 The single item uncapacitated lot-sizing problem with time-dependent batch sizes: NP-hard and polynomial casesAyse Akbalik and Christophe Rapine European Journal of Operational Research, 2013, vol. 229, issue 2, 353-363 Abstract: This paper considers the uncapacitated lot sizing problem with batch delivery, focusing on the general case of time-dependent batch sizes. We study the complexity of the problem, depending on the other cost parameters, namely the setup cost, the fixed cost per batch, the unit procurement cost and the unit holding cost. We establish that if any one of the cost parameters is allowed to be time-dependent, the problem is NP-hard. On the contrary, if all the cost parameters are stationary, and assuming no unit holding cost, we show that the problem is polynomially solvable in time O(T3), where T denotes the number of periods of the horizon. We also show that, in the case of divisible batch sizes, the problem with time varying setup costs, a stationary fixed cost per batch and no unit procurement nor holding cost can be solved in time O(T3 logT). Keywords: Inventory; Uncapacitated lot sizing; Batch delivery; Stepwise cost; Polynomial time algorithm; Complexity (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:229:y:2013:i:2:p:353-363 DOI: 10.1016/j.ejor.2013.02.052 Access Statistics for this article European Journal of Operational Research is currently edited by Roman Slowinski, Jesus Artalejo, Jean-Charles. Billaut, Robert Dyson and Lorenzo Peccati More articles in European Journal of Operational Research from Elsevier |
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