Optimizing production and transportation in a commit-to-delivery business mode

In problems involving the simultaneous optimization of production and transportation, the requirement that an order can only be shipped once its production has been completed is a natural one. One example is a problem of optimizing shipping costs subject to a production capacity constraint studied recently by Stecke and Zhao. Here we present an integer programming formulation for the case in which only completed orders can be shipped that leads to very tight dual bounds and enables one to solve instances of significant size to optimality.     

Electron microscopy studies on DNA recognition by DNA-PK

Advances in transmission electron microscopy coupled to increasingly powerful biocomputing techniques are opening enormous possibilities to understand the structure and function of complex biological processes performed by large multi-protein assemblies. This is an exciting time for electron microscopists because we can combine our efforts with X-ray crystallographers and NMR spectroscopists to reach the prospect of studying the structure and dynamics of the so-called ‘molecular machines’. One of these fascinating systems is the macromolecular complex formed around double-stranded DNA breaks (DSBs). Non-homologous end-joining (NHEJ) is the main DSBs repair pathway in mammalian cells, where a collection of proteins interact to rejoin two broken DNA ends. During NHEJ, DNA-dependent protein kinase (DNA-PK) binds damaged DNA with high affinity and acts as the main scaffold for other repair factors. Several studies have made use of the electron microscope to reveal the three-dimensional architecture of DNA-PK and the structural basis for the recognition of damaged DNA and the activation of DNA-PK's kinase activity.     

A Cucurbit[8]uril 2:2 Complex with a Negative pKa Shift

A viologen derivative carrying a benzimidazole group ( V-P-I ²⁺; viologen–phenylene–imidazole V-P-I ) can be dimerized in water using cucurbit[8]uril (CB[8]) in the form of a 2:2 complex resulting in a negative shift of the guest pK_a, by more than 1 pH unit, contrasting with the positive pK_a shift usually observed for CB-based complexes. Whereas 2:2 complex protonation is unclear by NMR, silver cations have been used for probing the accessibility of the imidazole groups of the 2:2 complexes. The protonation capacity of the buried imidazole groups is reduced, suggesting that CB[8] could trigger proton release upon 2:2 complex formation. The addition of CB[8] to a solution containing V-P- I ³⁺ indeed released protons as monitored by pH-metry and visualized by a coloured indicator. This property was used to induce a host/guest swapping, accompanied by a proton transfer, between V-P-I ³⁺ ⋅ CB[7] and a CB[8] complex of 1-methyl-4-(4-pyridyl)pyridinium. The origin of this negative pK_a shift is proposed to stand in an ideal charge state, and in the position of the two pH-responsive fragments inside the two CB[8] which, alike residues engulfed in proteins, favour the deprotonated form of the guest molecules. Such proton release triggered by a recognition event is reminiscent of several biological processes and may open new avenues toward bioinspired enzyme mimics catalyzing proton transfer or chemical reactions.     

Risk-Neutral Pricing for Arbitrage Pricing Theory

Journal of Optimization Theory and Applications - We consider infinite-dimensional optimization problems motivated by the financial model called Arbitrage Pricing Theory. Using probabilistic and...     

Local atomic and electronic structure in the LiVPO4(F,O) tavorite-type materials from solid-state NMR combined with DFT calculations

⁷Li, ³¹P, and ¹⁹F solid-state nuclear magnetic resonance (NMR) spectroscopy was used to investigate the local arrangement of oxygen and fluorine in LiVPO₄F_1-yO_y materials, interesting as positive electrode materials for Li-ion batteries. From the evolution of the 1D spectra versus y, 2D ⁷Li radiofrequency-driven recoupling (RFDR) experiments combined, and a tentative signal assignment based on density functional theory (DFT) calculations, it appears that F and O are not randomly dispersed on the bridging X position between two X–VO₄–X octahedra (X = O or F) but tend to segregate at a local scale. Using DFT calculations, we analyzed the impact of the different local environments on the local electronic structure. Depending on the nature of the VO₄X₂ environments, vanadium ions are either in the +III or in the +IV oxidation state and can exhibit different distributions of their unpaired electron(s) on the d orbitals. Based on those different local electronic structures and on the computed Fermi contact shifts, we discuss the impact on the spin transfer mechanism on adjacent nuclei and propose tentative signal assignments. The O/F clustering tendency is discussed in relation with the formation of short V^IVO vanadyl bonds with a very specific electronic structure and possible cooperative effect along the chain.     

Lifting,superadditivity, mixed integer rounding and single node flow sets revisited

In this survey we attempt to give a unified presentation of a variety of results on the lifting of valid inequalities, as well as a standard procedure combining mixed integer rounding with lifting for the development of strong valid inequalities for knapsack and single node flow sets. Our hope is that the latter can be used in practice to generate cutting planes for mixed integer programs. The survey contains essentially two parts. In the first we present lifting in a very general way, emphasizing superadditive lifting which allows one to lift simultaneously different sets of variables. In the second, our procedure for generating strong valid inequalities consists of reduction to a knapsack set with a single continuous variable, construction of a mixed integer rounding inequality, and superadditive lifting. It is applied to several generalizations of the 0–1 single node flow set. This paper appeared in 4OR, 1, 173–208 (2003). The first author is supported by the FNRS as a chercheur qualifié. This paper presents research results of the Belgian Program on Interuniversity Poles of Attraction initiated by the Belgian State, Prime Minister’s Office, Science Policy Programming. The scientific responsibility is assumed by the authors.     

Optimizing constrained subtrees of trees

Given a treeG = (V, E) and a weight function defined on subsets of its nodes, we consider two associated problems. The first, called the rooted subtree problem, is to find a maximum weight subtree, with a specified root, from a given set of subtrees.The second problem, called the subtree packing problem, is to find a maximum weight packing of node disjoint subtrees chosen from a given set of subtrees, where the value of each subtree may depend on its root.We show that the complexity status of both problems is related, and that the subtree packing problem is polynomial if and only if each rooted subtree problem is polynomial. In addition we show that the convex hulls of the feasible solutions to both problems are related: the convex hull of solutions to the packing problem is given by pasting together the convex hulls of the rooted subtree problems.We examine in detail the case where the set of feasible subtrees rooted at nodei consists of all subtrees with at mostk nodes. For this case we derive valid inequalities, and specify the convex hull whenk 4.Research supported in part by Nato Collaborative Research Grant CRG 900281, Science Program SC1-CT91-620 of the EEC, and contract No 26 of the programme Pôle d'attraction interuniversitaire of the Belgian government.     

Strong formulations for mixed integer programs: valid inequalities and extended formulations

 We examine progress over the last fifteen years in finding strong valid inequalities and tight extended formulations for simple mixed integer sets lying both on the ``easy' and ``hard' sides of the complexity frontier. Most progress has been made in studying sets arising from knapsack and single node flow sets, and a variety of sets motivated by different lot-sizing models. We conclude by citing briefly some of the more intriguing new avenues of research. Received: January 15, 2003 / Accepted: April 10, 2003 Published online: May 28, 2003 Key words. mixed integer programming – strong valid inequalities – convex hull – extended formulations – single node flow sets – lot-sizing This paper presents research results of the Belgian Program on Interuniversity Poles of Attraction initiated by the Belgian State, Prime Minister's Office, Science Policy Programming. The scientific responsibility is assumed by the authors. Research carried out with financial support of the project TMR-DONET nr. ERB FMRX–CT98–0202 of the European Union.