Invited Session Tue.1.MA 376

Tuesday, 10:30 - 12:00 h, Room: MA 376

Cluster 22: Stochastic optimization [...]

Multistage stochastic mixed 0-1 optimization: Algorithms and applications


Chair: Laureano Fernando Escudero



Tuesday, 10:30 - 10:55 h, Room: MA 376, Talk 1

Aitziber Unzueta
Scenario cluster Lagrangian decomposition

Coauthors: Unzueta Aitziber, Escudero F. Laureano, Garín Maria Araceli, Gloria Perez



We introduce four scenario cluster based Lagrangian decomposition (CLD) procedures for obtaining strong lower bounds to the (optimal) solution value of two-stage stochastic mixed 0-1 problems. At each iteration of the Lagrangian based procedures, the traditional aim consists of obtaining the solution value of the corresponding Lagrangian dual via solving scenario submodels once the nonanticipativity constraints have been dualized. Instead of considering a splitting variable representation over the set of scenarios, we propose to decompose the model into a set of scenario clusters. We compare the computational performance of the subgradient method, the volume algorithm, the progressive hedging algorithm and the dynamic constrained cutting plane scheme for different numbers of scenario clusters. Our computational experience shows that the CLD procedures outperform the traditional LD scheme for single scenarios both in the quality of the bounds and computational effort. Additionally, our CLD approach obtains very frequently the optimal solution of the problem outperforming the plain use of a state-of-the art MIP solver. An extensive computational experience is reported.



Tuesday, 11:00 - 11:25 h, Room: MA 376, Talk 2

Laureano Fernando Escudero
Stochastic tactical supply chain management under uncertainty

Coauthors: Juan F. Monge, Dolores Romero-Morales


The uncertainty in the supply tactical chain management (STSM) is due to the stochasticity inherent in some parameters for dynamic (multiperiod) planning problems, mainly, product demand and demand loss, production cost and resources availability, and it is treated via scenario analysis. We present a modeling framework for solving the multiperiod stochastic mixed 0-1 STCM problem. A scenario tree based scheme is used to represent the parameters' uncertainty and for designing the deterministic equivalent model (DEM) for risk management by implementing the risk averse strategies based on scenario immunization, average conditional value-at-risk and stochastic dominance constraints. Solving the huge DEM instances is not affordable by using plain MIP solvers. Instead of that, we present an extension of a stochastic dynamic programming metaheuristic, by including the handling of constraints linking variables from different scenarios and constraints that do have variables that do not belong to any specific scenario. Some computational experience is reported.



Tuesday, 11:30 - 11:55 h, Room: MA 376, Talk 3

Maria Araceli Garín
A BFC-MS algorithm for solving multistage mixed 0-1 stochastic problems with risk averse stochastic dominance constraints

Coauthors: Laureano F. Escudero, María Merino, Gloria Pérez


In the context of stochastic optimization, the multistage mixed 0-1 deterministic equivalent models (DEM) use to be very large and difficult to solve. So, the plain use of even MIP state-of-the art solvers for optimizing the related DEM requires an unaffordable computing effort or simply cannot be solved.The alternative is to use decomposition methods of the full model in smaller MIP submodels. Moreover, the general approach (so named risk neutral) has the inconvenience of providing a solution that ignores the variance of the objective value of the scenarios, and so, the occurrence of scenarios with an objective value below the expected one. In this work we present the optimization of the objective function expected value subject to stochastic dominance constraints for a set of profiles. The price to pay is that the DEM becomes much bigger, augmented by new variables and constraints. So, we present an extension of our BFC that consider nonsymmetric scenario trees, where a special treatment is given to the constraint s that link variables from different scenarios.


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