# Undominated Valid Inequalities for a Stochastic Capacitated Discrete Lot-sizing Problem with Lead Times, Cancellation and Postponement

### Carlos Testuri, Héctor Cancela, Víctor Albornoz

#### Abstract

The problem addresses the expected cost minimization of meeting the uncertain demand of a product during a discrete time planning horizon. The product is supplied by selecting fixed quantity shipments that have lead times. Due to the uncertainty of demand, corrective actions, such as shipment cancellations and postponements, must be taken with associated costs and delays. The problem is modeled as an extension of the discrete lot-sizing problem with different capacities and uncertain demand, which belongs to the N P-hard class. To improve the resolution of the problem by tightening its formulation, valid inequalities based on the (,̀S) inequalities approach are used. Given that the inequalities are highly dominated for most experimental instances, a scheme is established to determine undominated ones. Computational experiments are performed on the resolution of the model and variants that include subsets of undominated and representative valid inequalities for instances of several information structures of uncertainty. The experimental results allow to conclude that the inclusion of undominated and representative derived (,̀S) valid inequalities enable a more efficient resolution of the model.

Download#### Paper Citation

#### in Harvard Style

Testuri C., Cancela H. and Albornoz V. (2019). **Undominated Valid Inequalities for a Stochastic Capacitated Discrete Lot-sizing Problem with Lead Times, Cancellation and Postponement**.In *Proceedings of the 8th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,* ISBN 978-989-758-352-0, pages 390-397. DOI: 10.5220/0007395203900397

#### in Bibtex Style

@conference{icores19,

author={Carlos Testuri and Héctor Cancela and Víctor Albornoz},

title={Undominated Valid Inequalities for a Stochastic Capacitated Discrete Lot-sizing Problem with Lead Times, Cancellation and Postponement},

booktitle={Proceedings of the 8th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},

year={2019},

pages={390-397},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0007395203900397},

isbn={978-989-758-352-0},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 8th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,

TI - Undominated Valid Inequalities for a Stochastic Capacitated Discrete Lot-sizing Problem with Lead Times, Cancellation and Postponement

SN - 978-989-758-352-0

AU - Testuri C.

AU - Cancela H.

AU - Albornoz V.

PY - 2019

SP - 390

EP - 397

DO - 10.5220/0007395203900397