NP-hard and polynomial cases for the single-item lot sizing problem with batch ordering under capacity reservation contract

Ayse Akbalik, Atidel B. Hadj-Alouane, Nathalie Sauer and Houcem Ghribi

European Journal of Operational Research, 2017, vol. 257, issue 2, 483-493

Abstract: In this paper, we study the single-item lot sizing problem under a capacity reservation contract. A manufacturer is replenished by an external supplier with batch deliveries and a certain capacity is reserved at the supplier level with an advantageous cost. In addition to the classical ordering and inventory holding costs, for each batch ordered under the reserved capacity a fixed cost per batch is incurred; and for batches exceeding this capacity a higher fixed cost per batch is paid, typically through the purchase from the spot market. We identify various NP-hard cases, propose a pseudo-polynomial time dynamic programming algorithm under arbitrary parameters, show that the problem admits an FPTAS and give polynomial time algorithms for special cases. We finally state a list of open problems for further research.

Keywords: Inventory; Lot sizing; Capacity reservation contract; Complexity; Polynomial time algorithm (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (9)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:257:y:2017:i:2:p:483-493

DOI: 10.1016/j.ejor.2016.07.028

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