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.

Métodos cuantitativos versus métodos cualitativos en la economía de los Negocios. ¿Es una metodología reconciliable?

Changes in the organizational environment over the last three decades have increasingly led to traditional theories being called into question, by stimulating the search for new models suited to the new realities of business economics, generating a crisis or scientific revolution that may result in the appearance of a new paradigm. The positivism-phenomenology duality provokes an “epistemological crisis” in research in management sciences. But the existence of both approaches does not imply the election of one scientific orientation in frontal opposition to the other. From these two conceptions of research procedure, the methods applied can be classed into groups, quantitative and qualitative. The quantitative methodologies places great confidence in the ability of data and measurement to represent opinions or concepts, while qualitative methodologies focus on words and relations to describe a reality or situation. While the diversity of methods contribute to its development and indicates the maturity of an area, the methods must be suitably implemented to obtain significant, valid results. The methodology to be used is not going to depend solely on the type of study or the reality under examination, but also on the stage the research process has reached.

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Generating cluster submodels from a multistage stochastic mixed integer optimization model using break stage

We present a scheme to generate clusters submodels with stage ordering from a (symmetric or a nonsymmetric one) multistage stochastic mixed integer optimization model using break stage. We consider a stochastic model in compact representation and MPS format with a known scenario tree. The cluster submodels are built by storing first the 0-1 the variables, stage by stage, and then the continuous ones, also stage by stage. A C++ experimental code has been implemented for reordering the stochastic model as well as the cluster decomposition after the relaxation of the non-anticipativiy constraints until the so-called breakstage. The computational experience shows better performance of the stage ordering in terms of elapsed time in a randomly generated testbed of multistage stochastic mixed integer problems.

Studies of the age, growth, sexual maturity and spawning of populations of anchoveta (Cetengraulis mysticetus) of the coast of the Eastern Tropical Pacific Ocean

ENGLISH: Three hundred and twenty-six collections of anchoveta (Cetengraulis mysticetus), an important tuna bait species, taken between April 1951 and April 1960 from seven major baiting areas in the Eastern Tropical Pacific Ocean (Almejas Bay, Guaymas, Ahome Point, Banderas Bay, Gulf of Fonseca, coast of Colombia and Ecuador-Peru) are the basis of this study of age, growth, sexual maturity and spawning. The study of the temporal progression of modal size groups from plots of monthly length-frequency distributions provided estimates of age and rate of growth. The study of sexual maturity and time of spawning was based on gross examination of ovaries, and application of the gonad index. SPANISH: Trescientas veintiseis recolecciones de anchovetas (Cetengraulis mysticetus), una importante especie de carnada para la pesca del atún, cogidas entre abril de 1951 y abril de 1960 en siete de las mayores áreas de pesca de peces de carnada en el Océano Pacífico Oriental Tropical (Bahía de Almejas, Guaymas, Punta Ahome, Bahía Banderas, Golfo de Fonseca, y las costas de Colombia y de Ecuador- Perú), sirven de base a este estudio de la edad, crecimiento, madurez sexual y desove de dicha especie. El estudio de la progresión temporal de los grupos de tamaños modales según los gráficos de las distribuciones de la frecuencia de las longitudes proporcionó estimaciones de la edad y de la tasa de crecimiento. La investigación de la madurez sexual y la época de desove se basó en el examen macroscópico de los ovarios y en la aplicación del índice de gónadas.

Spawning, egg development, and early life history dynamics of arrowtooth flounder (Atheresthes stomias) in the Gulf of Alaska

Arrowtooth flounder (Atheresthes stomias) has the highest biomass of any groundfish species in the Gulf of Alaska, is a voracious predator of age 1 walleye pollock (Theragra chalcogramma), and is a major component in the diet of Steller sea lions (Eumetopias jubatus). Owing to its ecological importance in the Gulf of Alaska and the limited information available on its reproduction, interest has intensified in describing its spawning and early life history. A study was undertaken in late January–February 2001–2003 in the Gulf of Alaska to obtain information on adult spawning location, depth distribution, and sexual maturity, and to obtain fertilized eggs for laboratory studies. Adults were found 200–600 m deep east of Kodiak Island over the outer continental shelf and upper slope, and southwest along the shelf break to the Shumagin Islands. Most ripe females (oocytes extruded with light pressure) were found at 400 m and most ripe males (milt extruded with light pressure) were found at depths ≥450 m. Eggs were fertilized and incubated in the laboratory at 3.0°, 4.5°, and 6.0°C. Eggs were reared to hatching, but larvae did not survive long enough to complete yolk absorption and develop pigment. Eggs were staged according to morphological hallmarks and incubation data were used to produce a stage duration table and a regression model to estimate egg age based on water temperature and developmental stage. Arrowtooth flounder eggs (1.58–1.98 mm in diameter) were collected in ichthyoplankton surveys along the continental shelf edge, primarily at depths ≥400 m. Early-stage eggs were found in tows that sampled to depths of ≥450 m. Larvae, which hatch between 3.9 and 4.8 mm standard length, increased in abundance with depth. Observations on arrowtooth flounder eggs and early-stage larvae were used to complete the description of the published partial developmental series.(PDF file contains 34 pages.)

Development of kelp rockfish, Sebastes atrovirens (Jordan and Gilbert 1880), and brown rockfish, S. auriculatus (Girard 1854), from birth to pelagic juvenile stage, with notes on early larval development of black-and-yellow rockfish, S. chrysomelas (Jordan and Gilbert 1880), reared in the laboratory (Pisces: Sebastidae).

Larval kelp (Sebastes atrovirens), brown (S. auriculatus), and blackand-yellow (S. chrysomelas) rockfish were reared from known adults, to preflexion stage, nine days after birth for S. chrysomelas, to late postflexion stage for S. atrovirens, and to pelagic juvenile stage for S. auriculatus. Larval S. atrovirens and S. chrysomelas were about 4.6 mm body length (BL) and S. auriculatus about 5.2 mm BL at birth. Both S. atrovirens and S. auriculatus underwent notochord flexion at about 6–9 mm BL. Sebastes atrovirens transform to the pelagic juvenile stage at about 14–16 mm BL and S. auriculatus transformed at ca. 25 mm BL. Early larvae of all three species were characterized by melanistic pigment dorsally on the head, on the gut, on most of the ventral margin of the tail, and in a long series on the dorsal margin of the tail. Larval S. atrovirens and S. auriculatus developed a posterior bar on the tail during the flexion or postflexion stage. In S. atrovirens xanthic pigment resembled the melanistic pattern throughout larval development. Larval S. auriculatus lacked xanthophores except on the head until late preflexion stage, when a pattern much like the melanophore pattern gradually developed. Larval S. chrysomelas had extensive xanthic pigmentation dorsally, but none ventrally, in preflexion stage. All members of the Sebastes subgenus Pteropodus (S. atrovirens, S. auriculatus, S. carnatus, S. caurinus, S. chrysomelas, S. dalli, S. maliger, S. nebulosus, S. rastrelliger) are morphologically similar and all share the basic melanistic pigment pattern described here. Although the three species reared in this study can be distinguished on the basis of xanthic pigmentation, it seems unlikely that it will be possible to reliably identify field-collected larvae to species using traditional morphological and melanistic pigmentation characters. (PDF file contains 36 pages.)