Decomposition algorithms with parametric Gomory cuts for two-stage stochastic integer programs

We consider a class of two-stage stochastic integer programs with binary variables in the first stage and general integer variables in the second stage. We develop decomposition algorithms akin to the $L$ -shaped or Benders’ methods by utilizing Gomory cuts to obtain iteratively tighter approximations of the second-stage integer programs. We show that the proposed methodology is flexible in that it allows several modes of implementation, all of which lead to finitely convergent algorithms. We illustrate our algorithms using examples from the literature. We report computational results using the stochastic server location problem instances which suggest that our decomposition-based approach scales better with increases in the number of scenarios than a state-of-the art solver which was used to solve the deterministic equivalent formulation.     

Effect of conjugated core building block dibenzo[a,c]phenazine unit on π‐conjugated electrochromic polymers: Red‐shifted absorption

A comparative investigation was undertaken for the electrosynthesis and electrochemical properties of three different electroactive polymers having a conjugated core building block, dibenzo[a,c]phenazine. A series of monomers has been synthesized as regards to thiophene based units; thiophene, 3‐hexyl thiophene, and 3,4‐ethylenedioxythiophene. The effects of different donor substituents on the polymers' electrochemical properties were examined by cyclic voltammetry. Introducing highly electron‐donating (ethylene dioxy) group to the monomer enables solubility while also lowering the oxidation potential. The planarity of the monomer unit enhances π‐stacking and consequently lowering the E_g from 2.4 eV (PHTP) to 1.7 (PTBP). Cyclic voltammetry and spectroelectrochemical measurements revealed that 2,7‐bis(4‐hexylthiophen‐2‐yl)dibenzo[a,c]phenazine (HTP) and 2,7‐bis(2,3‐dihydrothieno[3,4‐b][1,4]dioxin‐5‐yl)dibenzo[a,c]phenazine (TBP) possessed electrochromic behavior. The colorimetry analysis revealed that while PTBP have a color change from red to blue, PHTP has yellow color at neutral state and blue color at oxidized state. Hence the presence of the phenazine derivative as the acceptor unit causes a red shift in the polymers' absorption to have a blue color. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 1714–1720, 2010     

Synthesis of new donor-acceptor polymers containing thiadiazoloquinoxaline and pyrazinoquinoxaline moieties: low-band gap, high optical contrast, and almost black colored materials

Two low band gap conjugated polymers, poly[4,9-bis(4-hexylthien-2-yl)-6,7-di(thien-2-yl)-[1,2,5]thiadiazolo[3,4-g]quinoxaline] (PHTTQ) and poly[5,10-bis(4-hexylthien-2-yl)-2,3,7,8-tetra(thien-2-yl)pyrazino[2,3-g]quinoxaline] (PHTPQ), consisting of alternating electron-rich 3-hexylthiophene and electron-deficient 6,7-di(thien-2-yl)-[1,2,5]thiadiazolo[3,4-g]quinoxaline (TTQ) and 2,3,7,8-tetra(thien-2-yl)-2,3-dihydropyrazino[2,3-g]quinoxaline (TPQ) units were synthesized electrochemically. The structures of the π-conjugated monomers were tailored using thiophene as the pendant group on the acceptor units (TTQ and TPQ). The electrochemical and optical properties of the polymers were investigated by cyclic voltammetry and UV-vis-NIR spectroscopy. The absorption spectra of PHTPQ, revealing a 1.0 eV band gap, exhibited three maxima at 352 nm, 535 nm, and 750 nm. Consequently, its absorption spectra cover the region between 400 and 800 nm, which make the polymer almost black in appearance. PHTTQ shows a λ_max value of 820 nm and a band gap of 0.8 eV which is very low among other [1,2,5]thiadiazolo[3,4-g]quinoxaline-containing donor-acceptor type polymers.     

On mixing sets arising in chance-constrained programming

The mixing set with a knapsack constraint arises in deterministic equivalent of chance-constrained programming problems with finite discrete distributions. We first consider the case that the chance-constrained program has equal probabilities for each scenario. We study the resulting mixing set with a cardinality constraint and propose facet-defining inequalities that subsume known explicit inequalities for this set. We extend these inequalities to obtain valid inequalities for the mixing set with a knapsack constraint. In addition, we propose a compact extended reformulation (with polynomial number of variables and constraints) that characterizes a linear programming equivalent of a single chance constraint with equal scenario probabilities. We introduce a blending procedure to find valid inequalities for intersection of multiple mixing sets. We propose a polynomial-size extended formulation for the intersection of multiple mixing sets with a knapsack constraint that is stronger than the original mixing formulation. We also give a compact extended linear program for the intersection of multiple mixing sets and a cardinality constraint for a special case. We illustrate the effectiveness of the proposed inequalities in our computational experiments with probabilistic lot-sizing problems.     

Catalytic acylation of amines with aldehydes or aldoximes

The simple nickel salt NiCl(2)·6H(2)O catalyzes the coupling of aldoximes with amines to give secondary or tertiary amide products. The aldoxime can be prepared in situ from the corresponding aldehyde. The use of (18)O-labeled oximes has allowed insight into the mechanism of this reaction.     

Strong valid inequalities for a class of concave submodular minimization problems under cardinality constraints

Mathematical Programming - We study the polyhedral convex hull structure of a mixed-integer set which arises in a class of cardinality-constrained concave submodular minimization problems. This...     

A Note on “Lot-sizing with fixed charges on stocks: The convex hull”

We update and complete the proof of Proposition 7 in Van Vyve and Ortega (2004) [1], which states that the projection of a facility location reformulation of an uncapacitated lot-sizing problem with fixed charges on stocks (ULSW) to the original space is equivalent to that of the tight shortest path reformulation of ULSW. Their proof is interesting and consists of two cases, only first of which is analyzed in detail. We show that the second case exhibits several challenges not present in the first one and necessitates an updated proof.