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Journal Articles INFORMS Journal on Computing Year : 2022

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 mixedinteger linear 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 subproblems, 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.
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Dates and versions

hal-03606367 , version 1 (11-03-2022)

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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. INFORMS Journal on Computing, 2022, 34 (2), pp.1024-1041. ⟨10.1287/ijoc.2021.1118⟩. ⟨hal-03606367⟩
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