Scenario Cluster Lagrangian Decomposition in two stage stochastic mixed 0-1 optimization

In this paper 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 four Lagrange multiplier updating procedures, namely the Subgradient Method, the Volume Algorithm, the Progressive Hedging Algorithm and the Dynamic Constrained Cutting Plane scheme for different numbers of scenario clusters and different dimensions of the original problem. Our computational experience shows that the CLD bound and its computational effort depend on the number of scenario clusters to consider. In any case, our results show that the CLD procedures outperform the traditional LD scheme for single scenarios both in the quality of the bounds and computational effort. All the procedures have been implemented in a C++ experimental code. A broad computational experience is reported on a test of randomly generated instances by using the MIP solvers COIN-OR and CPLEX for the auxiliary mixed 0-1 cluster submodels, this last solver within the open source engine COIN-OR. We also give computational evidence of the model tightening effect that the preprocessing techniques, cut generation and appending and parallel computing tools have in stochastic integer optimization. Finally, we have observed that the plain use of both solvers does not provide the optimal solution of the instances included in the testbed with which we have experimented but for two toy instances in affordable elapsed time. On the other hand the proposed procedures provide strong lower bounds (or the same solution value) in a considerably shorter elapsed time for the quasi-optimal solution obtained by other means for the original stochastic problem.

La evolución de la intensidad energética de la industria vasca entre 1982-2001: Un análisis de descomposición

In this article an index decomposition methodology is used to estimate the effect of intersectorial and intrasectorial changes in explaining the 38% reduction in industrial energy intensity in the Basque Autonomous Community from 1982 to 2001. Period-wise additive decomposition results show that (1) the decline is fully explained by intrasectorial changes and that (2) intersectorial changes have not contributed to reduce but to increase the energy intensity of the Basque industrial sector. However, timeseries decomposition analysis shows that (1) four different phases can be distinguished in the evolution of energy intensity of the Basque industry from 1982 to 2001 and (2) that the evolution of the “Iron and Steel” sector is determinant when explaining those phases. Moreover, the analysis stresses the necessity to disaggregate the “Iron and Steel” sector in order to be able to distinguish purely technological effects from the rest of intrasectorial changes.

Ceilings and Floors? Gender Wage Gaps by Education in Spain

Revised: 2006-11.-- Published as an article in: Journal of Population Economics, 2007, vol. 21 issue 3, pp. 751-776.

Cyclical Features of Uzawa-Lucas Endogenous Growth Model

This paper analyzes the cyclical properties of a generalized version of Uzawa-Lucas endogenous growth model. We study the dynamic features of different cyclical components of this model characterized by a variety of decomposition methods. The decomposition methods considered can be classified in two groups. On the one hand, we consider three statistical filters: the Hodrick-Prescott filter, the Baxter-King filter and Gonzalo-Granger decomposition. On the other hand, we use four model-based decomposition methods. The latter decomposition procedures share the property that the cyclical components obtained by these methods preserve the log-linear approximation of the Euler-equation restrictions imposed by the agent’s intertemporal optimization problem. The paper shows that both model dynamics and model performance substantially vary across decomposition methods. A parallel exercise is carried out with a standard real business cycle model. The results should help researchers to better understand the performance of Uzawa-Lucas model in relation to standard business cycle models under alternative definitions of the business cycle.