Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Combining polyhedral approaches and stochastic dual dynamic integer programming for solving the uncapacitated lot-sizing problem under uncertainty

Abstract : We study the uncapacitated lot-sizing problem with uncertain demand and costs. The problem is modeled as a multi-stage stochastic integer program in which the evolution of the uncertain parameters is represented by a scenario tree. To solve this problem, we propose a new extension of the stochastic dual dynamic integer programming algorithm (SDDiP). This extension aims at being more computationally efficient in the management of the expected cost-to-go functions involved in the model, in particular by reducing their number and by exploiting the current knowledge on the polyhedral structure of the stochastic uncapacitated lot-sizing problem. The algorithm is based on a partial decomposition of the problem into a set of stochastic sub-problems, each one involving a subset of nodes forming a sub-tree of the initial scenario tree. We then introduce a cutting-plane generation procedure that iteratively strengthens the linear relaxation of these sub-problems and enables the generation of additional strengthened Benders' cut, which improves the convergence of the method. We carry out extensive computational experiments on randomly generated large-size instances. Our numerical results show that the proposed algorithm significantly outperforms the SDDiP algorithm at providing good-quality solutions within the computation time limit.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

Cited literature [29 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02868707
Contributor : Franco Quezada <>
Submitted on : Monday, June 15, 2020 - 3:42:34 PM
Last modification on : Thursday, July 8, 2021 - 3:50:10 AM

File

HAL-SULS.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02868707, version 1

Citation

Franco Quezada, Céline Gicquel, Safia Kedad-Sidhoum. Combining polyhedral approaches and stochastic dual dynamic integer programming for solving the uncapacitated lot-sizing problem under uncertainty. 2020. ⟨hal-02868707⟩

Share

Metrics

Record views

90

Files downloads

80