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.

Two-Stage Stochastic Optimization. An Application in the Third Sector

[en] It is known that most of the problems applied in the real life present uncertainty. In the rst part of the dissertation, basic concepts and properties of the Stochastic Programming have been introduced to the reader, also known as Optimization under Uncertainty. Moreover, since stochastic programs are complex to compute, we have presented some other models such as wait-and-wee, expected value and the expected result of using expected value. The expected value of perfect information and the value of stochastic solution measures quantify how worthy the Stochastic Programming is, with respect to the other models. In the second part, it has been designed and implemented with the modeller GAMS and the optimizer CPLEX an application that optimizes the distribution of non-perishable products, guaranteeing some nutritional requirements with minimum cost. It has been developed within Hazia project, managed by Sortarazi association and associated with Food Bank of Biscay and Basic Social Services of several districts of Biscay.

Altruism in the (Social) Network

This paper explores the role of social integration on altruistic behavior. To this aim, we develop a two-stage experimental protocol based on the classic Dictator Game. In the first stage, we ask a group of 77 undergraduate students in Economics to elicit their social network; in the second stage, each of them has to unilaterally decide over the division of a fixed amount of money to be shared with another anonymous member in the group. Our experimental design allows to control for other variables known to be relevant for altruistic behavior: framing and friendship/acquaintance relations. Consistently with previous research, we find that subjects favor their friends and that framing enhances altruistic behavior. Once we control for these effects, social integration (measured by betweenness, a standard centrality measure in network theory) has a positive effect on giving: the larger social isolation within the group, the more likely it is the emergence of selfish behavior. These results suggest that information on the network structure in which subjects are embedded is crucial to account for their behavior.

Fishing effort validation and substitution possibilities among components: the case study of the VIII division European anchovy fishery

Command and control regulation programs, particularly input constraints, typically fail to achieve stated objectives, because fishermen may substitute unregulated for regulated inputs. It is, thus, essential to have an understanding of the internal structure of production technology. A primal formulation is used to estimate a translog production function at the vessels level that includes fishing effort and fisherman’s skill. The flexibility of the selected functional permits the analysis of the substitution possibilities among inputs by estimating the elasticity of substitution with no prior constraints. Particular attention is paid to the empirical validation of fishing effort as an aggregate input, which implies either, the acceptation of the joint hypothesis that inputs making up effort are weakly separable from the inputs out of the subgroup or considering that effort is an intermediate input produced by a non-separable two stage technology. Cross sectional data from the Spanish purse seine fleet operating in the VIII Division European anchovy fishery provide evidence of limited input substitution possibilities among the inputs making up the empirically validated fishing effort translog micro-production function.

A note on bargaining power and managerial delegation in multimarket oligopolies

In a two-stage delegation game model with Nash bargaining between a manager and an owner, an equivalence result is found between this game and Fershtman and Judd's strategic delegation game (Fershtman and Judd, 1987). Interestingly, although both games are equivalent in terms of profits under certain conditions, managers obtain greater rewards in the bargaining game. This results in a redistribution of profits between owners and managers.

Thrombotic Antiphospholipid Syndrome Shows Strong Haplotypic Association with SH2B3-ATXN2 Locus

Background : Thrombotic antiphospholipid syndrome is defined as a complex form of thrombophilia that is developed by a fraction of antiphospholipid antibody (aPLA) carriers. Little is known about the genetic risk factors involved in thrombosis development among aPLA carriers. Methods: To identify new loci conferring susceptibility to thrombotic antiphospholipid syndrome, a two-stage genotyping strategy was performed. In stage one, 19,000 CNV loci were genotyped in 14 thrombotic aPLA+ patients and 14 healthy controls by array-CGH. In stage two, significant CNV loci were fine-mapped in a larger cohort (85 thrombotic aPLA+, 100 non-thrombotic aPLA+ and 569 healthy controls). Results : Array-CGH and fine-mapping analysis led to the identification of 12q24.12 locus as a new susceptibility locus for thrombotic APS. Within this region, a TAC risk haplotype comprising one SNP in SH2B3 gene (rs3184504) and two SNPs in ATXN2 gene (rs10774625 and rs653178) exhibited the strongest association with thrombotic antiphospholipid syndrome (p-value = 5,9 × 10−4 OR 95% CI 1.84 (1.32–2.55)). Conclusion : The presence of a TAC risk haplotype in ATXN2-SH2B3 locus may contribute to increased thrombotic risk in aPLA carriers.

Some experiments on solving multistage stochastic mixed 0-1 programs with time stochastic dominance constraints

In this work we extend to the multistage case two recent risk averse measures for two-stage stochastic programs based on first- and second-order stochastic dominance constraints induced by mixed-integer linear recourse. Additionally, we consider Time Stochastic Dominance (TSD) along a given horizon. Given the dimensions of medium-sized problems augmented by the new variables and constraints required by those risk measures, it is unrealistic to solve the problem up to optimality by plain use of MIP solvers in a reasonable computing time, at least. Instead of it, decomposition algorithms of some type should be used. We present an extension of our Branch-and-Fix Coordination algorithm, so named BFC-TSD, where a special treatment is given to cross scenario group constraints that link variables from different scenario groups. A broad computational experience is presented by comparing the risk neutral approach and the tested risk averse strategies. The performance of the new version of the BFC algorithm versus the plain use of a state-of-the-artMIP solver is also reported.