Journées de l'optimisation 2007 Optimizations days

This paper considers the problem of testing for learning by doing effects on technical efficiency in a given industry. We argue that when such effects are present, there is catching-up in technical efficiency, a phenomenon that we characterize in terms of a first-order stochastic dominance relation. Applying existing stochastic dominance tests to this problem faces two major challenging complications : (i) technical efficiency scores are unobserved, which prevent having samples from the true distributions involved in the stochastic dominance relation, so that only samples from estimates are available, and (ii) the data on estimated technical efficiency scores have an unknown dependence structure. We propose adaptations of tests in Abadie(2002) and Linton, Maasoumi and Whang(2005) to the context where technical efficiency scores are estimated through either the linear programming data envelopment analysis method or the parametric stochastic frontier approach, which allow us to account for the dependence problem. But as in Simar-Zelenyuk(2006), the extent to which the use of estimated technical efficiency scores affects the performance of the tests remains an empirical issue. We conduct a Monte Carlo simulation study to assess the finite sample performance of the tests we propose. These tests are applied to the existence of catching-up in technical efficiency in the dairy production industry of the Province of Québec between 1993 and 2003.

Mine production scheduling refers to determination of extraction sequence, production rates and cut-off grades such a way as to maximize profit of venture. In the same time, geological and financial uncertainties make the problem more complicated. We developed a model based on stochastic programming to solve the problem. The objective function of this approach is to maximize metal quantity of each simulation in earlier extraction period and minimize deviations of the obtained mining and mill quantities among periods. Instead of cut-off grades, blocks are identified by a linear programming module based on target grades of each production period.

Multi-stage stochastic programming (MSP) problems often have very large number of scenarios and special structures which are tractable by decomposition. This paper presents a two-level decomposition method for a class of MSP problems. The decomposition is done on the dual of a MSP problem where the goal is to compare the simplex-based column generation technique with that of an interior-point based decomposition and column generation algorithm, namely the Analytic Center Cutting Plane Method (ACCPM).