capacitated lot sizing problems with inventory bounds

## Author

Listed:
• Ayse Akbalik

()

• Bernard Penz

()

• Christophe Rapine

()

## 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

## Suggested Citation

• Ayse Akbalik & Bernard Penz & Christophe Rapine, 2015. "Capacitated lot sizing problems with inventory bounds," Annals of Operations Research, Springer, vol. 229(1), pages 1-18, June.
• Handle: RePEc:spr:annopr:v:229:y:2015:i:1:p:1-18:10.1007/s10479-015-1816-6
DOI: 10.1007/s10479-015-1816-6
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File URL: http://hdl.handle.net/10.1007/s10479-015-1816-6

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## References listed on IDEAS

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Cited by:

1. repec:eee:ejores:v:263:y:2017:i:3:p:838-863 is not listed on IDEAS
2. Simon Emde, 2017. "Scheduling the replenishment of just-in-time supermarkets in assembly plants," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(1), pages 321-345, January.

### Keywords

Lot sizing problem; Multi-item; Single-item; Inventory bounds; Dynamic programming; Complexity;

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